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c7ce82f73344293c3eb4d2ab3986d7e6e4d3563baea2c37d878893f53e590d0f
|
def internal_coproduct(self):
"\n Return the inner coproduct of ``self`` in the basis of ``self``.\n\n The inner coproduct (also known as the Kronecker coproduct, as the\n internal coproduct, or as the second comultiplication on the ring of\n symmetric functions) is a ring homomorphism `\\Delta^\\times` from the\n ring of symmetric functions to the tensor product (over the base\n ring) of this ring with itself. It is uniquely characterized by the\n formula\n\n .. MATH::\n\n \\Delta^{\\times}(h_n) = \\sum_{\\lambda \\vdash n} s_{\\lambda}\n \\otimes s_{\\lambda} = \\sum_{\\lambda \\vdash n} h_{\\lambda} \\otimes\n m_{\\lambda} = \\sum_{\\lambda \\vdash n} m_{\\lambda} \\otimes\n h_{\\lambda},\n\n where `\\lambda \\vdash n` means `\\lambda` is a partition of `n`, and\n `n` is any nonnegative integer. It also satisfies\n\n .. MATH::\n\n \\Delta^\\times (p_n) = p_n \\otimes p_n\n\n for any positive integer `n`. If the base ring is a `\\QQ`-algebra, it\n also satisfies\n\n .. MATH::\n\n \\Delta^{\\times}(h_n) = \\sum_{\\lambda \\vdash n} z_{\\lambda}^{-1}\n p_{\\lambda} \\otimes p_{\\lambda},\n\n where\n\n .. MATH::\n\n z_{\\lambda} = \\prod_{i=1}^\\infty i^{m_i(\\lambda)} m_i(\\lambda)!\n\n with `m_i(\\lambda)` meaning the number of appearances of `i`\n in `\\lambda` (see :meth:`~sage.combinat.sf.sfa.zee`).\n\n The method :meth:`kronecker_coproduct` is a synonym of\n :meth:`internal_coproduct`.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(ZZ).s()\n sage: a = s([2,1])\n sage: a.internal_coproduct()\n s[1, 1, 1] # s[2, 1] + s[2, 1] # s[1, 1, 1] + s[2, 1] # s[2, 1] + s[2, 1] # s[3] + s[3] # s[2, 1]\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: b = e([2])\n sage: b.internal_coproduct()\n e[1, 1] # e[2] + e[2] # e[1, 1] - 2*e[2] # e[2]\n\n The internal coproduct is adjoint to the internal product with respect\n to the Hall inner product: Any three symmetric functions `f`, `g` and\n `h` satisfy `\\langle f * g, h \\rangle = \\sum_i \\langle f, h^{\\prime}_i\n \\rangle \\langle g, h^{\\prime\\prime}_i \\rangle`, where we write\n `\\Delta^{\\times}(h)` as `\\sum_i h^{\\prime}_i \\otimes\n h^{\\prime\\prime}_i`. Let us check this in degree `4`::\n\n sage: e = SymmetricFunctions(FiniteField(29)).e()\n sage: s = SymmetricFunctions(FiniteField(29)).s()\n sage: m = SymmetricFunctions(FiniteField(29)).m()\n sage: def tensor_incopr(f, g, h): # computes \\sum_i \\left< f, h'_i \\right> \\left< g, h''_i \\right>\n ....: result = h.base_ring().zero()\n ....: for partition_pair, coeff in h.internal_coproduct().monomial_coefficients().items():\n ....: result += coeff * h.parent()(f).scalar(partition_pair[0]) * h.parent()(g).scalar(partition_pair[1])\n ....: return result\n sage: all( all( all( tensor_incopr(e[u], s[v], m[w]) == (e[u].itensor(s[v])).scalar(m[w]) # long time (10s on sage.math, 2013)\n ....: for w in Partitions(5) )\n ....: for v in Partitions(2) )\n ....: for u in Partitions(3) )\n True\n\n Let us check the formulas for `\\Delta^{\\times}(h_n)` and\n `\\Delta^{\\times}(p_n)` given in the description of this method::\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: p = SymmetricFunctions(QQ).p()\n sage: h = SymmetricFunctions(QQ).h()\n sage: s = SymmetricFunctions(QQ).s()\n sage: all( s(h([n])).internal_coproduct() == sum([tensor([s(lam), s(lam)]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n sage: all( h([n]).internal_coproduct() == sum([tensor([h(lam), h(m(lam))]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n sage: all( factorial(n) * h([n]).internal_coproduct() == sum([lam.conjugacy_class_size() * tensor([h(p(lam)), h(p(lam))]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n\n TESTS::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([]).internal_coproduct()\n s[] # s[]\n "
parent = self.parent()
h = parent.realization_of().homogeneous()
s = parent.realization_of().schur()
from sage.categories.tensor import tensor
result = tensor([parent.zero(), parent.zero()])
from sage.misc.cachefunc import cached_function
@cached_function
def hnimage(n):
return sum((tensor([parent(s(lam)), parent(s(lam))]) for lam in Partitions(n)))
for (lam, a) in h(self).monomial_coefficients().items():
result += (a * prod((hnimage(i) for i in lam)))
return result
|
Return the inner coproduct of ``self`` in the basis of ``self``.
The inner coproduct (also known as the Kronecker coproduct, as the
internal coproduct, or as the second comultiplication on the ring of
symmetric functions) is a ring homomorphism `\Delta^\times` from the
ring of symmetric functions to the tensor product (over the base
ring) of this ring with itself. It is uniquely characterized by the
formula
.. MATH::
\Delta^{\times}(h_n) = \sum_{\lambda \vdash n} s_{\lambda}
\otimes s_{\lambda} = \sum_{\lambda \vdash n} h_{\lambda} \otimes
m_{\lambda} = \sum_{\lambda \vdash n} m_{\lambda} \otimes
h_{\lambda},
where `\lambda \vdash n` means `\lambda` is a partition of `n`, and
`n` is any nonnegative integer. It also satisfies
.. MATH::
\Delta^\times (p_n) = p_n \otimes p_n
for any positive integer `n`. If the base ring is a `\QQ`-algebra, it
also satisfies
.. MATH::
\Delta^{\times}(h_n) = \sum_{\lambda \vdash n} z_{\lambda}^{-1}
p_{\lambda} \otimes p_{\lambda},
where
.. MATH::
z_{\lambda} = \prod_{i=1}^\infty i^{m_i(\lambda)} m_i(\lambda)!
with `m_i(\lambda)` meaning the number of appearances of `i`
in `\lambda` (see :meth:`~sage.combinat.sf.sfa.zee`).
The method :meth:`kronecker_coproduct` is a synonym of
:meth:`internal_coproduct`.
EXAMPLES::
sage: s = SymmetricFunctions(ZZ).s()
sage: a = s([2,1])
sage: a.internal_coproduct()
s[1, 1, 1] # s[2, 1] + s[2, 1] # s[1, 1, 1] + s[2, 1] # s[2, 1] + s[2, 1] # s[3] + s[3] # s[2, 1]
sage: e = SymmetricFunctions(QQ).e()
sage: b = e([2])
sage: b.internal_coproduct()
e[1, 1] # e[2] + e[2] # e[1, 1] - 2*e[2] # e[2]
The internal coproduct is adjoint to the internal product with respect
to the Hall inner product: Any three symmetric functions `f`, `g` and
`h` satisfy `\langle f * g, h \rangle = \sum_i \langle f, h^{\prime}_i
\rangle \langle g, h^{\prime\prime}_i \rangle`, where we write
`\Delta^{\times}(h)` as `\sum_i h^{\prime}_i \otimes
h^{\prime\prime}_i`. Let us check this in degree `4`::
sage: e = SymmetricFunctions(FiniteField(29)).e()
sage: s = SymmetricFunctions(FiniteField(29)).s()
sage: m = SymmetricFunctions(FiniteField(29)).m()
sage: def tensor_incopr(f, g, h): # computes \sum_i \left< f, h'_i \right> \left< g, h''_i \right>
....: result = h.base_ring().zero()
....: for partition_pair, coeff in h.internal_coproduct().monomial_coefficients().items():
....: result += coeff * h.parent()(f).scalar(partition_pair[0]) * h.parent()(g).scalar(partition_pair[1])
....: return result
sage: all( all( all( tensor_incopr(e[u], s[v], m[w]) == (e[u].itensor(s[v])).scalar(m[w]) # long time (10s on sage.math, 2013)
....: for w in Partitions(5) )
....: for v in Partitions(2) )
....: for u in Partitions(3) )
True
Let us check the formulas for `\Delta^{\times}(h_n)` and
`\Delta^{\times}(p_n)` given in the description of this method::
sage: e = SymmetricFunctions(QQ).e()
sage: p = SymmetricFunctions(QQ).p()
sage: h = SymmetricFunctions(QQ).h()
sage: s = SymmetricFunctions(QQ).s()
sage: all( s(h([n])).internal_coproduct() == sum([tensor([s(lam), s(lam)]) for lam in Partitions(n)])
....: for n in range(6) )
True
sage: all( h([n]).internal_coproduct() == sum([tensor([h(lam), h(m(lam))]) for lam in Partitions(n)])
....: for n in range(6) )
True
sage: all( factorial(n) * h([n]).internal_coproduct() == sum([lam.conjugacy_class_size() * tensor([h(p(lam)), h(p(lam))]) for lam in Partitions(n)])
....: for n in range(6) )
True
TESTS::
sage: s = SymmetricFunctions(QQ).s()
sage: s([]).internal_coproduct()
s[] # s[]
|
src/sage/combinat/sf/sfa.py
|
internal_coproduct
|
bopopescu/sagesmc
| 5 |
python
|
def internal_coproduct(self):
"\n Return the inner coproduct of ``self`` in the basis of ``self``.\n\n The inner coproduct (also known as the Kronecker coproduct, as the\n internal coproduct, or as the second comultiplication on the ring of\n symmetric functions) is a ring homomorphism `\\Delta^\\times` from the\n ring of symmetric functions to the tensor product (over the base\n ring) of this ring with itself. It is uniquely characterized by the\n formula\n\n .. MATH::\n\n \\Delta^{\\times}(h_n) = \\sum_{\\lambda \\vdash n} s_{\\lambda}\n \\otimes s_{\\lambda} = \\sum_{\\lambda \\vdash n} h_{\\lambda} \\otimes\n m_{\\lambda} = \\sum_{\\lambda \\vdash n} m_{\\lambda} \\otimes\n h_{\\lambda},\n\n where `\\lambda \\vdash n` means `\\lambda` is a partition of `n`, and\n `n` is any nonnegative integer. It also satisfies\n\n .. MATH::\n\n \\Delta^\\times (p_n) = p_n \\otimes p_n\n\n for any positive integer `n`. If the base ring is a `\\QQ`-algebra, it\n also satisfies\n\n .. MATH::\n\n \\Delta^{\\times}(h_n) = \\sum_{\\lambda \\vdash n} z_{\\lambda}^{-1}\n p_{\\lambda} \\otimes p_{\\lambda},\n\n where\n\n .. MATH::\n\n z_{\\lambda} = \\prod_{i=1}^\\infty i^{m_i(\\lambda)} m_i(\\lambda)!\n\n with `m_i(\\lambda)` meaning the number of appearances of `i`\n in `\\lambda` (see :meth:`~sage.combinat.sf.sfa.zee`).\n\n The method :meth:`kronecker_coproduct` is a synonym of\n :meth:`internal_coproduct`.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(ZZ).s()\n sage: a = s([2,1])\n sage: a.internal_coproduct()\n s[1, 1, 1] # s[2, 1] + s[2, 1] # s[1, 1, 1] + s[2, 1] # s[2, 1] + s[2, 1] # s[3] + s[3] # s[2, 1]\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: b = e([2])\n sage: b.internal_coproduct()\n e[1, 1] # e[2] + e[2] # e[1, 1] - 2*e[2] # e[2]\n\n The internal coproduct is adjoint to the internal product with respect\n to the Hall inner product: Any three symmetric functions `f`, `g` and\n `h` satisfy `\\langle f * g, h \\rangle = \\sum_i \\langle f, h^{\\prime}_i\n \\rangle \\langle g, h^{\\prime\\prime}_i \\rangle`, where we write\n `\\Delta^{\\times}(h)` as `\\sum_i h^{\\prime}_i \\otimes\n h^{\\prime\\prime}_i`. Let us check this in degree `4`::\n\n sage: e = SymmetricFunctions(FiniteField(29)).e()\n sage: s = SymmetricFunctions(FiniteField(29)).s()\n sage: m = SymmetricFunctions(FiniteField(29)).m()\n sage: def tensor_incopr(f, g, h): # computes \\sum_i \\left< f, h'_i \\right> \\left< g, h_i \\right>\n ....: result = h.base_ring().zero()\n ....: for partition_pair, coeff in h.internal_coproduct().monomial_coefficients().items():\n ....: result += coeff * h.parent()(f).scalar(partition_pair[0]) * h.parent()(g).scalar(partition_pair[1])\n ....: return result\n sage: all( all( all( tensor_incopr(e[u], s[v], m[w]) == (e[u].itensor(s[v])).scalar(m[w]) # long time (10s on sage.math, 2013)\n ....: for w in Partitions(5) )\n ....: for v in Partitions(2) )\n ....: for u in Partitions(3) )\n True\n\n Let us check the formulas for `\\Delta^{\\times}(h_n)` and\n `\\Delta^{\\times}(p_n)` given in the description of this method::\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: p = SymmetricFunctions(QQ).p()\n sage: h = SymmetricFunctions(QQ).h()\n sage: s = SymmetricFunctions(QQ).s()\n sage: all( s(h([n])).internal_coproduct() == sum([tensor([s(lam), s(lam)]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n sage: all( h([n]).internal_coproduct() == sum([tensor([h(lam), h(m(lam))]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n sage: all( factorial(n) * h([n]).internal_coproduct() == sum([lam.conjugacy_class_size() * tensor([h(p(lam)), h(p(lam))]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n\n TESTS::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([]).internal_coproduct()\n s[] # s[]\n "
parent = self.parent()
h = parent.realization_of().homogeneous()
s = parent.realization_of().schur()
from sage.categories.tensor import tensor
result = tensor([parent.zero(), parent.zero()])
from sage.misc.cachefunc import cached_function
@cached_function
def hnimage(n):
return sum((tensor([parent(s(lam)), parent(s(lam))]) for lam in Partitions(n)))
for (lam, a) in h(self).monomial_coefficients().items():
result += (a * prod((hnimage(i) for i in lam)))
return result
|
def internal_coproduct(self):
"\n Return the inner coproduct of ``self`` in the basis of ``self``.\n\n The inner coproduct (also known as the Kronecker coproduct, as the\n internal coproduct, or as the second comultiplication on the ring of\n symmetric functions) is a ring homomorphism `\\Delta^\\times` from the\n ring of symmetric functions to the tensor product (over the base\n ring) of this ring with itself. It is uniquely characterized by the\n formula\n\n .. MATH::\n\n \\Delta^{\\times}(h_n) = \\sum_{\\lambda \\vdash n} s_{\\lambda}\n \\otimes s_{\\lambda} = \\sum_{\\lambda \\vdash n} h_{\\lambda} \\otimes\n m_{\\lambda} = \\sum_{\\lambda \\vdash n} m_{\\lambda} \\otimes\n h_{\\lambda},\n\n where `\\lambda \\vdash n` means `\\lambda` is a partition of `n`, and\n `n` is any nonnegative integer. It also satisfies\n\n .. MATH::\n\n \\Delta^\\times (p_n) = p_n \\otimes p_n\n\n for any positive integer `n`. If the base ring is a `\\QQ`-algebra, it\n also satisfies\n\n .. MATH::\n\n \\Delta^{\\times}(h_n) = \\sum_{\\lambda \\vdash n} z_{\\lambda}^{-1}\n p_{\\lambda} \\otimes p_{\\lambda},\n\n where\n\n .. MATH::\n\n z_{\\lambda} = \\prod_{i=1}^\\infty i^{m_i(\\lambda)} m_i(\\lambda)!\n\n with `m_i(\\lambda)` meaning the number of appearances of `i`\n in `\\lambda` (see :meth:`~sage.combinat.sf.sfa.zee`).\n\n The method :meth:`kronecker_coproduct` is a synonym of\n :meth:`internal_coproduct`.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(ZZ).s()\n sage: a = s([2,1])\n sage: a.internal_coproduct()\n s[1, 1, 1] # s[2, 1] + s[2, 1] # s[1, 1, 1] + s[2, 1] # s[2, 1] + s[2, 1] # s[3] + s[3] # s[2, 1]\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: b = e([2])\n sage: b.internal_coproduct()\n e[1, 1] # e[2] + e[2] # e[1, 1] - 2*e[2] # e[2]\n\n The internal coproduct is adjoint to the internal product with respect\n to the Hall inner product: Any three symmetric functions `f`, `g` and\n `h` satisfy `\\langle f * g, h \\rangle = \\sum_i \\langle f, h^{\\prime}_i\n \\rangle \\langle g, h^{\\prime\\prime}_i \\rangle`, where we write\n `\\Delta^{\\times}(h)` as `\\sum_i h^{\\prime}_i \\otimes\n h^{\\prime\\prime}_i`. Let us check this in degree `4`::\n\n sage: e = SymmetricFunctions(FiniteField(29)).e()\n sage: s = SymmetricFunctions(FiniteField(29)).s()\n sage: m = SymmetricFunctions(FiniteField(29)).m()\n sage: def tensor_incopr(f, g, h): # computes \\sum_i \\left< f, h'_i \\right> \\left< g, h_i \\right>\n ....: result = h.base_ring().zero()\n ....: for partition_pair, coeff in h.internal_coproduct().monomial_coefficients().items():\n ....: result += coeff * h.parent()(f).scalar(partition_pair[0]) * h.parent()(g).scalar(partition_pair[1])\n ....: return result\n sage: all( all( all( tensor_incopr(e[u], s[v], m[w]) == (e[u].itensor(s[v])).scalar(m[w]) # long time (10s on sage.math, 2013)\n ....: for w in Partitions(5) )\n ....: for v in Partitions(2) )\n ....: for u in Partitions(3) )\n True\n\n Let us check the formulas for `\\Delta^{\\times}(h_n)` and\n `\\Delta^{\\times}(p_n)` given in the description of this method::\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: p = SymmetricFunctions(QQ).p()\n sage: h = SymmetricFunctions(QQ).h()\n sage: s = SymmetricFunctions(QQ).s()\n sage: all( s(h([n])).internal_coproduct() == sum([tensor([s(lam), s(lam)]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n sage: all( h([n]).internal_coproduct() == sum([tensor([h(lam), h(m(lam))]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n sage: all( factorial(n) * h([n]).internal_coproduct() == sum([lam.conjugacy_class_size() * tensor([h(p(lam)), h(p(lam))]) for lam in Partitions(n)])\n ....: for n in range(6) )\n True\n\n TESTS::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([]).internal_coproduct()\n s[] # s[]\n "
parent = self.parent()
h = parent.realization_of().homogeneous()
s = parent.realization_of().schur()
from sage.categories.tensor import tensor
result = tensor([parent.zero(), parent.zero()])
from sage.misc.cachefunc import cached_function
@cached_function
def hnimage(n):
return sum((tensor([parent(s(lam)), parent(s(lam))]) for lam in Partitions(n)))
for (lam, a) in h(self).monomial_coefficients().items():
result += (a * prod((hnimage(i) for i in lam)))
return result<|docstring|>Return the inner coproduct of ``self`` in the basis of ``self``.
The inner coproduct (also known as the Kronecker coproduct, as the
internal coproduct, or as the second comultiplication on the ring of
symmetric functions) is a ring homomorphism `\Delta^\times` from the
ring of symmetric functions to the tensor product (over the base
ring) of this ring with itself. It is uniquely characterized by the
formula
.. MATH::
\Delta^{\times}(h_n) = \sum_{\lambda \vdash n} s_{\lambda}
\otimes s_{\lambda} = \sum_{\lambda \vdash n} h_{\lambda} \otimes
m_{\lambda} = \sum_{\lambda \vdash n} m_{\lambda} \otimes
h_{\lambda},
where `\lambda \vdash n` means `\lambda` is a partition of `n`, and
`n` is any nonnegative integer. It also satisfies
.. MATH::
\Delta^\times (p_n) = p_n \otimes p_n
for any positive integer `n`. If the base ring is a `\QQ`-algebra, it
also satisfies
.. MATH::
\Delta^{\times}(h_n) = \sum_{\lambda \vdash n} z_{\lambda}^{-1}
p_{\lambda} \otimes p_{\lambda},
where
.. MATH::
z_{\lambda} = \prod_{i=1}^\infty i^{m_i(\lambda)} m_i(\lambda)!
with `m_i(\lambda)` meaning the number of appearances of `i`
in `\lambda` (see :meth:`~sage.combinat.sf.sfa.zee`).
The method :meth:`kronecker_coproduct` is a synonym of
:meth:`internal_coproduct`.
EXAMPLES::
sage: s = SymmetricFunctions(ZZ).s()
sage: a = s([2,1])
sage: a.internal_coproduct()
s[1, 1, 1] # s[2, 1] + s[2, 1] # s[1, 1, 1] + s[2, 1] # s[2, 1] + s[2, 1] # s[3] + s[3] # s[2, 1]
sage: e = SymmetricFunctions(QQ).e()
sage: b = e([2])
sage: b.internal_coproduct()
e[1, 1] # e[2] + e[2] # e[1, 1] - 2*e[2] # e[2]
The internal coproduct is adjoint to the internal product with respect
to the Hall inner product: Any three symmetric functions `f`, `g` and
`h` satisfy `\langle f * g, h \rangle = \sum_i \langle f, h^{\prime}_i
\rangle \langle g, h^{\prime\prime}_i \rangle`, where we write
`\Delta^{\times}(h)` as `\sum_i h^{\prime}_i \otimes
h^{\prime\prime}_i`. Let us check this in degree `4`::
sage: e = SymmetricFunctions(FiniteField(29)).e()
sage: s = SymmetricFunctions(FiniteField(29)).s()
sage: m = SymmetricFunctions(FiniteField(29)).m()
sage: def tensor_incopr(f, g, h): # computes \sum_i \left< f, h'_i \right> \left< g, h''_i \right>
....: result = h.base_ring().zero()
....: for partition_pair, coeff in h.internal_coproduct().monomial_coefficients().items():
....: result += coeff * h.parent()(f).scalar(partition_pair[0]) * h.parent()(g).scalar(partition_pair[1])
....: return result
sage: all( all( all( tensor_incopr(e[u], s[v], m[w]) == (e[u].itensor(s[v])).scalar(m[w]) # long time (10s on sage.math, 2013)
....: for w in Partitions(5) )
....: for v in Partitions(2) )
....: for u in Partitions(3) )
True
Let us check the formulas for `\Delta^{\times}(h_n)` and
`\Delta^{\times}(p_n)` given in the description of this method::
sage: e = SymmetricFunctions(QQ).e()
sage: p = SymmetricFunctions(QQ).p()
sage: h = SymmetricFunctions(QQ).h()
sage: s = SymmetricFunctions(QQ).s()
sage: all( s(h([n])).internal_coproduct() == sum([tensor([s(lam), s(lam)]) for lam in Partitions(n)])
....: for n in range(6) )
True
sage: all( h([n]).internal_coproduct() == sum([tensor([h(lam), h(m(lam))]) for lam in Partitions(n)])
....: for n in range(6) )
True
sage: all( factorial(n) * h([n]).internal_coproduct() == sum([lam.conjugacy_class_size() * tensor([h(p(lam)), h(p(lam))]) for lam in Partitions(n)])
....: for n in range(6) )
True
TESTS::
sage: s = SymmetricFunctions(QQ).s()
sage: s([]).internal_coproduct()
s[] # s[]<|endoftext|>
|
9b073797d8c5beea515955ce6508e52f929e0baefb65da167cc027a0d4d4e422
|
def arithmetic_product(self, x):
'\n Return the arithmetic product of ``self`` and ``x`` in the\n basis of ``self``.\n\n The arithmetic product is a binary operation `\\boxdot` on the\n ring of symmetric functions which is bilinear in its two\n arguments and satisfies\n\n .. MATH::\n\n p_{\\lambda} \\boxdot p_{\\mu} = \\prod\\limits_{i \\geq 1, j \\geq 1}\n p_{\\mathrm{lcm}(\\lambda_i, \\mu_j)}^{\\mathrm{gcd}(\\lambda_i, \\mu_j)}\n\n for any two partitions `\\lambda = (\\lambda_1, \\lambda_2, \\lambda_3,\n \\dots )` and `\\mu = (\\mu_1, \\mu_2, \\mu_3, \\dots )` (where `p_{\\nu}`\n denotes the power-sum symmetric function indexed by the partition\n `\\nu`, and `p_i` denotes the `i`-th power-sum symmetric function).\n This is enough to define the arithmetic product if the base ring\n is torsion-free as a `\\ZZ`-module; for all other cases the\n arithmetic product is uniquely determined by requiring it to be\n functorial in the base ring. See\n http://mathoverflow.net/questions/138148/ for a discussion of\n this arithmetic product.\n\n If `f` and `g` are two symmetric functions which are homogeneous\n of degrees `a` and `b`, respectively, then `f \\boxdot g` is\n homogeneous of degree `ab`.\n\n The arithmetic product is commutative and associative and has\n unity `e_1 = p_1 = h_1`.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n\n OUTPUT:\n\n Arithmetic product of ``self`` with ``x``; this is a symmetric\n function over the same base ring as ``self``.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([2]).arithmetic_product(s([2]))\n s[1, 1, 1, 1] + 2*s[2, 2] + s[4]\n sage: s([2]).arithmetic_product(s([1,1]))\n s[2, 1, 1] + s[3, 1]\n\n The symmetric function ``e[1]`` is the unity for the arithmetic\n product::\n\n sage: e = SymmetricFunctions(ZZ).e()\n sage: all( e([1]).arithmetic_product(e(q)) == e(q) for q in Partitions(4) )\n True\n\n The arithmetic product is commutative::\n\n sage: e = SymmetricFunctions(FiniteField(19)).e()\n sage: m = SymmetricFunctions(FiniteField(19)).m()\n sage: all( all( e(p).arithmetic_product(m(q)) == m(q).arithmetic_product(e(p)) # long time (26s on sage.math, 2013)\n ....: for q in Partitions(4) )\n ....: for p in Partitions(4) )\n True\n\n .. NOTE::\n\n The currently existing implementation of this function is\n technically unsatisfactory. It distinguishes the case when the\n base ring is a `\\QQ`-algebra (in which case the arithmetic product\n can be easily computed using the power sum basis) from the case\n where it isn\'t. In the latter, it does a computation using\n universal coefficients, again distinguishing the case when it is\n able to compute the "corresponding" basis of the symmetric function\n algebra over `\\QQ` (using the ``corresponding_basis_over`` hack)\n from the case when it isn\'t (in which case it transforms everything\n into the Schur basis, which is slow).\n '
parent = self.parent()
if parent.has_coerce_map_from(QQ):
from sage.combinat.partition import Partition
from sage.rings.arith import gcd, lcm
from itertools import product, repeat, chain
p = parent.realization_of().power()
def f(lam, mu):
term_iterable = chain.from_iterable((repeat(lcm(pair), times=gcd(pair)) for pair in product(lam, mu)))
term_list = sorted(term_iterable, reverse=True)
res = Partition(term_list)
return p(res)
return parent(p._apply_multi_module_morphism(p(self), p(x), f))
comp_parent = parent
comp_self = self
corresponding_parent_over_QQ = parent.corresponding_basis_over(QQ)
if (corresponding_parent_over_QQ is None):
comp_parent = parent.realization_of().schur()
comp_self = comp_parent(self)
from sage.combinat.sf.sf import SymmetricFunctions
corresponding_parent_over_QQ = SymmetricFunctions(QQ).schur()
comp_x = comp_parent(x)
result = comp_parent.zero()
for (lam, a) in comp_self.monomial_coefficients().items():
for (mu, b) in comp_x.monomial_coefficients().items():
lam_star_mu = corresponding_parent_over_QQ(lam).arithmetic_product(corresponding_parent_over_QQ(mu))
for (nu, c) in lam_star_mu.monomial_coefficients().items():
result += (((a * b) * comp_parent.base_ring()(c)) * comp_parent(nu))
return parent(result)
|
Return the arithmetic product of ``self`` and ``x`` in the
basis of ``self``.
The arithmetic product is a binary operation `\boxdot` on the
ring of symmetric functions which is bilinear in its two
arguments and satisfies
.. MATH::
p_{\lambda} \boxdot p_{\mu} = \prod\limits_{i \geq 1, j \geq 1}
p_{\mathrm{lcm}(\lambda_i, \mu_j)}^{\mathrm{gcd}(\lambda_i, \mu_j)}
for any two partitions `\lambda = (\lambda_1, \lambda_2, \lambda_3,
\dots )` and `\mu = (\mu_1, \mu_2, \mu_3, \dots )` (where `p_{\nu}`
denotes the power-sum symmetric function indexed by the partition
`\nu`, and `p_i` denotes the `i`-th power-sum symmetric function).
This is enough to define the arithmetic product if the base ring
is torsion-free as a `\ZZ`-module; for all other cases the
arithmetic product is uniquely determined by requiring it to be
functorial in the base ring. See
http://mathoverflow.net/questions/138148/ for a discussion of
this arithmetic product.
If `f` and `g` are two symmetric functions which are homogeneous
of degrees `a` and `b`, respectively, then `f \boxdot g` is
homogeneous of degree `ab`.
The arithmetic product is commutative and associative and has
unity `e_1 = p_1 = h_1`.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the
same base ring as ``self``
OUTPUT:
Arithmetic product of ``self`` with ``x``; this is a symmetric
function over the same base ring as ``self``.
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s([2]).arithmetic_product(s([2]))
s[1, 1, 1, 1] + 2*s[2, 2] + s[4]
sage: s([2]).arithmetic_product(s([1,1]))
s[2, 1, 1] + s[3, 1]
The symmetric function ``e[1]`` is the unity for the arithmetic
product::
sage: e = SymmetricFunctions(ZZ).e()
sage: all( e([1]).arithmetic_product(e(q)) == e(q) for q in Partitions(4) )
True
The arithmetic product is commutative::
sage: e = SymmetricFunctions(FiniteField(19)).e()
sage: m = SymmetricFunctions(FiniteField(19)).m()
sage: all( all( e(p).arithmetic_product(m(q)) == m(q).arithmetic_product(e(p)) # long time (26s on sage.math, 2013)
....: for q in Partitions(4) )
....: for p in Partitions(4) )
True
.. NOTE::
The currently existing implementation of this function is
technically unsatisfactory. It distinguishes the case when the
base ring is a `\QQ`-algebra (in which case the arithmetic product
can be easily computed using the power sum basis) from the case
where it isn't. In the latter, it does a computation using
universal coefficients, again distinguishing the case when it is
able to compute the "corresponding" basis of the symmetric function
algebra over `\QQ` (using the ``corresponding_basis_over`` hack)
from the case when it isn't (in which case it transforms everything
into the Schur basis, which is slow).
|
src/sage/combinat/sf/sfa.py
|
arithmetic_product
|
bopopescu/sagesmc
| 5 |
python
|
def arithmetic_product(self, x):
'\n Return the arithmetic product of ``self`` and ``x`` in the\n basis of ``self``.\n\n The arithmetic product is a binary operation `\\boxdot` on the\n ring of symmetric functions which is bilinear in its two\n arguments and satisfies\n\n .. MATH::\n\n p_{\\lambda} \\boxdot p_{\\mu} = \\prod\\limits_{i \\geq 1, j \\geq 1}\n p_{\\mathrm{lcm}(\\lambda_i, \\mu_j)}^{\\mathrm{gcd}(\\lambda_i, \\mu_j)}\n\n for any two partitions `\\lambda = (\\lambda_1, \\lambda_2, \\lambda_3,\n \\dots )` and `\\mu = (\\mu_1, \\mu_2, \\mu_3, \\dots )` (where `p_{\\nu}`\n denotes the power-sum symmetric function indexed by the partition\n `\\nu`, and `p_i` denotes the `i`-th power-sum symmetric function).\n This is enough to define the arithmetic product if the base ring\n is torsion-free as a `\\ZZ`-module; for all other cases the\n arithmetic product is uniquely determined by requiring it to be\n functorial in the base ring. See\n http://mathoverflow.net/questions/138148/ for a discussion of\n this arithmetic product.\n\n If `f` and `g` are two symmetric functions which are homogeneous\n of degrees `a` and `b`, respectively, then `f \\boxdot g` is\n homogeneous of degree `ab`.\n\n The arithmetic product is commutative and associative and has\n unity `e_1 = p_1 = h_1`.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n\n OUTPUT:\n\n Arithmetic product of ``self`` with ``x``; this is a symmetric\n function over the same base ring as ``self``.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([2]).arithmetic_product(s([2]))\n s[1, 1, 1, 1] + 2*s[2, 2] + s[4]\n sage: s([2]).arithmetic_product(s([1,1]))\n s[2, 1, 1] + s[3, 1]\n\n The symmetric function ``e[1]`` is the unity for the arithmetic\n product::\n\n sage: e = SymmetricFunctions(ZZ).e()\n sage: all( e([1]).arithmetic_product(e(q)) == e(q) for q in Partitions(4) )\n True\n\n The arithmetic product is commutative::\n\n sage: e = SymmetricFunctions(FiniteField(19)).e()\n sage: m = SymmetricFunctions(FiniteField(19)).m()\n sage: all( all( e(p).arithmetic_product(m(q)) == m(q).arithmetic_product(e(p)) # long time (26s on sage.math, 2013)\n ....: for q in Partitions(4) )\n ....: for p in Partitions(4) )\n True\n\n .. NOTE::\n\n The currently existing implementation of this function is\n technically unsatisfactory. It distinguishes the case when the\n base ring is a `\\QQ`-algebra (in which case the arithmetic product\n can be easily computed using the power sum basis) from the case\n where it isn\'t. In the latter, it does a computation using\n universal coefficients, again distinguishing the case when it is\n able to compute the "corresponding" basis of the symmetric function\n algebra over `\\QQ` (using the ``corresponding_basis_over`` hack)\n from the case when it isn\'t (in which case it transforms everything\n into the Schur basis, which is slow).\n '
parent = self.parent()
if parent.has_coerce_map_from(QQ):
from sage.combinat.partition import Partition
from sage.rings.arith import gcd, lcm
from itertools import product, repeat, chain
p = parent.realization_of().power()
def f(lam, mu):
term_iterable = chain.from_iterable((repeat(lcm(pair), times=gcd(pair)) for pair in product(lam, mu)))
term_list = sorted(term_iterable, reverse=True)
res = Partition(term_list)
return p(res)
return parent(p._apply_multi_module_morphism(p(self), p(x), f))
comp_parent = parent
comp_self = self
corresponding_parent_over_QQ = parent.corresponding_basis_over(QQ)
if (corresponding_parent_over_QQ is None):
comp_parent = parent.realization_of().schur()
comp_self = comp_parent(self)
from sage.combinat.sf.sf import SymmetricFunctions
corresponding_parent_over_QQ = SymmetricFunctions(QQ).schur()
comp_x = comp_parent(x)
result = comp_parent.zero()
for (lam, a) in comp_self.monomial_coefficients().items():
for (mu, b) in comp_x.monomial_coefficients().items():
lam_star_mu = corresponding_parent_over_QQ(lam).arithmetic_product(corresponding_parent_over_QQ(mu))
for (nu, c) in lam_star_mu.monomial_coefficients().items():
result += (((a * b) * comp_parent.base_ring()(c)) * comp_parent(nu))
return parent(result)
|
def arithmetic_product(self, x):
'\n Return the arithmetic product of ``self`` and ``x`` in the\n basis of ``self``.\n\n The arithmetic product is a binary operation `\\boxdot` on the\n ring of symmetric functions which is bilinear in its two\n arguments and satisfies\n\n .. MATH::\n\n p_{\\lambda} \\boxdot p_{\\mu} = \\prod\\limits_{i \\geq 1, j \\geq 1}\n p_{\\mathrm{lcm}(\\lambda_i, \\mu_j)}^{\\mathrm{gcd}(\\lambda_i, \\mu_j)}\n\n for any two partitions `\\lambda = (\\lambda_1, \\lambda_2, \\lambda_3,\n \\dots )` and `\\mu = (\\mu_1, \\mu_2, \\mu_3, \\dots )` (where `p_{\\nu}`\n denotes the power-sum symmetric function indexed by the partition\n `\\nu`, and `p_i` denotes the `i`-th power-sum symmetric function).\n This is enough to define the arithmetic product if the base ring\n is torsion-free as a `\\ZZ`-module; for all other cases the\n arithmetic product is uniquely determined by requiring it to be\n functorial in the base ring. See\n http://mathoverflow.net/questions/138148/ for a discussion of\n this arithmetic product.\n\n If `f` and `g` are two symmetric functions which are homogeneous\n of degrees `a` and `b`, respectively, then `f \\boxdot g` is\n homogeneous of degree `ab`.\n\n The arithmetic product is commutative and associative and has\n unity `e_1 = p_1 = h_1`.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n\n OUTPUT:\n\n Arithmetic product of ``self`` with ``x``; this is a symmetric\n function over the same base ring as ``self``.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([2]).arithmetic_product(s([2]))\n s[1, 1, 1, 1] + 2*s[2, 2] + s[4]\n sage: s([2]).arithmetic_product(s([1,1]))\n s[2, 1, 1] + s[3, 1]\n\n The symmetric function ``e[1]`` is the unity for the arithmetic\n product::\n\n sage: e = SymmetricFunctions(ZZ).e()\n sage: all( e([1]).arithmetic_product(e(q)) == e(q) for q in Partitions(4) )\n True\n\n The arithmetic product is commutative::\n\n sage: e = SymmetricFunctions(FiniteField(19)).e()\n sage: m = SymmetricFunctions(FiniteField(19)).m()\n sage: all( all( e(p).arithmetic_product(m(q)) == m(q).arithmetic_product(e(p)) # long time (26s on sage.math, 2013)\n ....: for q in Partitions(4) )\n ....: for p in Partitions(4) )\n True\n\n .. NOTE::\n\n The currently existing implementation of this function is\n technically unsatisfactory. It distinguishes the case when the\n base ring is a `\\QQ`-algebra (in which case the arithmetic product\n can be easily computed using the power sum basis) from the case\n where it isn\'t. In the latter, it does a computation using\n universal coefficients, again distinguishing the case when it is\n able to compute the "corresponding" basis of the symmetric function\n algebra over `\\QQ` (using the ``corresponding_basis_over`` hack)\n from the case when it isn\'t (in which case it transforms everything\n into the Schur basis, which is slow).\n '
parent = self.parent()
if parent.has_coerce_map_from(QQ):
from sage.combinat.partition import Partition
from sage.rings.arith import gcd, lcm
from itertools import product, repeat, chain
p = parent.realization_of().power()
def f(lam, mu):
term_iterable = chain.from_iterable((repeat(lcm(pair), times=gcd(pair)) for pair in product(lam, mu)))
term_list = sorted(term_iterable, reverse=True)
res = Partition(term_list)
return p(res)
return parent(p._apply_multi_module_morphism(p(self), p(x), f))
comp_parent = parent
comp_self = self
corresponding_parent_over_QQ = parent.corresponding_basis_over(QQ)
if (corresponding_parent_over_QQ is None):
comp_parent = parent.realization_of().schur()
comp_self = comp_parent(self)
from sage.combinat.sf.sf import SymmetricFunctions
corresponding_parent_over_QQ = SymmetricFunctions(QQ).schur()
comp_x = comp_parent(x)
result = comp_parent.zero()
for (lam, a) in comp_self.monomial_coefficients().items():
for (mu, b) in comp_x.monomial_coefficients().items():
lam_star_mu = corresponding_parent_over_QQ(lam).arithmetic_product(corresponding_parent_over_QQ(mu))
for (nu, c) in lam_star_mu.monomial_coefficients().items():
result += (((a * b) * comp_parent.base_ring()(c)) * comp_parent(nu))
return parent(result)<|docstring|>Return the arithmetic product of ``self`` and ``x`` in the
basis of ``self``.
The arithmetic product is a binary operation `\boxdot` on the
ring of symmetric functions which is bilinear in its two
arguments and satisfies
.. MATH::
p_{\lambda} \boxdot p_{\mu} = \prod\limits_{i \geq 1, j \geq 1}
p_{\mathrm{lcm}(\lambda_i, \mu_j)}^{\mathrm{gcd}(\lambda_i, \mu_j)}
for any two partitions `\lambda = (\lambda_1, \lambda_2, \lambda_3,
\dots )` and `\mu = (\mu_1, \mu_2, \mu_3, \dots )` (where `p_{\nu}`
denotes the power-sum symmetric function indexed by the partition
`\nu`, and `p_i` denotes the `i`-th power-sum symmetric function).
This is enough to define the arithmetic product if the base ring
is torsion-free as a `\ZZ`-module; for all other cases the
arithmetic product is uniquely determined by requiring it to be
functorial in the base ring. See
http://mathoverflow.net/questions/138148/ for a discussion of
this arithmetic product.
If `f` and `g` are two symmetric functions which are homogeneous
of degrees `a` and `b`, respectively, then `f \boxdot g` is
homogeneous of degree `ab`.
The arithmetic product is commutative and associative and has
unity `e_1 = p_1 = h_1`.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the
same base ring as ``self``
OUTPUT:
Arithmetic product of ``self`` with ``x``; this is a symmetric
function over the same base ring as ``self``.
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s([2]).arithmetic_product(s([2]))
s[1, 1, 1, 1] + 2*s[2, 2] + s[4]
sage: s([2]).arithmetic_product(s([1,1]))
s[2, 1, 1] + s[3, 1]
The symmetric function ``e[1]`` is the unity for the arithmetic
product::
sage: e = SymmetricFunctions(ZZ).e()
sage: all( e([1]).arithmetic_product(e(q)) == e(q) for q in Partitions(4) )
True
The arithmetic product is commutative::
sage: e = SymmetricFunctions(FiniteField(19)).e()
sage: m = SymmetricFunctions(FiniteField(19)).m()
sage: all( all( e(p).arithmetic_product(m(q)) == m(q).arithmetic_product(e(p)) # long time (26s on sage.math, 2013)
....: for q in Partitions(4) )
....: for p in Partitions(4) )
True
.. NOTE::
The currently existing implementation of this function is
technically unsatisfactory. It distinguishes the case when the
base ring is a `\QQ`-algebra (in which case the arithmetic product
can be easily computed using the power sum basis) from the case
where it isn't. In the latter, it does a computation using
universal coefficients, again distinguishing the case when it is
able to compute the "corresponding" basis of the symmetric function
algebra over `\QQ` (using the ``corresponding_basis_over`` hack)
from the case when it isn't (in which case it transforms everything
into the Schur basis, which is slow).<|endoftext|>
|
eae7a1ee7188ae66bccfce0d9ec5d2cf2ce763a565e532087c50c862c90283ab
|
def nabla(self, q=None, t=None, power=1):
"\n Return the value of the nabla operator applied to ``self``.\n\n The eigenvectors of the nabla operator are the Macdonald polynomials in\n the Ht basis.\n\n If the parameter ``power`` is an integer then it calculates\n nabla to that integer. The default value of ``power`` is 1.\n\n INPUT:\n\n - ``q``, ``t`` -- optional parameters (default: ``None``, in which\n case ``q`` and ``t`` are used)\n - ``power`` -- (default: ``1``) an integer indicating how many times to\n apply the operator `\\nabla`. Negative values of ``power``\n indicate powers of `\\nabla^{-1}`.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))\n sage: p = Sym.power()\n sage: p([1,1]).nabla()\n (-1/2*q*t+1/2*q+1/2*t+1/2)*p[1, 1] + (1/2*q*t-1/2*q-1/2*t+1/2)*p[2]\n sage: p([2,1]).nabla(q=1)\n (-t-1)*p[1, 1, 1] + t*p[2, 1]\n sage: p([2]).nabla(q=1)*p([1]).nabla(q=1)\n (-t-1)*p[1, 1, 1] + t*p[2, 1]\n sage: s = Sym.schur()\n sage: s([2,1]).nabla()\n (-q^3*t-q^2*t^2-q*t^3)*s[1, 1, 1] + (-q^2*t-q*t^2)*s[2, 1]\n sage: s([1,1,1]).nabla()\n (q^3+q^2*t+q*t^2+t^3+q*t)*s[1, 1, 1] + (q^2+q*t+t^2+q+t)*s[2, 1] + s[3]\n sage: s([1,1,1]).nabla(t=1)\n (q^3+q^2+2*q+1)*s[1, 1, 1] + (q^2+2*q+2)*s[2, 1] + s[3]\n sage: s(0).nabla()\n 0\n sage: s(1).nabla()\n s[]\n sage: s([2,1]).nabla(power=-1)\n ((-q-t)/(q^2*t^2))*s[2, 1] + ((-q^2-q*t-t^2)/(q^3*t^3))*s[3]\n sage: (s([2])+s([3])).nabla()\n (-q*t)*s[1, 1] + (q^3*t^2+q^2*t^3)*s[1, 1, 1] + q^2*t^2*s[2, 1]\n "
parent = self.parent()
BR = parent.base_ring()
if (q is None):
if hasattr(parent, 'q'):
q = parent.q
else:
q = BR(QQ['q'].gen())
if (t is None):
if hasattr(parent, 't'):
t = parent.t
else:
t = BR(QQ['t'].gen())
Ht = parent.realization_of().macdonald(q=q, t=t).Ht()
return parent(Ht(self).nabla(power=power))
|
Return the value of the nabla operator applied to ``self``.
The eigenvectors of the nabla operator are the Macdonald polynomials in
the Ht basis.
If the parameter ``power`` is an integer then it calculates
nabla to that integer. The default value of ``power`` is 1.
INPUT:
- ``q``, ``t`` -- optional parameters (default: ``None``, in which
case ``q`` and ``t`` are used)
- ``power`` -- (default: ``1``) an integer indicating how many times to
apply the operator `\nabla`. Negative values of ``power``
indicate powers of `\nabla^{-1}`.
EXAMPLES::
sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))
sage: p = Sym.power()
sage: p([1,1]).nabla()
(-1/2*q*t+1/2*q+1/2*t+1/2)*p[1, 1] + (1/2*q*t-1/2*q-1/2*t+1/2)*p[2]
sage: p([2,1]).nabla(q=1)
(-t-1)*p[1, 1, 1] + t*p[2, 1]
sage: p([2]).nabla(q=1)*p([1]).nabla(q=1)
(-t-1)*p[1, 1, 1] + t*p[2, 1]
sage: s = Sym.schur()
sage: s([2,1]).nabla()
(-q^3*t-q^2*t^2-q*t^3)*s[1, 1, 1] + (-q^2*t-q*t^2)*s[2, 1]
sage: s([1,1,1]).nabla()
(q^3+q^2*t+q*t^2+t^3+q*t)*s[1, 1, 1] + (q^2+q*t+t^2+q+t)*s[2, 1] + s[3]
sage: s([1,1,1]).nabla(t=1)
(q^3+q^2+2*q+1)*s[1, 1, 1] + (q^2+2*q+2)*s[2, 1] + s[3]
sage: s(0).nabla()
0
sage: s(1).nabla()
s[]
sage: s([2,1]).nabla(power=-1)
((-q-t)/(q^2*t^2))*s[2, 1] + ((-q^2-q*t-t^2)/(q^3*t^3))*s[3]
sage: (s([2])+s([3])).nabla()
(-q*t)*s[1, 1] + (q^3*t^2+q^2*t^3)*s[1, 1, 1] + q^2*t^2*s[2, 1]
|
src/sage/combinat/sf/sfa.py
|
nabla
|
bopopescu/sagesmc
| 5 |
python
|
def nabla(self, q=None, t=None, power=1):
"\n Return the value of the nabla operator applied to ``self``.\n\n The eigenvectors of the nabla operator are the Macdonald polynomials in\n the Ht basis.\n\n If the parameter ``power`` is an integer then it calculates\n nabla to that integer. The default value of ``power`` is 1.\n\n INPUT:\n\n - ``q``, ``t`` -- optional parameters (default: ``None``, in which\n case ``q`` and ``t`` are used)\n - ``power`` -- (default: ``1``) an integer indicating how many times to\n apply the operator `\\nabla`. Negative values of ``power``\n indicate powers of `\\nabla^{-1}`.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))\n sage: p = Sym.power()\n sage: p([1,1]).nabla()\n (-1/2*q*t+1/2*q+1/2*t+1/2)*p[1, 1] + (1/2*q*t-1/2*q-1/2*t+1/2)*p[2]\n sage: p([2,1]).nabla(q=1)\n (-t-1)*p[1, 1, 1] + t*p[2, 1]\n sage: p([2]).nabla(q=1)*p([1]).nabla(q=1)\n (-t-1)*p[1, 1, 1] + t*p[2, 1]\n sage: s = Sym.schur()\n sage: s([2,1]).nabla()\n (-q^3*t-q^2*t^2-q*t^3)*s[1, 1, 1] + (-q^2*t-q*t^2)*s[2, 1]\n sage: s([1,1,1]).nabla()\n (q^3+q^2*t+q*t^2+t^3+q*t)*s[1, 1, 1] + (q^2+q*t+t^2+q+t)*s[2, 1] + s[3]\n sage: s([1,1,1]).nabla(t=1)\n (q^3+q^2+2*q+1)*s[1, 1, 1] + (q^2+2*q+2)*s[2, 1] + s[3]\n sage: s(0).nabla()\n 0\n sage: s(1).nabla()\n s[]\n sage: s([2,1]).nabla(power=-1)\n ((-q-t)/(q^2*t^2))*s[2, 1] + ((-q^2-q*t-t^2)/(q^3*t^3))*s[3]\n sage: (s([2])+s([3])).nabla()\n (-q*t)*s[1, 1] + (q^3*t^2+q^2*t^3)*s[1, 1, 1] + q^2*t^2*s[2, 1]\n "
parent = self.parent()
BR = parent.base_ring()
if (q is None):
if hasattr(parent, 'q'):
q = parent.q
else:
q = BR(QQ['q'].gen())
if (t is None):
if hasattr(parent, 't'):
t = parent.t
else:
t = BR(QQ['t'].gen())
Ht = parent.realization_of().macdonald(q=q, t=t).Ht()
return parent(Ht(self).nabla(power=power))
|
def nabla(self, q=None, t=None, power=1):
"\n Return the value of the nabla operator applied to ``self``.\n\n The eigenvectors of the nabla operator are the Macdonald polynomials in\n the Ht basis.\n\n If the parameter ``power`` is an integer then it calculates\n nabla to that integer. The default value of ``power`` is 1.\n\n INPUT:\n\n - ``q``, ``t`` -- optional parameters (default: ``None``, in which\n case ``q`` and ``t`` are used)\n - ``power`` -- (default: ``1``) an integer indicating how many times to\n apply the operator `\\nabla`. Negative values of ``power``\n indicate powers of `\\nabla^{-1}`.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))\n sage: p = Sym.power()\n sage: p([1,1]).nabla()\n (-1/2*q*t+1/2*q+1/2*t+1/2)*p[1, 1] + (1/2*q*t-1/2*q-1/2*t+1/2)*p[2]\n sage: p([2,1]).nabla(q=1)\n (-t-1)*p[1, 1, 1] + t*p[2, 1]\n sage: p([2]).nabla(q=1)*p([1]).nabla(q=1)\n (-t-1)*p[1, 1, 1] + t*p[2, 1]\n sage: s = Sym.schur()\n sage: s([2,1]).nabla()\n (-q^3*t-q^2*t^2-q*t^3)*s[1, 1, 1] + (-q^2*t-q*t^2)*s[2, 1]\n sage: s([1,1,1]).nabla()\n (q^3+q^2*t+q*t^2+t^3+q*t)*s[1, 1, 1] + (q^2+q*t+t^2+q+t)*s[2, 1] + s[3]\n sage: s([1,1,1]).nabla(t=1)\n (q^3+q^2+2*q+1)*s[1, 1, 1] + (q^2+2*q+2)*s[2, 1] + s[3]\n sage: s(0).nabla()\n 0\n sage: s(1).nabla()\n s[]\n sage: s([2,1]).nabla(power=-1)\n ((-q-t)/(q^2*t^2))*s[2, 1] + ((-q^2-q*t-t^2)/(q^3*t^3))*s[3]\n sage: (s([2])+s([3])).nabla()\n (-q*t)*s[1, 1] + (q^3*t^2+q^2*t^3)*s[1, 1, 1] + q^2*t^2*s[2, 1]\n "
parent = self.parent()
BR = parent.base_ring()
if (q is None):
if hasattr(parent, 'q'):
q = parent.q
else:
q = BR(QQ['q'].gen())
if (t is None):
if hasattr(parent, 't'):
t = parent.t
else:
t = BR(QQ['t'].gen())
Ht = parent.realization_of().macdonald(q=q, t=t).Ht()
return parent(Ht(self).nabla(power=power))<|docstring|>Return the value of the nabla operator applied to ``self``.
The eigenvectors of the nabla operator are the Macdonald polynomials in
the Ht basis.
If the parameter ``power`` is an integer then it calculates
nabla to that integer. The default value of ``power`` is 1.
INPUT:
- ``q``, ``t`` -- optional parameters (default: ``None``, in which
case ``q`` and ``t`` are used)
- ``power`` -- (default: ``1``) an integer indicating how many times to
apply the operator `\nabla`. Negative values of ``power``
indicate powers of `\nabla^{-1}`.
EXAMPLES::
sage: Sym = SymmetricFunctions(FractionField(QQ['q','t']))
sage: p = Sym.power()
sage: p([1,1]).nabla()
(-1/2*q*t+1/2*q+1/2*t+1/2)*p[1, 1] + (1/2*q*t-1/2*q-1/2*t+1/2)*p[2]
sage: p([2,1]).nabla(q=1)
(-t-1)*p[1, 1, 1] + t*p[2, 1]
sage: p([2]).nabla(q=1)*p([1]).nabla(q=1)
(-t-1)*p[1, 1, 1] + t*p[2, 1]
sage: s = Sym.schur()
sage: s([2,1]).nabla()
(-q^3*t-q^2*t^2-q*t^3)*s[1, 1, 1] + (-q^2*t-q*t^2)*s[2, 1]
sage: s([1,1,1]).nabla()
(q^3+q^2*t+q*t^2+t^3+q*t)*s[1, 1, 1] + (q^2+q*t+t^2+q+t)*s[2, 1] + s[3]
sage: s([1,1,1]).nabla(t=1)
(q^3+q^2+2*q+1)*s[1, 1, 1] + (q^2+2*q+2)*s[2, 1] + s[3]
sage: s(0).nabla()
0
sage: s(1).nabla()
s[]
sage: s([2,1]).nabla(power=-1)
((-q-t)/(q^2*t^2))*s[2, 1] + ((-q^2-q*t-t^2)/(q^3*t^3))*s[3]
sage: (s([2])+s([3])).nabla()
(-q*t)*s[1, 1] + (q^3*t^2+q^2*t^3)*s[1, 1, 1] + q^2*t^2*s[2, 1]<|endoftext|>
|
4fc253ea207b8b72b0a814469a2607125ebd97e8a2ad61df0e545db9b7aa867d
|
def scalar(self, x, zee=None):
'\n Return standard scalar product between ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n\n - ``zee`` -- an optional function on partitions giving\n the value for the scalar product between `p_{\\mu}` and `p_{\\mu}`\n (default is to use the standard :meth:`~sage.combinat.sf.sfa.zee` function)\n\n This is the default implementation that converts both ``self`` and\n ``x`` into either Schur functions (if ``zee`` is not specified) or\n power-sum functions (if ``zee`` is specified) and performs the scalar\n product in that basis.\n\n EXAMPLES::\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: h = SymmetricFunctions(QQ).h()\n sage: m = SymmetricFunctions(QQ).m()\n sage: p4 = Partitions(4)\n sage: matrix([ [e(a).scalar(h(b)) for a in p4] for b in p4])\n [ 0 0 0 0 1]\n [ 0 0 0 1 4]\n [ 0 0 1 2 6]\n [ 0 1 2 5 12]\n [ 1 4 6 12 24]\n sage: matrix([ [h(a).scalar(e(b)) for a in p4] for b in p4])\n [ 0 0 0 0 1]\n [ 0 0 0 1 4]\n [ 0 0 1 2 6]\n [ 0 1 2 5 12]\n [ 1 4 6 12 24]\n sage: matrix([ [m(a).scalar(e(b)) for a in p4] for b in p4])\n [-1 2 1 -3 1]\n [ 0 1 0 -2 1]\n [ 0 0 1 -2 1]\n [ 0 0 0 -1 1]\n [ 0 0 0 0 1]\n sage: matrix([ [m(a).scalar(h(b)) for a in p4] for b in p4])\n [1 0 0 0 0]\n [0 1 0 0 0]\n [0 0 1 0 0]\n [0 0 0 1 0]\n [0 0 0 0 1]\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: m(p[3,2]).scalar(p[3,2], zee=lambda mu: 2**mu.length())\n 4\n sage: m(p[3,2]).scalar(p[2,2,1], lambda mu: 1)\n 0\n sage: m[3,2].scalar(h[3,2], zee=lambda mu: 2**mu.length())\n 2/3\n\n TESTS::\n\n sage: m(1).scalar(h(1))\n 1\n sage: m(0).scalar(h(1))\n 0\n sage: m(1).scalar(h(0))\n 0\n sage: m(0).scalar(h(0))\n 0\n\n Over the integers, too (as long as ``zee`` is not set)::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: m = Sym.m()\n sage: m([2]).scalar(m([2]))\n 2\n '
if (zee is None):
s = self.parent().realization_of().schur()
s_self = s(self)
s_x = s(x)
return s_self.scalar(s_x)
else:
p = self.parent().realization_of().power()
p_self = p(self)
p_x = p(x)
return sum((((zee(mu) * p_x.coefficient(mu)) * p_self.coefficient(mu)) for mu in p_self.support()))
|
Return standard scalar product between ``self`` and ``x``.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the
same base ring as ``self``
- ``zee`` -- an optional function on partitions giving
the value for the scalar product between `p_{\mu}` and `p_{\mu}`
(default is to use the standard :meth:`~sage.combinat.sf.sfa.zee` function)
This is the default implementation that converts both ``self`` and
``x`` into either Schur functions (if ``zee`` is not specified) or
power-sum functions (if ``zee`` is specified) and performs the scalar
product in that basis.
EXAMPLES::
sage: e = SymmetricFunctions(QQ).e()
sage: h = SymmetricFunctions(QQ).h()
sage: m = SymmetricFunctions(QQ).m()
sage: p4 = Partitions(4)
sage: matrix([ [e(a).scalar(h(b)) for a in p4] for b in p4])
[ 0 0 0 0 1]
[ 0 0 0 1 4]
[ 0 0 1 2 6]
[ 0 1 2 5 12]
[ 1 4 6 12 24]
sage: matrix([ [h(a).scalar(e(b)) for a in p4] for b in p4])
[ 0 0 0 0 1]
[ 0 0 0 1 4]
[ 0 0 1 2 6]
[ 0 1 2 5 12]
[ 1 4 6 12 24]
sage: matrix([ [m(a).scalar(e(b)) for a in p4] for b in p4])
[-1 2 1 -3 1]
[ 0 1 0 -2 1]
[ 0 0 1 -2 1]
[ 0 0 0 -1 1]
[ 0 0 0 0 1]
sage: matrix([ [m(a).scalar(h(b)) for a in p4] for b in p4])
[1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
sage: p = SymmetricFunctions(QQ).p()
sage: m(p[3,2]).scalar(p[3,2], zee=lambda mu: 2**mu.length())
4
sage: m(p[3,2]).scalar(p[2,2,1], lambda mu: 1)
0
sage: m[3,2].scalar(h[3,2], zee=lambda mu: 2**mu.length())
2/3
TESTS::
sage: m(1).scalar(h(1))
1
sage: m(0).scalar(h(1))
0
sage: m(1).scalar(h(0))
0
sage: m(0).scalar(h(0))
0
Over the integers, too (as long as ``zee`` is not set)::
sage: Sym = SymmetricFunctions(ZZ)
sage: m = Sym.m()
sage: m([2]).scalar(m([2]))
2
|
src/sage/combinat/sf/sfa.py
|
scalar
|
bopopescu/sagesmc
| 5 |
python
|
def scalar(self, x, zee=None):
'\n Return standard scalar product between ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n\n - ``zee`` -- an optional function on partitions giving\n the value for the scalar product between `p_{\\mu}` and `p_{\\mu}`\n (default is to use the standard :meth:`~sage.combinat.sf.sfa.zee` function)\n\n This is the default implementation that converts both ``self`` and\n ``x`` into either Schur functions (if ``zee`` is not specified) or\n power-sum functions (if ``zee`` is specified) and performs the scalar\n product in that basis.\n\n EXAMPLES::\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: h = SymmetricFunctions(QQ).h()\n sage: m = SymmetricFunctions(QQ).m()\n sage: p4 = Partitions(4)\n sage: matrix([ [e(a).scalar(h(b)) for a in p4] for b in p4])\n [ 0 0 0 0 1]\n [ 0 0 0 1 4]\n [ 0 0 1 2 6]\n [ 0 1 2 5 12]\n [ 1 4 6 12 24]\n sage: matrix([ [h(a).scalar(e(b)) for a in p4] for b in p4])\n [ 0 0 0 0 1]\n [ 0 0 0 1 4]\n [ 0 0 1 2 6]\n [ 0 1 2 5 12]\n [ 1 4 6 12 24]\n sage: matrix([ [m(a).scalar(e(b)) for a in p4] for b in p4])\n [-1 2 1 -3 1]\n [ 0 1 0 -2 1]\n [ 0 0 1 -2 1]\n [ 0 0 0 -1 1]\n [ 0 0 0 0 1]\n sage: matrix([ [m(a).scalar(h(b)) for a in p4] for b in p4])\n [1 0 0 0 0]\n [0 1 0 0 0]\n [0 0 1 0 0]\n [0 0 0 1 0]\n [0 0 0 0 1]\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: m(p[3,2]).scalar(p[3,2], zee=lambda mu: 2**mu.length())\n 4\n sage: m(p[3,2]).scalar(p[2,2,1], lambda mu: 1)\n 0\n sage: m[3,2].scalar(h[3,2], zee=lambda mu: 2**mu.length())\n 2/3\n\n TESTS::\n\n sage: m(1).scalar(h(1))\n 1\n sage: m(0).scalar(h(1))\n 0\n sage: m(1).scalar(h(0))\n 0\n sage: m(0).scalar(h(0))\n 0\n\n Over the integers, too (as long as ``zee`` is not set)::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: m = Sym.m()\n sage: m([2]).scalar(m([2]))\n 2\n '
if (zee is None):
s = self.parent().realization_of().schur()
s_self = s(self)
s_x = s(x)
return s_self.scalar(s_x)
else:
p = self.parent().realization_of().power()
p_self = p(self)
p_x = p(x)
return sum((((zee(mu) * p_x.coefficient(mu)) * p_self.coefficient(mu)) for mu in p_self.support()))
|
def scalar(self, x, zee=None):
'\n Return standard scalar product between ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n\n - ``zee`` -- an optional function on partitions giving\n the value for the scalar product between `p_{\\mu}` and `p_{\\mu}`\n (default is to use the standard :meth:`~sage.combinat.sf.sfa.zee` function)\n\n This is the default implementation that converts both ``self`` and\n ``x`` into either Schur functions (if ``zee`` is not specified) or\n power-sum functions (if ``zee`` is specified) and performs the scalar\n product in that basis.\n\n EXAMPLES::\n\n sage: e = SymmetricFunctions(QQ).e()\n sage: h = SymmetricFunctions(QQ).h()\n sage: m = SymmetricFunctions(QQ).m()\n sage: p4 = Partitions(4)\n sage: matrix([ [e(a).scalar(h(b)) for a in p4] for b in p4])\n [ 0 0 0 0 1]\n [ 0 0 0 1 4]\n [ 0 0 1 2 6]\n [ 0 1 2 5 12]\n [ 1 4 6 12 24]\n sage: matrix([ [h(a).scalar(e(b)) for a in p4] for b in p4])\n [ 0 0 0 0 1]\n [ 0 0 0 1 4]\n [ 0 0 1 2 6]\n [ 0 1 2 5 12]\n [ 1 4 6 12 24]\n sage: matrix([ [m(a).scalar(e(b)) for a in p4] for b in p4])\n [-1 2 1 -3 1]\n [ 0 1 0 -2 1]\n [ 0 0 1 -2 1]\n [ 0 0 0 -1 1]\n [ 0 0 0 0 1]\n sage: matrix([ [m(a).scalar(h(b)) for a in p4] for b in p4])\n [1 0 0 0 0]\n [0 1 0 0 0]\n [0 0 1 0 0]\n [0 0 0 1 0]\n [0 0 0 0 1]\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: m(p[3,2]).scalar(p[3,2], zee=lambda mu: 2**mu.length())\n 4\n sage: m(p[3,2]).scalar(p[2,2,1], lambda mu: 1)\n 0\n sage: m[3,2].scalar(h[3,2], zee=lambda mu: 2**mu.length())\n 2/3\n\n TESTS::\n\n sage: m(1).scalar(h(1))\n 1\n sage: m(0).scalar(h(1))\n 0\n sage: m(1).scalar(h(0))\n 0\n sage: m(0).scalar(h(0))\n 0\n\n Over the integers, too (as long as ``zee`` is not set)::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: m = Sym.m()\n sage: m([2]).scalar(m([2]))\n 2\n '
if (zee is None):
s = self.parent().realization_of().schur()
s_self = s(self)
s_x = s(x)
return s_self.scalar(s_x)
else:
p = self.parent().realization_of().power()
p_self = p(self)
p_x = p(x)
return sum((((zee(mu) * p_x.coefficient(mu)) * p_self.coefficient(mu)) for mu in p_self.support()))<|docstring|>Return standard scalar product between ``self`` and ``x``.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the
same base ring as ``self``
- ``zee`` -- an optional function on partitions giving
the value for the scalar product between `p_{\mu}` and `p_{\mu}`
(default is to use the standard :meth:`~sage.combinat.sf.sfa.zee` function)
This is the default implementation that converts both ``self`` and
``x`` into either Schur functions (if ``zee`` is not specified) or
power-sum functions (if ``zee`` is specified) and performs the scalar
product in that basis.
EXAMPLES::
sage: e = SymmetricFunctions(QQ).e()
sage: h = SymmetricFunctions(QQ).h()
sage: m = SymmetricFunctions(QQ).m()
sage: p4 = Partitions(4)
sage: matrix([ [e(a).scalar(h(b)) for a in p4] for b in p4])
[ 0 0 0 0 1]
[ 0 0 0 1 4]
[ 0 0 1 2 6]
[ 0 1 2 5 12]
[ 1 4 6 12 24]
sage: matrix([ [h(a).scalar(e(b)) for a in p4] for b in p4])
[ 0 0 0 0 1]
[ 0 0 0 1 4]
[ 0 0 1 2 6]
[ 0 1 2 5 12]
[ 1 4 6 12 24]
sage: matrix([ [m(a).scalar(e(b)) for a in p4] for b in p4])
[-1 2 1 -3 1]
[ 0 1 0 -2 1]
[ 0 0 1 -2 1]
[ 0 0 0 -1 1]
[ 0 0 0 0 1]
sage: matrix([ [m(a).scalar(h(b)) for a in p4] for b in p4])
[1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
sage: p = SymmetricFunctions(QQ).p()
sage: m(p[3,2]).scalar(p[3,2], zee=lambda mu: 2**mu.length())
4
sage: m(p[3,2]).scalar(p[2,2,1], lambda mu: 1)
0
sage: m[3,2].scalar(h[3,2], zee=lambda mu: 2**mu.length())
2/3
TESTS::
sage: m(1).scalar(h(1))
1
sage: m(0).scalar(h(1))
0
sage: m(1).scalar(h(0))
0
sage: m(0).scalar(h(0))
0
Over the integers, too (as long as ``zee`` is not set)::
sage: Sym = SymmetricFunctions(ZZ)
sage: m = Sym.m()
sage: m([2]).scalar(m([2]))
2<|endoftext|>
|
7dc5781ba34711d04a897ce99acb774bd7bd2f63363b14d8019083ac98034acc
|
def scalar_qt(self, x, q=None, t=None):
"\n Returns the `q,t`-deformed standard Hall-Littlewood scalar product of\n ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n - ``q``, ``t`` -- parameters (default: ``None`` in which case ``q``\n and ``t`` are used)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1])\n sage: sp = a.scalar_qt(a); factor(sp)\n (t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)\n sage: sp.parent()\n Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field\n sage: a.scalar_qt(a,q=0)\n (-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)\n sage: a.scalar_qt(a,t=0)\n -q^3 + 2*q^2 - 2*q + 1\n sage: a.scalar_qt(a,5,7) # q=5 and t=7\n 490/1539\n sage: (x,y) = var('x,y')\n sage: a.scalar_qt(a,q=x,t=y)\n 1/3*(x^3 - 1)/(y^3 - 1) + 2/3*(x - 1)^3/(y - 1)^3\n sage: Rn = QQ['q','t','y','z'].fraction_field()\n sage: (q,t,y,z) = Rn.gens()\n sage: Mac = SymmetricFunctions(Rn).macdonald(q=y,t=z)\n sage: a = Mac._sym.schur()([2,1])\n sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a),q,t))\n (t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)\n sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a)))\n (z - 1)^-3 * (y - 1) * (z^2 + z + 1)^-1 * (y^2*z^2 - y*z^2 + y^2 - 2*y*z + z^2 - y + 1)\n "
parent = self.parent()
p = parent.realization_of().power()
if (t is None):
if hasattr(parent, 't'):
t = self.parent().t
elif (q is None):
t = QQ[('q', 't')].gens()[1]
else:
t = QQ['t'].gen()
if (q is None):
if hasattr(parent, 'q'):
q = parent.q
else:
q = QQ[('q', 't')].gens()[0]
f = (lambda part1, part2: part1.centralizer_size(t=t, q=q))
return p._apply_multi_module_morphism(p(self), p(x), f, orthogonal=True)
|
Returns the `q,t`-deformed standard Hall-Littlewood scalar product of
``self`` and ``x``.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the same
base ring as ``self``
- ``q``, ``t`` -- parameters (default: ``None`` in which case ``q``
and ``t`` are used)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1])
sage: sp = a.scalar_qt(a); factor(sp)
(t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)
sage: sp.parent()
Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field
sage: a.scalar_qt(a,q=0)
(-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)
sage: a.scalar_qt(a,t=0)
-q^3 + 2*q^2 - 2*q + 1
sage: a.scalar_qt(a,5,7) # q=5 and t=7
490/1539
sage: (x,y) = var('x,y')
sage: a.scalar_qt(a,q=x,t=y)
1/3*(x^3 - 1)/(y^3 - 1) + 2/3*(x - 1)^3/(y - 1)^3
sage: Rn = QQ['q','t','y','z'].fraction_field()
sage: (q,t,y,z) = Rn.gens()
sage: Mac = SymmetricFunctions(Rn).macdonald(q=y,t=z)
sage: a = Mac._sym.schur()([2,1])
sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a),q,t))
(t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)
sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a)))
(z - 1)^-3 * (y - 1) * (z^2 + z + 1)^-1 * (y^2*z^2 - y*z^2 + y^2 - 2*y*z + z^2 - y + 1)
|
src/sage/combinat/sf/sfa.py
|
scalar_qt
|
bopopescu/sagesmc
| 5 |
python
|
def scalar_qt(self, x, q=None, t=None):
"\n Returns the `q,t`-deformed standard Hall-Littlewood scalar product of\n ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n - ``q``, ``t`` -- parameters (default: ``None`` in which case ``q``\n and ``t`` are used)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1])\n sage: sp = a.scalar_qt(a); factor(sp)\n (t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)\n sage: sp.parent()\n Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field\n sage: a.scalar_qt(a,q=0)\n (-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)\n sage: a.scalar_qt(a,t=0)\n -q^3 + 2*q^2 - 2*q + 1\n sage: a.scalar_qt(a,5,7) # q=5 and t=7\n 490/1539\n sage: (x,y) = var('x,y')\n sage: a.scalar_qt(a,q=x,t=y)\n 1/3*(x^3 - 1)/(y^3 - 1) + 2/3*(x - 1)^3/(y - 1)^3\n sage: Rn = QQ['q','t','y','z'].fraction_field()\n sage: (q,t,y,z) = Rn.gens()\n sage: Mac = SymmetricFunctions(Rn).macdonald(q=y,t=z)\n sage: a = Mac._sym.schur()([2,1])\n sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a),q,t))\n (t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)\n sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a)))\n (z - 1)^-3 * (y - 1) * (z^2 + z + 1)^-1 * (y^2*z^2 - y*z^2 + y^2 - 2*y*z + z^2 - y + 1)\n "
parent = self.parent()
p = parent.realization_of().power()
if (t is None):
if hasattr(parent, 't'):
t = self.parent().t
elif (q is None):
t = QQ[('q', 't')].gens()[1]
else:
t = QQ['t'].gen()
if (q is None):
if hasattr(parent, 'q'):
q = parent.q
else:
q = QQ[('q', 't')].gens()[0]
f = (lambda part1, part2: part1.centralizer_size(t=t, q=q))
return p._apply_multi_module_morphism(p(self), p(x), f, orthogonal=True)
|
def scalar_qt(self, x, q=None, t=None):
"\n Returns the `q,t`-deformed standard Hall-Littlewood scalar product of\n ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n - ``q``, ``t`` -- parameters (default: ``None`` in which case ``q``\n and ``t`` are used)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1])\n sage: sp = a.scalar_qt(a); factor(sp)\n (t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)\n sage: sp.parent()\n Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field\n sage: a.scalar_qt(a,q=0)\n (-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)\n sage: a.scalar_qt(a,t=0)\n -q^3 + 2*q^2 - 2*q + 1\n sage: a.scalar_qt(a,5,7) # q=5 and t=7\n 490/1539\n sage: (x,y) = var('x,y')\n sage: a.scalar_qt(a,q=x,t=y)\n 1/3*(x^3 - 1)/(y^3 - 1) + 2/3*(x - 1)^3/(y - 1)^3\n sage: Rn = QQ['q','t','y','z'].fraction_field()\n sage: (q,t,y,z) = Rn.gens()\n sage: Mac = SymmetricFunctions(Rn).macdonald(q=y,t=z)\n sage: a = Mac._sym.schur()([2,1])\n sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a),q,t))\n (t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)\n sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a)))\n (z - 1)^-3 * (y - 1) * (z^2 + z + 1)^-1 * (y^2*z^2 - y*z^2 + y^2 - 2*y*z + z^2 - y + 1)\n "
parent = self.parent()
p = parent.realization_of().power()
if (t is None):
if hasattr(parent, 't'):
t = self.parent().t
elif (q is None):
t = QQ[('q', 't')].gens()[1]
else:
t = QQ['t'].gen()
if (q is None):
if hasattr(parent, 'q'):
q = parent.q
else:
q = QQ[('q', 't')].gens()[0]
f = (lambda part1, part2: part1.centralizer_size(t=t, q=q))
return p._apply_multi_module_morphism(p(self), p(x), f, orthogonal=True)<|docstring|>Returns the `q,t`-deformed standard Hall-Littlewood scalar product of
``self`` and ``x``.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the same
base ring as ``self``
- ``q``, ``t`` -- parameters (default: ``None`` in which case ``q``
and ``t`` are used)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1])
sage: sp = a.scalar_qt(a); factor(sp)
(t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)
sage: sp.parent()
Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field
sage: a.scalar_qt(a,q=0)
(-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)
sage: a.scalar_qt(a,t=0)
-q^3 + 2*q^2 - 2*q + 1
sage: a.scalar_qt(a,5,7) # q=5 and t=7
490/1539
sage: (x,y) = var('x,y')
sage: a.scalar_qt(a,q=x,t=y)
1/3*(x^3 - 1)/(y^3 - 1) + 2/3*(x - 1)^3/(y - 1)^3
sage: Rn = QQ['q','t','y','z'].fraction_field()
sage: (q,t,y,z) = Rn.gens()
sage: Mac = SymmetricFunctions(Rn).macdonald(q=y,t=z)
sage: a = Mac._sym.schur()([2,1])
sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a),q,t))
(t - 1)^-3 * (q - 1) * (t^2 + t + 1)^-1 * (q^2*t^2 - q*t^2 + q^2 - 2*q*t + t^2 - q + 1)
sage: factor(Mac.P()(a).scalar_qt(Mac.Q()(a)))
(z - 1)^-3 * (y - 1) * (z^2 + z + 1)^-1 * (y^2*z^2 - y*z^2 + y^2 - 2*y*z + z^2 - y + 1)<|endoftext|>
|
185a92258e3e1c6e1b95b36e789d082e071cf8289657630636671986755a50f0
|
def scalar_t(self, x, t=None):
'\n Return the `t`-deformed standard Hall-Littlewood scalar product of\n ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n - ``t`` -- parameter (default: ``None``, in which case ``t`` is used)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1])\n sage: sp = a.scalar_t(a); sp\n (-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)\n sage: sp.parent()\n Fraction Field of Univariate Polynomial Ring in t over Rational Field\n '
return self.scalar_qt(x, q=self.base_ring().zero(), t=t)
|
Return the `t`-deformed standard Hall-Littlewood scalar product of
``self`` and ``x``.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the same
base ring as ``self``
- ``t`` -- parameter (default: ``None``, in which case ``t`` is used)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1])
sage: sp = a.scalar_t(a); sp
(-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)
sage: sp.parent()
Fraction Field of Univariate Polynomial Ring in t over Rational Field
|
src/sage/combinat/sf/sfa.py
|
scalar_t
|
bopopescu/sagesmc
| 5 |
python
|
def scalar_t(self, x, t=None):
'\n Return the `t`-deformed standard Hall-Littlewood scalar product of\n ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n - ``t`` -- parameter (default: ``None``, in which case ``t`` is used)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1])\n sage: sp = a.scalar_t(a); sp\n (-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)\n sage: sp.parent()\n Fraction Field of Univariate Polynomial Ring in t over Rational Field\n '
return self.scalar_qt(x, q=self.base_ring().zero(), t=t)
|
def scalar_t(self, x, t=None):
'\n Return the `t`-deformed standard Hall-Littlewood scalar product of\n ``self`` and ``x``.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n - ``t`` -- parameter (default: ``None``, in which case ``t`` is used)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1])\n sage: sp = a.scalar_t(a); sp\n (-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)\n sage: sp.parent()\n Fraction Field of Univariate Polynomial Ring in t over Rational Field\n '
return self.scalar_qt(x, q=self.base_ring().zero(), t=t)<|docstring|>Return the `t`-deformed standard Hall-Littlewood scalar product of
``self`` and ``x``.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the same
base ring as ``self``
- ``t`` -- parameter (default: ``None``, in which case ``t`` is used)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1])
sage: sp = a.scalar_t(a); sp
(-t^2 - 1)/(t^5 - 2*t^4 + t^3 - t^2 + 2*t - 1)
sage: sp.parent()
Fraction Field of Univariate Polynomial Ring in t over Rational Field<|endoftext|>
|
e390b6784cb5771cd1647f80f32084a431ca8ead0ecd6ba5fd628c462cb804cb
|
def scalar_jack(self, x, t=None):
"\n Return the Jack-scalar product beween ``self`` and ``x``.\n\n This scalar product is defined so that the power sum elements\n `p_{\\mu}` are orthogonal and `\\langle p_{\\mu}, p_{\\mu} \\rangle =\n z_{\\mu} t^{\\ell(\\mu)}`, where `\\ell(\\mu)` denotes the length of\n `\\mu`.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n - ``t`` -- an optional parameter (default: ``None`` in which\n case ``t`` is used)\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ['t']).power()\n sage: matrix([[p(mu).scalar_jack(p(nu)) for nu in Partitions(4)] for mu in Partitions(4)])\n [ 4*t 0 0 0 0]\n [ 0 3*t^2 0 0 0]\n [ 0 0 8*t^2 0 0]\n [ 0 0 0 4*t^3 0]\n [ 0 0 0 0 24*t^4]\n sage: matrix([[p(mu).scalar_jack(p(nu),2) for nu in Partitions(4)] for mu in Partitions(4)])\n [ 8 0 0 0 0]\n [ 0 12 0 0 0]\n [ 0 0 32 0 0]\n [ 0 0 0 32 0]\n [ 0 0 0 0 384]\n sage: JQ = SymmetricFunctions(QQ['t'].fraction_field()).jack().Q()\n sage: matrix([[JQ(mu).scalar_jack(JQ(nu)) for nu in Partitions(3)] for mu in Partitions(3)])\n [(2*t^2 + 3*t + 1)/(6*t^3) 0 0]\n [ 0 (t + 2)/(2*t^3 + t^2) 0]\n [ 0 0 6/(t^3 + 3*t^2 + 2*t)]\n "
parent = self.parent()
if (t is None):
if hasattr(parent, 't'):
t = self.parent().t
else:
t = QQ['t'].gen()
zee = (lambda part: (part.centralizer_size() * (t ** part.length())))
return self.scalar(x, zee)
|
Return the Jack-scalar product beween ``self`` and ``x``.
This scalar product is defined so that the power sum elements
`p_{\mu}` are orthogonal and `\langle p_{\mu}, p_{\mu} \rangle =
z_{\mu} t^{\ell(\mu)}`, where `\ell(\mu)` denotes the length of
`\mu`.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the
same base ring as ``self``
- ``t`` -- an optional parameter (default: ``None`` in which
case ``t`` is used)
EXAMPLES::
sage: p = SymmetricFunctions(QQ['t']).power()
sage: matrix([[p(mu).scalar_jack(p(nu)) for nu in Partitions(4)] for mu in Partitions(4)])
[ 4*t 0 0 0 0]
[ 0 3*t^2 0 0 0]
[ 0 0 8*t^2 0 0]
[ 0 0 0 4*t^3 0]
[ 0 0 0 0 24*t^4]
sage: matrix([[p(mu).scalar_jack(p(nu),2) for nu in Partitions(4)] for mu in Partitions(4)])
[ 8 0 0 0 0]
[ 0 12 0 0 0]
[ 0 0 32 0 0]
[ 0 0 0 32 0]
[ 0 0 0 0 384]
sage: JQ = SymmetricFunctions(QQ['t'].fraction_field()).jack().Q()
sage: matrix([[JQ(mu).scalar_jack(JQ(nu)) for nu in Partitions(3)] for mu in Partitions(3)])
[(2*t^2 + 3*t + 1)/(6*t^3) 0 0]
[ 0 (t + 2)/(2*t^3 + t^2) 0]
[ 0 0 6/(t^3 + 3*t^2 + 2*t)]
|
src/sage/combinat/sf/sfa.py
|
scalar_jack
|
bopopescu/sagesmc
| 5 |
python
|
def scalar_jack(self, x, t=None):
"\n Return the Jack-scalar product beween ``self`` and ``x``.\n\n This scalar product is defined so that the power sum elements\n `p_{\\mu}` are orthogonal and `\\langle p_{\\mu}, p_{\\mu} \\rangle =\n z_{\\mu} t^{\\ell(\\mu)}`, where `\\ell(\\mu)` denotes the length of\n `\\mu`.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n - ``t`` -- an optional parameter (default: ``None`` in which\n case ``t`` is used)\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ['t']).power()\n sage: matrix([[p(mu).scalar_jack(p(nu)) for nu in Partitions(4)] for mu in Partitions(4)])\n [ 4*t 0 0 0 0]\n [ 0 3*t^2 0 0 0]\n [ 0 0 8*t^2 0 0]\n [ 0 0 0 4*t^3 0]\n [ 0 0 0 0 24*t^4]\n sage: matrix([[p(mu).scalar_jack(p(nu),2) for nu in Partitions(4)] for mu in Partitions(4)])\n [ 8 0 0 0 0]\n [ 0 12 0 0 0]\n [ 0 0 32 0 0]\n [ 0 0 0 32 0]\n [ 0 0 0 0 384]\n sage: JQ = SymmetricFunctions(QQ['t'].fraction_field()).jack().Q()\n sage: matrix([[JQ(mu).scalar_jack(JQ(nu)) for nu in Partitions(3)] for mu in Partitions(3)])\n [(2*t^2 + 3*t + 1)/(6*t^3) 0 0]\n [ 0 (t + 2)/(2*t^3 + t^2) 0]\n [ 0 0 6/(t^3 + 3*t^2 + 2*t)]\n "
parent = self.parent()
if (t is None):
if hasattr(parent, 't'):
t = self.parent().t
else:
t = QQ['t'].gen()
zee = (lambda part: (part.centralizer_size() * (t ** part.length())))
return self.scalar(x, zee)
|
def scalar_jack(self, x, t=None):
"\n Return the Jack-scalar product beween ``self`` and ``x``.\n\n This scalar product is defined so that the power sum elements\n `p_{\\mu}` are orthogonal and `\\langle p_{\\mu}, p_{\\mu} \\rangle =\n z_{\\mu} t^{\\ell(\\mu)}`, where `\\ell(\\mu)` denotes the length of\n `\\mu`.\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the\n same base ring as ``self``\n - ``t`` -- an optional parameter (default: ``None`` in which\n case ``t`` is used)\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ['t']).power()\n sage: matrix([[p(mu).scalar_jack(p(nu)) for nu in Partitions(4)] for mu in Partitions(4)])\n [ 4*t 0 0 0 0]\n [ 0 3*t^2 0 0 0]\n [ 0 0 8*t^2 0 0]\n [ 0 0 0 4*t^3 0]\n [ 0 0 0 0 24*t^4]\n sage: matrix([[p(mu).scalar_jack(p(nu),2) for nu in Partitions(4)] for mu in Partitions(4)])\n [ 8 0 0 0 0]\n [ 0 12 0 0 0]\n [ 0 0 32 0 0]\n [ 0 0 0 32 0]\n [ 0 0 0 0 384]\n sage: JQ = SymmetricFunctions(QQ['t'].fraction_field()).jack().Q()\n sage: matrix([[JQ(mu).scalar_jack(JQ(nu)) for nu in Partitions(3)] for mu in Partitions(3)])\n [(2*t^2 + 3*t + 1)/(6*t^3) 0 0]\n [ 0 (t + 2)/(2*t^3 + t^2) 0]\n [ 0 0 6/(t^3 + 3*t^2 + 2*t)]\n "
parent = self.parent()
if (t is None):
if hasattr(parent, 't'):
t = self.parent().t
else:
t = QQ['t'].gen()
zee = (lambda part: (part.centralizer_size() * (t ** part.length())))
return self.scalar(x, zee)<|docstring|>Return the Jack-scalar product beween ``self`` and ``x``.
This scalar product is defined so that the power sum elements
`p_{\mu}` are orthogonal and `\langle p_{\mu}, p_{\mu} \rangle =
z_{\mu} t^{\ell(\mu)}`, where `\ell(\mu)` denotes the length of
`\mu`.
INPUT:
- ``x`` -- element of the ring of symmetric functions over the
same base ring as ``self``
- ``t`` -- an optional parameter (default: ``None`` in which
case ``t`` is used)
EXAMPLES::
sage: p = SymmetricFunctions(QQ['t']).power()
sage: matrix([[p(mu).scalar_jack(p(nu)) for nu in Partitions(4)] for mu in Partitions(4)])
[ 4*t 0 0 0 0]
[ 0 3*t^2 0 0 0]
[ 0 0 8*t^2 0 0]
[ 0 0 0 4*t^3 0]
[ 0 0 0 0 24*t^4]
sage: matrix([[p(mu).scalar_jack(p(nu),2) for nu in Partitions(4)] for mu in Partitions(4)])
[ 8 0 0 0 0]
[ 0 12 0 0 0]
[ 0 0 32 0 0]
[ 0 0 0 32 0]
[ 0 0 0 0 384]
sage: JQ = SymmetricFunctions(QQ['t'].fraction_field()).jack().Q()
sage: matrix([[JQ(mu).scalar_jack(JQ(nu)) for nu in Partitions(3)] for mu in Partitions(3)])
[(2*t^2 + 3*t + 1)/(6*t^3) 0 0]
[ 0 (t + 2)/(2*t^3 + t^2) 0]
[ 0 0 6/(t^3 + 3*t^2 + 2*t)]<|endoftext|>
|
655b20f3ea0f2b041723e83ec744a9eea8d5a85619937fd295ec496ccc670b38
|
def derivative_with_respect_to_p1(self, n=1):
"\n Return the symmetric function obtained by taking the derivative of\n ``self`` with respect to the power-sum symmetric function `p_1`\n when the expansion of ``self`` in the power-sum basis is considered\n as a polynomial in `p_k`'s (with `k \\geq 1`).\n\n This is the same as skewing ``self`` by the first power-sum symmetric\n function `p_1`.\n\n INPUT:\n\n - ``n`` -- (default: 1) nonnegative integer which determines\n which power of the derivative is taken\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: a = p([1,1,1])\n sage: a.derivative_with_respect_to_p1()\n 3*p[1, 1]\n sage: a.derivative_with_respect_to_p1(1)\n 3*p[1, 1]\n sage: a.derivative_with_respect_to_p1(2)\n 6*p[1]\n sage: a.derivative_with_respect_to_p1(3)\n 6*p[]\n\n ::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([3]).derivative_with_respect_to_p1()\n s[2]\n sage: s([2,1]).derivative_with_respect_to_p1()\n s[1, 1] + s[2]\n sage: s([1,1,1]).derivative_with_respect_to_p1()\n s[1, 1]\n sage: s(0).derivative_with_respect_to_p1()\n 0\n sage: s(1).derivative_with_respect_to_p1()\n 0\n sage: s([1]).derivative_with_respect_to_p1()\n s[]\n\n Let us check that taking the derivative with respect to ``p[1]``\n is equivalent to skewing by ``p[1]``::\n\n sage: p1 = s([1])\n sage: all( s(lam).derivative_with_respect_to_p1()\n ....: == s(lam).skew_by(p1) for lam in Partitions(4) )\n True\n "
p = self.parent().realization_of().power()
res = p(self)
for i in range(n):
res = res._derivative_with_respect_to_p1()
return self.parent()(res)
|
Return the symmetric function obtained by taking the derivative of
``self`` with respect to the power-sum symmetric function `p_1`
when the expansion of ``self`` in the power-sum basis is considered
as a polynomial in `p_k`'s (with `k \geq 1`).
This is the same as skewing ``self`` by the first power-sum symmetric
function `p_1`.
INPUT:
- ``n`` -- (default: 1) nonnegative integer which determines
which power of the derivative is taken
EXAMPLES::
sage: p = SymmetricFunctions(QQ).p()
sage: a = p([1,1,1])
sage: a.derivative_with_respect_to_p1()
3*p[1, 1]
sage: a.derivative_with_respect_to_p1(1)
3*p[1, 1]
sage: a.derivative_with_respect_to_p1(2)
6*p[1]
sage: a.derivative_with_respect_to_p1(3)
6*p[]
::
sage: s = SymmetricFunctions(QQ).s()
sage: s([3]).derivative_with_respect_to_p1()
s[2]
sage: s([2,1]).derivative_with_respect_to_p1()
s[1, 1] + s[2]
sage: s([1,1,1]).derivative_with_respect_to_p1()
s[1, 1]
sage: s(0).derivative_with_respect_to_p1()
0
sage: s(1).derivative_with_respect_to_p1()
0
sage: s([1]).derivative_with_respect_to_p1()
s[]
Let us check that taking the derivative with respect to ``p[1]``
is equivalent to skewing by ``p[1]``::
sage: p1 = s([1])
sage: all( s(lam).derivative_with_respect_to_p1()
....: == s(lam).skew_by(p1) for lam in Partitions(4) )
True
|
src/sage/combinat/sf/sfa.py
|
derivative_with_respect_to_p1
|
bopopescu/sagesmc
| 5 |
python
|
def derivative_with_respect_to_p1(self, n=1):
"\n Return the symmetric function obtained by taking the derivative of\n ``self`` with respect to the power-sum symmetric function `p_1`\n when the expansion of ``self`` in the power-sum basis is considered\n as a polynomial in `p_k`'s (with `k \\geq 1`).\n\n This is the same as skewing ``self`` by the first power-sum symmetric\n function `p_1`.\n\n INPUT:\n\n - ``n`` -- (default: 1) nonnegative integer which determines\n which power of the derivative is taken\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: a = p([1,1,1])\n sage: a.derivative_with_respect_to_p1()\n 3*p[1, 1]\n sage: a.derivative_with_respect_to_p1(1)\n 3*p[1, 1]\n sage: a.derivative_with_respect_to_p1(2)\n 6*p[1]\n sage: a.derivative_with_respect_to_p1(3)\n 6*p[]\n\n ::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([3]).derivative_with_respect_to_p1()\n s[2]\n sage: s([2,1]).derivative_with_respect_to_p1()\n s[1, 1] + s[2]\n sage: s([1,1,1]).derivative_with_respect_to_p1()\n s[1, 1]\n sage: s(0).derivative_with_respect_to_p1()\n 0\n sage: s(1).derivative_with_respect_to_p1()\n 0\n sage: s([1]).derivative_with_respect_to_p1()\n s[]\n\n Let us check that taking the derivative with respect to ``p[1]``\n is equivalent to skewing by ``p[1]``::\n\n sage: p1 = s([1])\n sage: all( s(lam).derivative_with_respect_to_p1()\n ....: == s(lam).skew_by(p1) for lam in Partitions(4) )\n True\n "
p = self.parent().realization_of().power()
res = p(self)
for i in range(n):
res = res._derivative_with_respect_to_p1()
return self.parent()(res)
|
def derivative_with_respect_to_p1(self, n=1):
"\n Return the symmetric function obtained by taking the derivative of\n ``self`` with respect to the power-sum symmetric function `p_1`\n when the expansion of ``self`` in the power-sum basis is considered\n as a polynomial in `p_k`'s (with `k \\geq 1`).\n\n This is the same as skewing ``self`` by the first power-sum symmetric\n function `p_1`.\n\n INPUT:\n\n - ``n`` -- (default: 1) nonnegative integer which determines\n which power of the derivative is taken\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: a = p([1,1,1])\n sage: a.derivative_with_respect_to_p1()\n 3*p[1, 1]\n sage: a.derivative_with_respect_to_p1(1)\n 3*p[1, 1]\n sage: a.derivative_with_respect_to_p1(2)\n 6*p[1]\n sage: a.derivative_with_respect_to_p1(3)\n 6*p[]\n\n ::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([3]).derivative_with_respect_to_p1()\n s[2]\n sage: s([2,1]).derivative_with_respect_to_p1()\n s[1, 1] + s[2]\n sage: s([1,1,1]).derivative_with_respect_to_p1()\n s[1, 1]\n sage: s(0).derivative_with_respect_to_p1()\n 0\n sage: s(1).derivative_with_respect_to_p1()\n 0\n sage: s([1]).derivative_with_respect_to_p1()\n s[]\n\n Let us check that taking the derivative with respect to ``p[1]``\n is equivalent to skewing by ``p[1]``::\n\n sage: p1 = s([1])\n sage: all( s(lam).derivative_with_respect_to_p1()\n ....: == s(lam).skew_by(p1) for lam in Partitions(4) )\n True\n "
p = self.parent().realization_of().power()
res = p(self)
for i in range(n):
res = res._derivative_with_respect_to_p1()
return self.parent()(res)<|docstring|>Return the symmetric function obtained by taking the derivative of
``self`` with respect to the power-sum symmetric function `p_1`
when the expansion of ``self`` in the power-sum basis is considered
as a polynomial in `p_k`'s (with `k \geq 1`).
This is the same as skewing ``self`` by the first power-sum symmetric
function `p_1`.
INPUT:
- ``n`` -- (default: 1) nonnegative integer which determines
which power of the derivative is taken
EXAMPLES::
sage: p = SymmetricFunctions(QQ).p()
sage: a = p([1,1,1])
sage: a.derivative_with_respect_to_p1()
3*p[1, 1]
sage: a.derivative_with_respect_to_p1(1)
3*p[1, 1]
sage: a.derivative_with_respect_to_p1(2)
6*p[1]
sage: a.derivative_with_respect_to_p1(3)
6*p[]
::
sage: s = SymmetricFunctions(QQ).s()
sage: s([3]).derivative_with_respect_to_p1()
s[2]
sage: s([2,1]).derivative_with_respect_to_p1()
s[1, 1] + s[2]
sage: s([1,1,1]).derivative_with_respect_to_p1()
s[1, 1]
sage: s(0).derivative_with_respect_to_p1()
0
sage: s(1).derivative_with_respect_to_p1()
0
sage: s([1]).derivative_with_respect_to_p1()
s[]
Let us check that taking the derivative with respect to ``p[1]``
is equivalent to skewing by ``p[1]``::
sage: p1 = s([1])
sage: all( s(lam).derivative_with_respect_to_p1()
....: == s(lam).skew_by(p1) for lam in Partitions(4) )
True<|endoftext|>
|
8be38db63656c992d2f159bfae00a5624f3a328fdba2db41badfed0de6f353cf
|
def frobenius(self, n):
'\n Return the image of the symmetric function ``self`` under the\n `n`-th Frobenius operator.\n\n The `n`-th Frobenius operator `\\mathbf{f}_n` is defined to be the\n map from the ring of symmetric functions to itself that sends\n every symmetric function `P(x_1, x_2, x_3, \\ldots)` to\n `P(x_1^n, x_2^n, x_3^n, \\ldots)`. This operator `\\mathbf{f}_n`\n is a Hopf algebra endomorphism, and satisfies\n\n .. MATH::\n\n \\mathbf{f}_n m_{(\\lambda_1, \\lambda_2, \\lambda_3, \\ldots)} =\n m_{(n\\lambda_1, n\\lambda_2, n\\lambda_3, \\ldots)}\n\n for every partition `(\\lambda_1, \\lambda_2, \\lambda_3, \\ldots)`\n (where `m` means the monomial basis). Moreover,\n `\\mathbf{f}_n (p_r) = p_{nr}` for every positive integer `r` (where\n `p_k` denotes the `k`-th powersum symmetric function).\n\n The `n`-th Frobenius operator is also called the `n`-th\n Frobenius endomorphism. It is not related to the Frobenius map\n which connects the ring of symmetric functions with the\n representation theory of the symmetric group.\n\n The `n`-th Frobenius operator is also the `n`-th Adams operator\n of the `\\Lambda`-ring of symmetric functions over the integers.\n\n The `n`-th Frobenius operator can also be described via plethysm:\n Every symmetric function `P` satisfies\n `\\mathbf{f}_n(P) = p_n \\circ P = P \\circ p_n`,\n where `p_n` is the `n`-th powersum symmetric function, and `\\circ`\n denotes (outer) plethysm.\n\n :meth:`adams_operation` serves as alias for :meth:`frobenius`, since the\n Frobenius operators are the Adams operations of the `\\Lambda`-ring\n of symmetric functions.\n\n INPUT:\n\n - ``n`` -- a positive integer\n\n OUTPUT:\n\n The result of applying the `n`-th Frobenius operator (on the ring of\n symmetric functions) to ``self``.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: h = Sym.h()\n sage: s = Sym.s()\n sage: m = Sym.m()\n sage: s[3].frobenius(2)\n -s[3, 3] + s[4, 2] - s[5, 1] + s[6]\n sage: m[4,2,1].frobenius(3)\n m[12, 6, 3]\n sage: p[4,2,1].frobenius(3)\n p[12, 6, 3]\n sage: h[4].frobenius(2)\n h[4, 4] - 2*h[5, 3] + 2*h[6, 2] - 2*h[7, 1] + 2*h[8]\n\n The Frobenius endomorphisms are multiplicative::\n\n sage: all( all( s(lam).frobenius(3) * s(mu).frobenius(3)\n ....: == (s(lam) * s(mu)).frobenius(3)\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(3) )\n True\n sage: all( all( m(lam).frobenius(2) * m(mu).frobenius(2)\n ....: == (m(lam) * m(mu)).frobenius(2)\n ....: for mu in Partitions(4) )\n ....: for lam in Partitions(4) )\n True\n sage: all( all( p(lam).frobenius(2) * p(mu).frobenius(2)\n ....: == (p(lam) * p(mu)).frobenius(2)\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(4) )\n True\n\n Being Hopf algebra endomorphisms, the Frobenius operators\n commute with the antipode::\n\n sage: all( p(lam).frobenius(4).antipode()\n ....: == p(lam).antipode().frobenius(4)\n ....: for lam in Partitions(3) )\n True\n\n Testing the `\\mathbf{f}_n(P) = p_n \\circ P = P \\circ p_n`\n equality (over `\\QQ`, since plethysm is currently not\n defined over `\\ZZ` in Sage)::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: s = Sym.s()\n sage: p = Sym.p()\n sage: all( s(lam).frobenius(3) == s(lam).plethysm(p[3])\n ....: == s(p[3].plethysm(s(lam)))\n ....: for lam in Partitions(4) )\n True\n\n By Exercise 7.61 in Stanley\'s EC2 [STA]_ (see the errata on his\n website), `\\mathbf{f}_n(h_m)` is a linear combination of\n Schur polynomials (of straight shapes) using coefficients `0`,\n `1` and `-1` only; moreover, all partitions whose Schur\n polynomials occur with coefficient `\\neq 0` in this\n combination have empty `n`-cores. Let us check this on\n examples::\n\n sage: all( all( all( (coeff == -1 or coeff == 1)\n ....: and lam.core(n) == Partition([])\n ....: for lam, coeff in s([m]).frobenius(n).monomial_coefficients().items() )\n ....: for n in range(2, 4) )\n ....: for m in range(4) )\n True\n\n .. SEEALSO::\n\n :meth:`plethysm`\n\n .. TODO::\n\n This method is fast on the monomial and the powersum\n bases, while all other bases get converted to the\n monomial basis. For most bases, this is probably the\n quickest way to do, but at least the Schur basis should\n have a better option. (Quoting from Stanley\'s EC2 [STA]_:\n "D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236,\n or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp.\n Math. 34 (1984), 109-153".)\n '
parent = self.parent()
m = parent.realization_of().monomial()
from sage.combinat.partition import Partition
dct = {Partition(map((lambda i: (n * i)), lam)): coeff for (lam, coeff) in m(self).monomial_coefficients().items()}
result_in_m_basis = m._from_dict(dct)
return parent(result_in_m_basis)
|
Return the image of the symmetric function ``self`` under the
`n`-th Frobenius operator.
The `n`-th Frobenius operator `\mathbf{f}_n` is defined to be the
map from the ring of symmetric functions to itself that sends
every symmetric function `P(x_1, x_2, x_3, \ldots)` to
`P(x_1^n, x_2^n, x_3^n, \ldots)`. This operator `\mathbf{f}_n`
is a Hopf algebra endomorphism, and satisfies
.. MATH::
\mathbf{f}_n m_{(\lambda_1, \lambda_2, \lambda_3, \ldots)} =
m_{(n\lambda_1, n\lambda_2, n\lambda_3, \ldots)}
for every partition `(\lambda_1, \lambda_2, \lambda_3, \ldots)`
(where `m` means the monomial basis). Moreover,
`\mathbf{f}_n (p_r) = p_{nr}` for every positive integer `r` (where
`p_k` denotes the `k`-th powersum symmetric function).
The `n`-th Frobenius operator is also called the `n`-th
Frobenius endomorphism. It is not related to the Frobenius map
which connects the ring of symmetric functions with the
representation theory of the symmetric group.
The `n`-th Frobenius operator is also the `n`-th Adams operator
of the `\Lambda`-ring of symmetric functions over the integers.
The `n`-th Frobenius operator can also be described via plethysm:
Every symmetric function `P` satisfies
`\mathbf{f}_n(P) = p_n \circ P = P \circ p_n`,
where `p_n` is the `n`-th powersum symmetric function, and `\circ`
denotes (outer) plethysm.
:meth:`adams_operation` serves as alias for :meth:`frobenius`, since the
Frobenius operators are the Adams operations of the `\Lambda`-ring
of symmetric functions.
INPUT:
- ``n`` -- a positive integer
OUTPUT:
The result of applying the `n`-th Frobenius operator (on the ring of
symmetric functions) to ``self``.
EXAMPLES::
sage: Sym = SymmetricFunctions(ZZ)
sage: p = Sym.p()
sage: h = Sym.h()
sage: s = Sym.s()
sage: m = Sym.m()
sage: s[3].frobenius(2)
-s[3, 3] + s[4, 2] - s[5, 1] + s[6]
sage: m[4,2,1].frobenius(3)
m[12, 6, 3]
sage: p[4,2,1].frobenius(3)
p[12, 6, 3]
sage: h[4].frobenius(2)
h[4, 4] - 2*h[5, 3] + 2*h[6, 2] - 2*h[7, 1] + 2*h[8]
The Frobenius endomorphisms are multiplicative::
sage: all( all( s(lam).frobenius(3) * s(mu).frobenius(3)
....: == (s(lam) * s(mu)).frobenius(3)
....: for mu in Partitions(3) )
....: for lam in Partitions(3) )
True
sage: all( all( m(lam).frobenius(2) * m(mu).frobenius(2)
....: == (m(lam) * m(mu)).frobenius(2)
....: for mu in Partitions(4) )
....: for lam in Partitions(4) )
True
sage: all( all( p(lam).frobenius(2) * p(mu).frobenius(2)
....: == (p(lam) * p(mu)).frobenius(2)
....: for mu in Partitions(3) )
....: for lam in Partitions(4) )
True
Being Hopf algebra endomorphisms, the Frobenius operators
commute with the antipode::
sage: all( p(lam).frobenius(4).antipode()
....: == p(lam).antipode().frobenius(4)
....: for lam in Partitions(3) )
True
Testing the `\mathbf{f}_n(P) = p_n \circ P = P \circ p_n`
equality (over `\QQ`, since plethysm is currently not
defined over `\ZZ` in Sage)::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.s()
sage: p = Sym.p()
sage: all( s(lam).frobenius(3) == s(lam).plethysm(p[3])
....: == s(p[3].plethysm(s(lam)))
....: for lam in Partitions(4) )
True
By Exercise 7.61 in Stanley's EC2 [STA]_ (see the errata on his
website), `\mathbf{f}_n(h_m)` is a linear combination of
Schur polynomials (of straight shapes) using coefficients `0`,
`1` and `-1` only; moreover, all partitions whose Schur
polynomials occur with coefficient `\neq 0` in this
combination have empty `n`-cores. Let us check this on
examples::
sage: all( all( all( (coeff == -1 or coeff == 1)
....: and lam.core(n) == Partition([])
....: for lam, coeff in s([m]).frobenius(n).monomial_coefficients().items() )
....: for n in range(2, 4) )
....: for m in range(4) )
True
.. SEEALSO::
:meth:`plethysm`
.. TODO::
This method is fast on the monomial and the powersum
bases, while all other bases get converted to the
monomial basis. For most bases, this is probably the
quickest way to do, but at least the Schur basis should
have a better option. (Quoting from Stanley's EC2 [STA]_:
"D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236,
or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp.
Math. 34 (1984), 109-153".)
|
src/sage/combinat/sf/sfa.py
|
frobenius
|
bopopescu/sagesmc
| 5 |
python
|
def frobenius(self, n):
'\n Return the image of the symmetric function ``self`` under the\n `n`-th Frobenius operator.\n\n The `n`-th Frobenius operator `\\mathbf{f}_n` is defined to be the\n map from the ring of symmetric functions to itself that sends\n every symmetric function `P(x_1, x_2, x_3, \\ldots)` to\n `P(x_1^n, x_2^n, x_3^n, \\ldots)`. This operator `\\mathbf{f}_n`\n is a Hopf algebra endomorphism, and satisfies\n\n .. MATH::\n\n \\mathbf{f}_n m_{(\\lambda_1, \\lambda_2, \\lambda_3, \\ldots)} =\n m_{(n\\lambda_1, n\\lambda_2, n\\lambda_3, \\ldots)}\n\n for every partition `(\\lambda_1, \\lambda_2, \\lambda_3, \\ldots)`\n (where `m` means the monomial basis). Moreover,\n `\\mathbf{f}_n (p_r) = p_{nr}` for every positive integer `r` (where\n `p_k` denotes the `k`-th powersum symmetric function).\n\n The `n`-th Frobenius operator is also called the `n`-th\n Frobenius endomorphism. It is not related to the Frobenius map\n which connects the ring of symmetric functions with the\n representation theory of the symmetric group.\n\n The `n`-th Frobenius operator is also the `n`-th Adams operator\n of the `\\Lambda`-ring of symmetric functions over the integers.\n\n The `n`-th Frobenius operator can also be described via plethysm:\n Every symmetric function `P` satisfies\n `\\mathbf{f}_n(P) = p_n \\circ P = P \\circ p_n`,\n where `p_n` is the `n`-th powersum symmetric function, and `\\circ`\n denotes (outer) plethysm.\n\n :meth:`adams_operation` serves as alias for :meth:`frobenius`, since the\n Frobenius operators are the Adams operations of the `\\Lambda`-ring\n of symmetric functions.\n\n INPUT:\n\n - ``n`` -- a positive integer\n\n OUTPUT:\n\n The result of applying the `n`-th Frobenius operator (on the ring of\n symmetric functions) to ``self``.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: h = Sym.h()\n sage: s = Sym.s()\n sage: m = Sym.m()\n sage: s[3].frobenius(2)\n -s[3, 3] + s[4, 2] - s[5, 1] + s[6]\n sage: m[4,2,1].frobenius(3)\n m[12, 6, 3]\n sage: p[4,2,1].frobenius(3)\n p[12, 6, 3]\n sage: h[4].frobenius(2)\n h[4, 4] - 2*h[5, 3] + 2*h[6, 2] - 2*h[7, 1] + 2*h[8]\n\n The Frobenius endomorphisms are multiplicative::\n\n sage: all( all( s(lam).frobenius(3) * s(mu).frobenius(3)\n ....: == (s(lam) * s(mu)).frobenius(3)\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(3) )\n True\n sage: all( all( m(lam).frobenius(2) * m(mu).frobenius(2)\n ....: == (m(lam) * m(mu)).frobenius(2)\n ....: for mu in Partitions(4) )\n ....: for lam in Partitions(4) )\n True\n sage: all( all( p(lam).frobenius(2) * p(mu).frobenius(2)\n ....: == (p(lam) * p(mu)).frobenius(2)\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(4) )\n True\n\n Being Hopf algebra endomorphisms, the Frobenius operators\n commute with the antipode::\n\n sage: all( p(lam).frobenius(4).antipode()\n ....: == p(lam).antipode().frobenius(4)\n ....: for lam in Partitions(3) )\n True\n\n Testing the `\\mathbf{f}_n(P) = p_n \\circ P = P \\circ p_n`\n equality (over `\\QQ`, since plethysm is currently not\n defined over `\\ZZ` in Sage)::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: s = Sym.s()\n sage: p = Sym.p()\n sage: all( s(lam).frobenius(3) == s(lam).plethysm(p[3])\n ....: == s(p[3].plethysm(s(lam)))\n ....: for lam in Partitions(4) )\n True\n\n By Exercise 7.61 in Stanley\'s EC2 [STA]_ (see the errata on his\n website), `\\mathbf{f}_n(h_m)` is a linear combination of\n Schur polynomials (of straight shapes) using coefficients `0`,\n `1` and `-1` only; moreover, all partitions whose Schur\n polynomials occur with coefficient `\\neq 0` in this\n combination have empty `n`-cores. Let us check this on\n examples::\n\n sage: all( all( all( (coeff == -1 or coeff == 1)\n ....: and lam.core(n) == Partition([])\n ....: for lam, coeff in s([m]).frobenius(n).monomial_coefficients().items() )\n ....: for n in range(2, 4) )\n ....: for m in range(4) )\n True\n\n .. SEEALSO::\n\n :meth:`plethysm`\n\n .. TODO::\n\n This method is fast on the monomial and the powersum\n bases, while all other bases get converted to the\n monomial basis. For most bases, this is probably the\n quickest way to do, but at least the Schur basis should\n have a better option. (Quoting from Stanley\'s EC2 [STA]_:\n "D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236,\n or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp.\n Math. 34 (1984), 109-153".)\n '
parent = self.parent()
m = parent.realization_of().monomial()
from sage.combinat.partition import Partition
dct = {Partition(map((lambda i: (n * i)), lam)): coeff for (lam, coeff) in m(self).monomial_coefficients().items()}
result_in_m_basis = m._from_dict(dct)
return parent(result_in_m_basis)
|
def frobenius(self, n):
'\n Return the image of the symmetric function ``self`` under the\n `n`-th Frobenius operator.\n\n The `n`-th Frobenius operator `\\mathbf{f}_n` is defined to be the\n map from the ring of symmetric functions to itself that sends\n every symmetric function `P(x_1, x_2, x_3, \\ldots)` to\n `P(x_1^n, x_2^n, x_3^n, \\ldots)`. This operator `\\mathbf{f}_n`\n is a Hopf algebra endomorphism, and satisfies\n\n .. MATH::\n\n \\mathbf{f}_n m_{(\\lambda_1, \\lambda_2, \\lambda_3, \\ldots)} =\n m_{(n\\lambda_1, n\\lambda_2, n\\lambda_3, \\ldots)}\n\n for every partition `(\\lambda_1, \\lambda_2, \\lambda_3, \\ldots)`\n (where `m` means the monomial basis). Moreover,\n `\\mathbf{f}_n (p_r) = p_{nr}` for every positive integer `r` (where\n `p_k` denotes the `k`-th powersum symmetric function).\n\n The `n`-th Frobenius operator is also called the `n`-th\n Frobenius endomorphism. It is not related to the Frobenius map\n which connects the ring of symmetric functions with the\n representation theory of the symmetric group.\n\n The `n`-th Frobenius operator is also the `n`-th Adams operator\n of the `\\Lambda`-ring of symmetric functions over the integers.\n\n The `n`-th Frobenius operator can also be described via plethysm:\n Every symmetric function `P` satisfies\n `\\mathbf{f}_n(P) = p_n \\circ P = P \\circ p_n`,\n where `p_n` is the `n`-th powersum symmetric function, and `\\circ`\n denotes (outer) plethysm.\n\n :meth:`adams_operation` serves as alias for :meth:`frobenius`, since the\n Frobenius operators are the Adams operations of the `\\Lambda`-ring\n of symmetric functions.\n\n INPUT:\n\n - ``n`` -- a positive integer\n\n OUTPUT:\n\n The result of applying the `n`-th Frobenius operator (on the ring of\n symmetric functions) to ``self``.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: h = Sym.h()\n sage: s = Sym.s()\n sage: m = Sym.m()\n sage: s[3].frobenius(2)\n -s[3, 3] + s[4, 2] - s[5, 1] + s[6]\n sage: m[4,2,1].frobenius(3)\n m[12, 6, 3]\n sage: p[4,2,1].frobenius(3)\n p[12, 6, 3]\n sage: h[4].frobenius(2)\n h[4, 4] - 2*h[5, 3] + 2*h[6, 2] - 2*h[7, 1] + 2*h[8]\n\n The Frobenius endomorphisms are multiplicative::\n\n sage: all( all( s(lam).frobenius(3) * s(mu).frobenius(3)\n ....: == (s(lam) * s(mu)).frobenius(3)\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(3) )\n True\n sage: all( all( m(lam).frobenius(2) * m(mu).frobenius(2)\n ....: == (m(lam) * m(mu)).frobenius(2)\n ....: for mu in Partitions(4) )\n ....: for lam in Partitions(4) )\n True\n sage: all( all( p(lam).frobenius(2) * p(mu).frobenius(2)\n ....: == (p(lam) * p(mu)).frobenius(2)\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(4) )\n True\n\n Being Hopf algebra endomorphisms, the Frobenius operators\n commute with the antipode::\n\n sage: all( p(lam).frobenius(4).antipode()\n ....: == p(lam).antipode().frobenius(4)\n ....: for lam in Partitions(3) )\n True\n\n Testing the `\\mathbf{f}_n(P) = p_n \\circ P = P \\circ p_n`\n equality (over `\\QQ`, since plethysm is currently not\n defined over `\\ZZ` in Sage)::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: s = Sym.s()\n sage: p = Sym.p()\n sage: all( s(lam).frobenius(3) == s(lam).plethysm(p[3])\n ....: == s(p[3].plethysm(s(lam)))\n ....: for lam in Partitions(4) )\n True\n\n By Exercise 7.61 in Stanley\'s EC2 [STA]_ (see the errata on his\n website), `\\mathbf{f}_n(h_m)` is a linear combination of\n Schur polynomials (of straight shapes) using coefficients `0`,\n `1` and `-1` only; moreover, all partitions whose Schur\n polynomials occur with coefficient `\\neq 0` in this\n combination have empty `n`-cores. Let us check this on\n examples::\n\n sage: all( all( all( (coeff == -1 or coeff == 1)\n ....: and lam.core(n) == Partition([])\n ....: for lam, coeff in s([m]).frobenius(n).monomial_coefficients().items() )\n ....: for n in range(2, 4) )\n ....: for m in range(4) )\n True\n\n .. SEEALSO::\n\n :meth:`plethysm`\n\n .. TODO::\n\n This method is fast on the monomial and the powersum\n bases, while all other bases get converted to the\n monomial basis. For most bases, this is probably the\n quickest way to do, but at least the Schur basis should\n have a better option. (Quoting from Stanley\'s EC2 [STA]_:\n "D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236,\n or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp.\n Math. 34 (1984), 109-153".)\n '
parent = self.parent()
m = parent.realization_of().monomial()
from sage.combinat.partition import Partition
dct = {Partition(map((lambda i: (n * i)), lam)): coeff for (lam, coeff) in m(self).monomial_coefficients().items()}
result_in_m_basis = m._from_dict(dct)
return parent(result_in_m_basis)<|docstring|>Return the image of the symmetric function ``self`` under the
`n`-th Frobenius operator.
The `n`-th Frobenius operator `\mathbf{f}_n` is defined to be the
map from the ring of symmetric functions to itself that sends
every symmetric function `P(x_1, x_2, x_3, \ldots)` to
`P(x_1^n, x_2^n, x_3^n, \ldots)`. This operator `\mathbf{f}_n`
is a Hopf algebra endomorphism, and satisfies
.. MATH::
\mathbf{f}_n m_{(\lambda_1, \lambda_2, \lambda_3, \ldots)} =
m_{(n\lambda_1, n\lambda_2, n\lambda_3, \ldots)}
for every partition `(\lambda_1, \lambda_2, \lambda_3, \ldots)`
(where `m` means the monomial basis). Moreover,
`\mathbf{f}_n (p_r) = p_{nr}` for every positive integer `r` (where
`p_k` denotes the `k`-th powersum symmetric function).
The `n`-th Frobenius operator is also called the `n`-th
Frobenius endomorphism. It is not related to the Frobenius map
which connects the ring of symmetric functions with the
representation theory of the symmetric group.
The `n`-th Frobenius operator is also the `n`-th Adams operator
of the `\Lambda`-ring of symmetric functions over the integers.
The `n`-th Frobenius operator can also be described via plethysm:
Every symmetric function `P` satisfies
`\mathbf{f}_n(P) = p_n \circ P = P \circ p_n`,
where `p_n` is the `n`-th powersum symmetric function, and `\circ`
denotes (outer) plethysm.
:meth:`adams_operation` serves as alias for :meth:`frobenius`, since the
Frobenius operators are the Adams operations of the `\Lambda`-ring
of symmetric functions.
INPUT:
- ``n`` -- a positive integer
OUTPUT:
The result of applying the `n`-th Frobenius operator (on the ring of
symmetric functions) to ``self``.
EXAMPLES::
sage: Sym = SymmetricFunctions(ZZ)
sage: p = Sym.p()
sage: h = Sym.h()
sage: s = Sym.s()
sage: m = Sym.m()
sage: s[3].frobenius(2)
-s[3, 3] + s[4, 2] - s[5, 1] + s[6]
sage: m[4,2,1].frobenius(3)
m[12, 6, 3]
sage: p[4,2,1].frobenius(3)
p[12, 6, 3]
sage: h[4].frobenius(2)
h[4, 4] - 2*h[5, 3] + 2*h[6, 2] - 2*h[7, 1] + 2*h[8]
The Frobenius endomorphisms are multiplicative::
sage: all( all( s(lam).frobenius(3) * s(mu).frobenius(3)
....: == (s(lam) * s(mu)).frobenius(3)
....: for mu in Partitions(3) )
....: for lam in Partitions(3) )
True
sage: all( all( m(lam).frobenius(2) * m(mu).frobenius(2)
....: == (m(lam) * m(mu)).frobenius(2)
....: for mu in Partitions(4) )
....: for lam in Partitions(4) )
True
sage: all( all( p(lam).frobenius(2) * p(mu).frobenius(2)
....: == (p(lam) * p(mu)).frobenius(2)
....: for mu in Partitions(3) )
....: for lam in Partitions(4) )
True
Being Hopf algebra endomorphisms, the Frobenius operators
commute with the antipode::
sage: all( p(lam).frobenius(4).antipode()
....: == p(lam).antipode().frobenius(4)
....: for lam in Partitions(3) )
True
Testing the `\mathbf{f}_n(P) = p_n \circ P = P \circ p_n`
equality (over `\QQ`, since plethysm is currently not
defined over `\ZZ` in Sage)::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.s()
sage: p = Sym.p()
sage: all( s(lam).frobenius(3) == s(lam).plethysm(p[3])
....: == s(p[3].plethysm(s(lam)))
....: for lam in Partitions(4) )
True
By Exercise 7.61 in Stanley's EC2 [STA]_ (see the errata on his
website), `\mathbf{f}_n(h_m)` is a linear combination of
Schur polynomials (of straight shapes) using coefficients `0`,
`1` and `-1` only; moreover, all partitions whose Schur
polynomials occur with coefficient `\neq 0` in this
combination have empty `n`-cores. Let us check this on
examples::
sage: all( all( all( (coeff == -1 or coeff == 1)
....: and lam.core(n) == Partition([])
....: for lam, coeff in s([m]).frobenius(n).monomial_coefficients().items() )
....: for n in range(2, 4) )
....: for m in range(4) )
True
.. SEEALSO::
:meth:`plethysm`
.. TODO::
This method is fast on the monomial and the powersum
bases, while all other bases get converted to the
monomial basis. For most bases, this is probably the
quickest way to do, but at least the Schur basis should
have a better option. (Quoting from Stanley's EC2 [STA]_:
"D. G. Duncan, J. London Math. Soc. 27 (1952), 235-236,
or Y. M. Chen, A. M. Garsia, and J. B. Remmel, Contemp.
Math. 34 (1984), 109-153".)<|endoftext|>
|
14d6f658c1c83d4133a3ba4bd48caab351108bbdb6545982eacb8589a1b131ca
|
def verschiebung(self, n):
'\n Return the image of the symmetric function ``self`` under the\n `n`-th Verschiebung operator.\n\n The `n`-th Verschiebung operator `\\mathbf{V}_n` is defined to be\n the unique algebra endomorphism `V` of the ring of symmetric\n functions that satisfies `V(h_r) = h_{r/n}` for every positive\n integer `r` divisible by `n`, and satisfies `V(h_r) = 0` for\n every positive integer `r` not divisible by `n`. This operator\n `\\mathbf{V}_n` is a Hopf algebra endomorphism. For every\n nonnegative integer `r` with `n \\mid r`, it satisfies\n\n .. MATH::\n\n \\mathbf{V}_n(h_r) = h_{r/n},\n \\quad \\mathbf{V}_n(p_r) = n p_{r/n},\n \\quad \\mathbf{V}_n(e_r) = (-1)^{r - r/n} e_{r/n}\n\n (where `h` is the complete homogeneous basis, `p` is the\n powersum basis, and `e` is the elementary basis). For every\n nonnegative integer `r` with `n \\nmid r`, it satisfes\n\n .. MATH::\n\n \\mathbf{V}_n(h_r) = \\mathbf{V}_n(p_r) = \\mathbf{V}_n(e_r) = 0.\n\n The `n`-th Verschiebung operator is also called the `n`-th\n Verschiebung endomorphism. Its name derives from the Verschiebung\n (German for "shift") endomorphism of the Witt vectors.\n\n The `n`-th Verschiebung operator is adjoint to the `n`-th\n Frobenius operator (see :meth:`frobenius` for its definition)\n with respect to the Hall scalar product (:meth:`scalar`).\n\n The action of the `n`-th Verschiebung operator on the Schur basis\n can also be computed explicitly. The following (probably clumsier\n than necessary) description can be obtained by solving exercise\n 7.61 in Stanley\'s [STA]_.\n\n Let `\\lambda` be a partition. Let `n` be a positive integer. If\n the `n`-core of `\\lambda` is nonempty, then\n `\\mathbf{V}_n(s_\\lambda) = 0`. Otherwise, the following method\n computes `\\mathbf{V}_n(s_\\lambda)`: Write the partition `\\lambda`\n in the form `(\\lambda_1, \\lambda_2, \\ldots, \\lambda_{ns})` for some\n nonnegative integer `s`. (If `n` does not divide the length of\n `\\lambda`, then this is achieved by adding trailing zeroes to\n `\\lambda`.) Set `\\beta_i = \\lambda_i + ns - i` for every\n `s \\in \\{ 1, 2, \\ldots, ns \\}`. Then,\n `(\\beta_1, \\beta_2, \\ldots, \\beta_{ns})` is a strictly decreasing\n sequence of nonnegative integers. Stably sort the list\n `(1, 2, \\ldots, ns)` in order of (weakly) increasing remainder of\n `-1 - \\beta_i` modulo `n`. Let `\\xi` be the sign of the\n permutation that is used for this sorting. Let `\\psi` be the sign\n of the permutation that is used to stably sort the list\n `(1, 2, \\ldots, ns)` in order of (weakly) increasing remainder of\n `i - 1` modulo `n`. (Notice that `\\psi = (-1)^{n(n-1)s(s-1)/4}`.)\n Then, `\\mathbf{V}_n(s_\\lambda) = \\xi \\psi \\prod_{i = 0}^{n - 1}\n s_{\\lambda^{(i)}}`, where\n `(\\lambda^{(0)}, \\lambda^{(1)}, \\ldots, \\lambda^{(n - 1)})`\n is the `n`-quotient of `\\lambda`.\n\n INPUT:\n\n - ``n`` -- a positive integer\n\n OUTPUT:\n\n The result of applying the `n`-th Verschiebung operator (on the ring of\n symmetric functions) to ``self``.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: h = Sym.h()\n sage: s = Sym.s()\n sage: m = Sym.m()\n sage: s[3].verschiebung(2)\n 0\n sage: s[3].verschiebung(3)\n s[1]\n sage: p[3].verschiebung(3)\n 3*p[1]\n sage: m[3,2,1].verschiebung(3)\n -18*m[1, 1] - 3*m[2]\n sage: p[3,2,1].verschiebung(3)\n 0\n sage: h[4].verschiebung(2)\n h[2]\n sage: p[2].verschiebung(2)\n 2*p[1]\n sage: m[3,2,1].verschiebung(6)\n 12*m[1]\n\n The Verschiebung endomorphisms are multiplicative::\n\n sage: all( all( s(lam).verschiebung(2) * s(mu).verschiebung(2)\n ....: == (s(lam) * s(mu)).verschiebung(2)\n ....: for mu in Partitions(4) )\n ....: for lam in Partitions(4) )\n True\n\n Being Hopf algebra endomorphisms, the Verschiebung operators\n commute with the antipode::\n\n sage: all( p(lam).verschiebung(3).antipode()\n ....: == p(lam).antipode().verschiebung(3)\n ....: for lam in Partitions(6) )\n True\n\n Testing the adjointness between the Frobenius operators\n `\\mathbf{f}_n` and the Verschiebung operators\n `\\mathbf{V}_n`::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: s = Sym.s()\n sage: p = Sym.p()\n sage: all( all( s(lam).verschiebung(2).scalar(p(mu))\n ....: == s(lam).scalar(p(mu).frobenius(2))\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(6) )\n True\n '
parent = self.parent()
h = parent.realization_of().homogeneous()
h_coords_of_self = h(self).monomial_coefficients().items()
from sage.combinat.partition import Partition
dct = {Partition(map((lambda i: (i // n)), lam)): coeff for (lam, coeff) in h_coords_of_self if all((((i % n) == 0) for i in lam))}
result_in_h_basis = h._from_dict(dct)
return parent(result_in_h_basis)
|
Return the image of the symmetric function ``self`` under the
`n`-th Verschiebung operator.
The `n`-th Verschiebung operator `\mathbf{V}_n` is defined to be
the unique algebra endomorphism `V` of the ring of symmetric
functions that satisfies `V(h_r) = h_{r/n}` for every positive
integer `r` divisible by `n`, and satisfies `V(h_r) = 0` for
every positive integer `r` not divisible by `n`. This operator
`\mathbf{V}_n` is a Hopf algebra endomorphism. For every
nonnegative integer `r` with `n \mid r`, it satisfies
.. MATH::
\mathbf{V}_n(h_r) = h_{r/n},
\quad \mathbf{V}_n(p_r) = n p_{r/n},
\quad \mathbf{V}_n(e_r) = (-1)^{r - r/n} e_{r/n}
(where `h` is the complete homogeneous basis, `p` is the
powersum basis, and `e` is the elementary basis). For every
nonnegative integer `r` with `n \nmid r`, it satisfes
.. MATH::
\mathbf{V}_n(h_r) = \mathbf{V}_n(p_r) = \mathbf{V}_n(e_r) = 0.
The `n`-th Verschiebung operator is also called the `n`-th
Verschiebung endomorphism. Its name derives from the Verschiebung
(German for "shift") endomorphism of the Witt vectors.
The `n`-th Verschiebung operator is adjoint to the `n`-th
Frobenius operator (see :meth:`frobenius` for its definition)
with respect to the Hall scalar product (:meth:`scalar`).
The action of the `n`-th Verschiebung operator on the Schur basis
can also be computed explicitly. The following (probably clumsier
than necessary) description can be obtained by solving exercise
7.61 in Stanley's [STA]_.
Let `\lambda` be a partition. Let `n` be a positive integer. If
the `n`-core of `\lambda` is nonempty, then
`\mathbf{V}_n(s_\lambda) = 0`. Otherwise, the following method
computes `\mathbf{V}_n(s_\lambda)`: Write the partition `\lambda`
in the form `(\lambda_1, \lambda_2, \ldots, \lambda_{ns})` for some
nonnegative integer `s`. (If `n` does not divide the length of
`\lambda`, then this is achieved by adding trailing zeroes to
`\lambda`.) Set `\beta_i = \lambda_i + ns - i` for every
`s \in \{ 1, 2, \ldots, ns \}`. Then,
`(\beta_1, \beta_2, \ldots, \beta_{ns})` is a strictly decreasing
sequence of nonnegative integers. Stably sort the list
`(1, 2, \ldots, ns)` in order of (weakly) increasing remainder of
`-1 - \beta_i` modulo `n`. Let `\xi` be the sign of the
permutation that is used for this sorting. Let `\psi` be the sign
of the permutation that is used to stably sort the list
`(1, 2, \ldots, ns)` in order of (weakly) increasing remainder of
`i - 1` modulo `n`. (Notice that `\psi = (-1)^{n(n-1)s(s-1)/4}`.)
Then, `\mathbf{V}_n(s_\lambda) = \xi \psi \prod_{i = 0}^{n - 1}
s_{\lambda^{(i)}}`, where
`(\lambda^{(0)}, \lambda^{(1)}, \ldots, \lambda^{(n - 1)})`
is the `n`-quotient of `\lambda`.
INPUT:
- ``n`` -- a positive integer
OUTPUT:
The result of applying the `n`-th Verschiebung operator (on the ring of
symmetric functions) to ``self``.
EXAMPLES::
sage: Sym = SymmetricFunctions(ZZ)
sage: p = Sym.p()
sage: h = Sym.h()
sage: s = Sym.s()
sage: m = Sym.m()
sage: s[3].verschiebung(2)
0
sage: s[3].verschiebung(3)
s[1]
sage: p[3].verschiebung(3)
3*p[1]
sage: m[3,2,1].verschiebung(3)
-18*m[1, 1] - 3*m[2]
sage: p[3,2,1].verschiebung(3)
0
sage: h[4].verschiebung(2)
h[2]
sage: p[2].verschiebung(2)
2*p[1]
sage: m[3,2,1].verschiebung(6)
12*m[1]
The Verschiebung endomorphisms are multiplicative::
sage: all( all( s(lam).verschiebung(2) * s(mu).verschiebung(2)
....: == (s(lam) * s(mu)).verschiebung(2)
....: for mu in Partitions(4) )
....: for lam in Partitions(4) )
True
Being Hopf algebra endomorphisms, the Verschiebung operators
commute with the antipode::
sage: all( p(lam).verschiebung(3).antipode()
....: == p(lam).antipode().verschiebung(3)
....: for lam in Partitions(6) )
True
Testing the adjointness between the Frobenius operators
`\mathbf{f}_n` and the Verschiebung operators
`\mathbf{V}_n`::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.s()
sage: p = Sym.p()
sage: all( all( s(lam).verschiebung(2).scalar(p(mu))
....: == s(lam).scalar(p(mu).frobenius(2))
....: for mu in Partitions(3) )
....: for lam in Partitions(6) )
True
|
src/sage/combinat/sf/sfa.py
|
verschiebung
|
bopopescu/sagesmc
| 5 |
python
|
def verschiebung(self, n):
'\n Return the image of the symmetric function ``self`` under the\n `n`-th Verschiebung operator.\n\n The `n`-th Verschiebung operator `\\mathbf{V}_n` is defined to be\n the unique algebra endomorphism `V` of the ring of symmetric\n functions that satisfies `V(h_r) = h_{r/n}` for every positive\n integer `r` divisible by `n`, and satisfies `V(h_r) = 0` for\n every positive integer `r` not divisible by `n`. This operator\n `\\mathbf{V}_n` is a Hopf algebra endomorphism. For every\n nonnegative integer `r` with `n \\mid r`, it satisfies\n\n .. MATH::\n\n \\mathbf{V}_n(h_r) = h_{r/n},\n \\quad \\mathbf{V}_n(p_r) = n p_{r/n},\n \\quad \\mathbf{V}_n(e_r) = (-1)^{r - r/n} e_{r/n}\n\n (where `h` is the complete homogeneous basis, `p` is the\n powersum basis, and `e` is the elementary basis). For every\n nonnegative integer `r` with `n \\nmid r`, it satisfes\n\n .. MATH::\n\n \\mathbf{V}_n(h_r) = \\mathbf{V}_n(p_r) = \\mathbf{V}_n(e_r) = 0.\n\n The `n`-th Verschiebung operator is also called the `n`-th\n Verschiebung endomorphism. Its name derives from the Verschiebung\n (German for "shift") endomorphism of the Witt vectors.\n\n The `n`-th Verschiebung operator is adjoint to the `n`-th\n Frobenius operator (see :meth:`frobenius` for its definition)\n with respect to the Hall scalar product (:meth:`scalar`).\n\n The action of the `n`-th Verschiebung operator on the Schur basis\n can also be computed explicitly. The following (probably clumsier\n than necessary) description can be obtained by solving exercise\n 7.61 in Stanley\'s [STA]_.\n\n Let `\\lambda` be a partition. Let `n` be a positive integer. If\n the `n`-core of `\\lambda` is nonempty, then\n `\\mathbf{V}_n(s_\\lambda) = 0`. Otherwise, the following method\n computes `\\mathbf{V}_n(s_\\lambda)`: Write the partition `\\lambda`\n in the form `(\\lambda_1, \\lambda_2, \\ldots, \\lambda_{ns})` for some\n nonnegative integer `s`. (If `n` does not divide the length of\n `\\lambda`, then this is achieved by adding trailing zeroes to\n `\\lambda`.) Set `\\beta_i = \\lambda_i + ns - i` for every\n `s \\in \\{ 1, 2, \\ldots, ns \\}`. Then,\n `(\\beta_1, \\beta_2, \\ldots, \\beta_{ns})` is a strictly decreasing\n sequence of nonnegative integers. Stably sort the list\n `(1, 2, \\ldots, ns)` in order of (weakly) increasing remainder of\n `-1 - \\beta_i` modulo `n`. Let `\\xi` be the sign of the\n permutation that is used for this sorting. Let `\\psi` be the sign\n of the permutation that is used to stably sort the list\n `(1, 2, \\ldots, ns)` in order of (weakly) increasing remainder of\n `i - 1` modulo `n`. (Notice that `\\psi = (-1)^{n(n-1)s(s-1)/4}`.)\n Then, `\\mathbf{V}_n(s_\\lambda) = \\xi \\psi \\prod_{i = 0}^{n - 1}\n s_{\\lambda^{(i)}}`, where\n `(\\lambda^{(0)}, \\lambda^{(1)}, \\ldots, \\lambda^{(n - 1)})`\n is the `n`-quotient of `\\lambda`.\n\n INPUT:\n\n - ``n`` -- a positive integer\n\n OUTPUT:\n\n The result of applying the `n`-th Verschiebung operator (on the ring of\n symmetric functions) to ``self``.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: h = Sym.h()\n sage: s = Sym.s()\n sage: m = Sym.m()\n sage: s[3].verschiebung(2)\n 0\n sage: s[3].verschiebung(3)\n s[1]\n sage: p[3].verschiebung(3)\n 3*p[1]\n sage: m[3,2,1].verschiebung(3)\n -18*m[1, 1] - 3*m[2]\n sage: p[3,2,1].verschiebung(3)\n 0\n sage: h[4].verschiebung(2)\n h[2]\n sage: p[2].verschiebung(2)\n 2*p[1]\n sage: m[3,2,1].verschiebung(6)\n 12*m[1]\n\n The Verschiebung endomorphisms are multiplicative::\n\n sage: all( all( s(lam).verschiebung(2) * s(mu).verschiebung(2)\n ....: == (s(lam) * s(mu)).verschiebung(2)\n ....: for mu in Partitions(4) )\n ....: for lam in Partitions(4) )\n True\n\n Being Hopf algebra endomorphisms, the Verschiebung operators\n commute with the antipode::\n\n sage: all( p(lam).verschiebung(3).antipode()\n ....: == p(lam).antipode().verschiebung(3)\n ....: for lam in Partitions(6) )\n True\n\n Testing the adjointness between the Frobenius operators\n `\\mathbf{f}_n` and the Verschiebung operators\n `\\mathbf{V}_n`::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: s = Sym.s()\n sage: p = Sym.p()\n sage: all( all( s(lam).verschiebung(2).scalar(p(mu))\n ....: == s(lam).scalar(p(mu).frobenius(2))\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(6) )\n True\n '
parent = self.parent()
h = parent.realization_of().homogeneous()
h_coords_of_self = h(self).monomial_coefficients().items()
from sage.combinat.partition import Partition
dct = {Partition(map((lambda i: (i // n)), lam)): coeff for (lam, coeff) in h_coords_of_self if all((((i % n) == 0) for i in lam))}
result_in_h_basis = h._from_dict(dct)
return parent(result_in_h_basis)
|
def verschiebung(self, n):
'\n Return the image of the symmetric function ``self`` under the\n `n`-th Verschiebung operator.\n\n The `n`-th Verschiebung operator `\\mathbf{V}_n` is defined to be\n the unique algebra endomorphism `V` of the ring of symmetric\n functions that satisfies `V(h_r) = h_{r/n}` for every positive\n integer `r` divisible by `n`, and satisfies `V(h_r) = 0` for\n every positive integer `r` not divisible by `n`. This operator\n `\\mathbf{V}_n` is a Hopf algebra endomorphism. For every\n nonnegative integer `r` with `n \\mid r`, it satisfies\n\n .. MATH::\n\n \\mathbf{V}_n(h_r) = h_{r/n},\n \\quad \\mathbf{V}_n(p_r) = n p_{r/n},\n \\quad \\mathbf{V}_n(e_r) = (-1)^{r - r/n} e_{r/n}\n\n (where `h` is the complete homogeneous basis, `p` is the\n powersum basis, and `e` is the elementary basis). For every\n nonnegative integer `r` with `n \\nmid r`, it satisfes\n\n .. MATH::\n\n \\mathbf{V}_n(h_r) = \\mathbf{V}_n(p_r) = \\mathbf{V}_n(e_r) = 0.\n\n The `n`-th Verschiebung operator is also called the `n`-th\n Verschiebung endomorphism. Its name derives from the Verschiebung\n (German for "shift") endomorphism of the Witt vectors.\n\n The `n`-th Verschiebung operator is adjoint to the `n`-th\n Frobenius operator (see :meth:`frobenius` for its definition)\n with respect to the Hall scalar product (:meth:`scalar`).\n\n The action of the `n`-th Verschiebung operator on the Schur basis\n can also be computed explicitly. The following (probably clumsier\n than necessary) description can be obtained by solving exercise\n 7.61 in Stanley\'s [STA]_.\n\n Let `\\lambda` be a partition. Let `n` be a positive integer. If\n the `n`-core of `\\lambda` is nonempty, then\n `\\mathbf{V}_n(s_\\lambda) = 0`. Otherwise, the following method\n computes `\\mathbf{V}_n(s_\\lambda)`: Write the partition `\\lambda`\n in the form `(\\lambda_1, \\lambda_2, \\ldots, \\lambda_{ns})` for some\n nonnegative integer `s`. (If `n` does not divide the length of\n `\\lambda`, then this is achieved by adding trailing zeroes to\n `\\lambda`.) Set `\\beta_i = \\lambda_i + ns - i` for every\n `s \\in \\{ 1, 2, \\ldots, ns \\}`. Then,\n `(\\beta_1, \\beta_2, \\ldots, \\beta_{ns})` is a strictly decreasing\n sequence of nonnegative integers. Stably sort the list\n `(1, 2, \\ldots, ns)` in order of (weakly) increasing remainder of\n `-1 - \\beta_i` modulo `n`. Let `\\xi` be the sign of the\n permutation that is used for this sorting. Let `\\psi` be the sign\n of the permutation that is used to stably sort the list\n `(1, 2, \\ldots, ns)` in order of (weakly) increasing remainder of\n `i - 1` modulo `n`. (Notice that `\\psi = (-1)^{n(n-1)s(s-1)/4}`.)\n Then, `\\mathbf{V}_n(s_\\lambda) = \\xi \\psi \\prod_{i = 0}^{n - 1}\n s_{\\lambda^{(i)}}`, where\n `(\\lambda^{(0)}, \\lambda^{(1)}, \\ldots, \\lambda^{(n - 1)})`\n is the `n`-quotient of `\\lambda`.\n\n INPUT:\n\n - ``n`` -- a positive integer\n\n OUTPUT:\n\n The result of applying the `n`-th Verschiebung operator (on the ring of\n symmetric functions) to ``self``.\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: h = Sym.h()\n sage: s = Sym.s()\n sage: m = Sym.m()\n sage: s[3].verschiebung(2)\n 0\n sage: s[3].verschiebung(3)\n s[1]\n sage: p[3].verschiebung(3)\n 3*p[1]\n sage: m[3,2,1].verschiebung(3)\n -18*m[1, 1] - 3*m[2]\n sage: p[3,2,1].verschiebung(3)\n 0\n sage: h[4].verschiebung(2)\n h[2]\n sage: p[2].verschiebung(2)\n 2*p[1]\n sage: m[3,2,1].verschiebung(6)\n 12*m[1]\n\n The Verschiebung endomorphisms are multiplicative::\n\n sage: all( all( s(lam).verschiebung(2) * s(mu).verschiebung(2)\n ....: == (s(lam) * s(mu)).verschiebung(2)\n ....: for mu in Partitions(4) )\n ....: for lam in Partitions(4) )\n True\n\n Being Hopf algebra endomorphisms, the Verschiebung operators\n commute with the antipode::\n\n sage: all( p(lam).verschiebung(3).antipode()\n ....: == p(lam).antipode().verschiebung(3)\n ....: for lam in Partitions(6) )\n True\n\n Testing the adjointness between the Frobenius operators\n `\\mathbf{f}_n` and the Verschiebung operators\n `\\mathbf{V}_n`::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: s = Sym.s()\n sage: p = Sym.p()\n sage: all( all( s(lam).verschiebung(2).scalar(p(mu))\n ....: == s(lam).scalar(p(mu).frobenius(2))\n ....: for mu in Partitions(3) )\n ....: for lam in Partitions(6) )\n True\n '
parent = self.parent()
h = parent.realization_of().homogeneous()
h_coords_of_self = h(self).monomial_coefficients().items()
from sage.combinat.partition import Partition
dct = {Partition(map((lambda i: (i // n)), lam)): coeff for (lam, coeff) in h_coords_of_self if all((((i % n) == 0) for i in lam))}
result_in_h_basis = h._from_dict(dct)
return parent(result_in_h_basis)<|docstring|>Return the image of the symmetric function ``self`` under the
`n`-th Verschiebung operator.
The `n`-th Verschiebung operator `\mathbf{V}_n` is defined to be
the unique algebra endomorphism `V` of the ring of symmetric
functions that satisfies `V(h_r) = h_{r/n}` for every positive
integer `r` divisible by `n`, and satisfies `V(h_r) = 0` for
every positive integer `r` not divisible by `n`. This operator
`\mathbf{V}_n` is a Hopf algebra endomorphism. For every
nonnegative integer `r` with `n \mid r`, it satisfies
.. MATH::
\mathbf{V}_n(h_r) = h_{r/n},
\quad \mathbf{V}_n(p_r) = n p_{r/n},
\quad \mathbf{V}_n(e_r) = (-1)^{r - r/n} e_{r/n}
(where `h` is the complete homogeneous basis, `p` is the
powersum basis, and `e` is the elementary basis). For every
nonnegative integer `r` with `n \nmid r`, it satisfes
.. MATH::
\mathbf{V}_n(h_r) = \mathbf{V}_n(p_r) = \mathbf{V}_n(e_r) = 0.
The `n`-th Verschiebung operator is also called the `n`-th
Verschiebung endomorphism. Its name derives from the Verschiebung
(German for "shift") endomorphism of the Witt vectors.
The `n`-th Verschiebung operator is adjoint to the `n`-th
Frobenius operator (see :meth:`frobenius` for its definition)
with respect to the Hall scalar product (:meth:`scalar`).
The action of the `n`-th Verschiebung operator on the Schur basis
can also be computed explicitly. The following (probably clumsier
than necessary) description can be obtained by solving exercise
7.61 in Stanley's [STA]_.
Let `\lambda` be a partition. Let `n` be a positive integer. If
the `n`-core of `\lambda` is nonempty, then
`\mathbf{V}_n(s_\lambda) = 0`. Otherwise, the following method
computes `\mathbf{V}_n(s_\lambda)`: Write the partition `\lambda`
in the form `(\lambda_1, \lambda_2, \ldots, \lambda_{ns})` for some
nonnegative integer `s`. (If `n` does not divide the length of
`\lambda`, then this is achieved by adding trailing zeroes to
`\lambda`.) Set `\beta_i = \lambda_i + ns - i` for every
`s \in \{ 1, 2, \ldots, ns \}`. Then,
`(\beta_1, \beta_2, \ldots, \beta_{ns})` is a strictly decreasing
sequence of nonnegative integers. Stably sort the list
`(1, 2, \ldots, ns)` in order of (weakly) increasing remainder of
`-1 - \beta_i` modulo `n`. Let `\xi` be the sign of the
permutation that is used for this sorting. Let `\psi` be the sign
of the permutation that is used to stably sort the list
`(1, 2, \ldots, ns)` in order of (weakly) increasing remainder of
`i - 1` modulo `n`. (Notice that `\psi = (-1)^{n(n-1)s(s-1)/4}`.)
Then, `\mathbf{V}_n(s_\lambda) = \xi \psi \prod_{i = 0}^{n - 1}
s_{\lambda^{(i)}}`, where
`(\lambda^{(0)}, \lambda^{(1)}, \ldots, \lambda^{(n - 1)})`
is the `n`-quotient of `\lambda`.
INPUT:
- ``n`` -- a positive integer
OUTPUT:
The result of applying the `n`-th Verschiebung operator (on the ring of
symmetric functions) to ``self``.
EXAMPLES::
sage: Sym = SymmetricFunctions(ZZ)
sage: p = Sym.p()
sage: h = Sym.h()
sage: s = Sym.s()
sage: m = Sym.m()
sage: s[3].verschiebung(2)
0
sage: s[3].verschiebung(3)
s[1]
sage: p[3].verschiebung(3)
3*p[1]
sage: m[3,2,1].verschiebung(3)
-18*m[1, 1] - 3*m[2]
sage: p[3,2,1].verschiebung(3)
0
sage: h[4].verschiebung(2)
h[2]
sage: p[2].verschiebung(2)
2*p[1]
sage: m[3,2,1].verschiebung(6)
12*m[1]
The Verschiebung endomorphisms are multiplicative::
sage: all( all( s(lam).verschiebung(2) * s(mu).verschiebung(2)
....: == (s(lam) * s(mu)).verschiebung(2)
....: for mu in Partitions(4) )
....: for lam in Partitions(4) )
True
Being Hopf algebra endomorphisms, the Verschiebung operators
commute with the antipode::
sage: all( p(lam).verschiebung(3).antipode()
....: == p(lam).antipode().verschiebung(3)
....: for lam in Partitions(6) )
True
Testing the adjointness between the Frobenius operators
`\mathbf{f}_n` and the Verschiebung operators
`\mathbf{V}_n`::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.s()
sage: p = Sym.p()
sage: all( all( s(lam).verschiebung(2).scalar(p(mu))
....: == s(lam).scalar(p(mu).frobenius(2))
....: for mu in Partitions(3) )
....: for lam in Partitions(6) )
True<|endoftext|>
|
704cb400316b4bde9033f4136dfbc94840289ff4e69f52fe4dcbf622679cd697
|
def _expand(self, condition, n, alphabet='x'):
"\n Expand the symmetric function as a symmetric polynomial in ``n``\n variables.\n\n INPUT:\n\n - ``condition`` -- a function on partitions with a boolean output,\n selecting only certain terms (namely, only the items failing\n the condition are being expanded)\n\n - ``n`` -- a nonnegative integer\n\n - ``alphabet`` -- (default: ``'x'``) a variable for the expansion\n\n OUTPUT:\n\n A monomial expansion of an instance of ``self`` in `n` variables.\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: a = p([2])+p([3])\n sage: a._expand(lambda part: False, 3)\n x0^3 + x1^3 + x2^3 + x0^2 + x1^2 + x2^2\n sage: a._expand(lambda part: max(part)>2, 3)\n x0^2 + x1^2 + x2^2\n sage: p(0).expand(3)\n 0\n sage: p([]).expand(3)\n 1\n\n .. NOTE::\n\n The term corresponding to the empty partition is always\n selected, even if ``condition`` returns ``False`` or an\n error when applied to the empty partition. This is in\n order to simplify using the ``_expand`` method with\n conditions like ``lambda part: max(part) < 3`` which\n would require extra work to handle the empty partition.\n "
import classical
parent = self.parent()
resPR = PolynomialRing(parent.base_ring(), n, alphabet)
if (self == parent.zero()):
return resPR.zero()
e = eval((('symmetrica.compute_' + str(classical.translate[parent.basis_name()]).lower()) + '_with_alphabet'))
def f(part):
if (part == []):
return resPR.one()
else:
return (resPR.zero() if condition(part) else resPR(e(part, n, alphabet)))
return parent._apply_module_morphism(self, f)
|
Expand the symmetric function as a symmetric polynomial in ``n``
variables.
INPUT:
- ``condition`` -- a function on partitions with a boolean output,
selecting only certain terms (namely, only the items failing
the condition are being expanded)
- ``n`` -- a nonnegative integer
- ``alphabet`` -- (default: ``'x'``) a variable for the expansion
OUTPUT:
A monomial expansion of an instance of ``self`` in `n` variables.
EXAMPLES::
sage: p = SymmetricFunctions(QQ).p()
sage: a = p([2])+p([3])
sage: a._expand(lambda part: False, 3)
x0^3 + x1^3 + x2^3 + x0^2 + x1^2 + x2^2
sage: a._expand(lambda part: max(part)>2, 3)
x0^2 + x1^2 + x2^2
sage: p(0).expand(3)
0
sage: p([]).expand(3)
1
.. NOTE::
The term corresponding to the empty partition is always
selected, even if ``condition`` returns ``False`` or an
error when applied to the empty partition. This is in
order to simplify using the ``_expand`` method with
conditions like ``lambda part: max(part) < 3`` which
would require extra work to handle the empty partition.
|
src/sage/combinat/sf/sfa.py
|
_expand
|
bopopescu/sagesmc
| 5 |
python
|
def _expand(self, condition, n, alphabet='x'):
"\n Expand the symmetric function as a symmetric polynomial in ``n``\n variables.\n\n INPUT:\n\n - ``condition`` -- a function on partitions with a boolean output,\n selecting only certain terms (namely, only the items failing\n the condition are being expanded)\n\n - ``n`` -- a nonnegative integer\n\n - ``alphabet`` -- (default: ``'x'``) a variable for the expansion\n\n OUTPUT:\n\n A monomial expansion of an instance of ``self`` in `n` variables.\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: a = p([2])+p([3])\n sage: a._expand(lambda part: False, 3)\n x0^3 + x1^3 + x2^3 + x0^2 + x1^2 + x2^2\n sage: a._expand(lambda part: max(part)>2, 3)\n x0^2 + x1^2 + x2^2\n sage: p(0).expand(3)\n 0\n sage: p([]).expand(3)\n 1\n\n .. NOTE::\n\n The term corresponding to the empty partition is always\n selected, even if ``condition`` returns ``False`` or an\n error when applied to the empty partition. This is in\n order to simplify using the ``_expand`` method with\n conditions like ``lambda part: max(part) < 3`` which\n would require extra work to handle the empty partition.\n "
import classical
parent = self.parent()
resPR = PolynomialRing(parent.base_ring(), n, alphabet)
if (self == parent.zero()):
return resPR.zero()
e = eval((('symmetrica.compute_' + str(classical.translate[parent.basis_name()]).lower()) + '_with_alphabet'))
def f(part):
if (part == []):
return resPR.one()
else:
return (resPR.zero() if condition(part) else resPR(e(part, n, alphabet)))
return parent._apply_module_morphism(self, f)
|
def _expand(self, condition, n, alphabet='x'):
"\n Expand the symmetric function as a symmetric polynomial in ``n``\n variables.\n\n INPUT:\n\n - ``condition`` -- a function on partitions with a boolean output,\n selecting only certain terms (namely, only the items failing\n the condition are being expanded)\n\n - ``n`` -- a nonnegative integer\n\n - ``alphabet`` -- (default: ``'x'``) a variable for the expansion\n\n OUTPUT:\n\n A monomial expansion of an instance of ``self`` in `n` variables.\n\n EXAMPLES::\n\n sage: p = SymmetricFunctions(QQ).p()\n sage: a = p([2])+p([3])\n sage: a._expand(lambda part: False, 3)\n x0^3 + x1^3 + x2^3 + x0^2 + x1^2 + x2^2\n sage: a._expand(lambda part: max(part)>2, 3)\n x0^2 + x1^2 + x2^2\n sage: p(0).expand(3)\n 0\n sage: p([]).expand(3)\n 1\n\n .. NOTE::\n\n The term corresponding to the empty partition is always\n selected, even if ``condition`` returns ``False`` or an\n error when applied to the empty partition. This is in\n order to simplify using the ``_expand`` method with\n conditions like ``lambda part: max(part) < 3`` which\n would require extra work to handle the empty partition.\n "
import classical
parent = self.parent()
resPR = PolynomialRing(parent.base_ring(), n, alphabet)
if (self == parent.zero()):
return resPR.zero()
e = eval((('symmetrica.compute_' + str(classical.translate[parent.basis_name()]).lower()) + '_with_alphabet'))
def f(part):
if (part == []):
return resPR.one()
else:
return (resPR.zero() if condition(part) else resPR(e(part, n, alphabet)))
return parent._apply_module_morphism(self, f)<|docstring|>Expand the symmetric function as a symmetric polynomial in ``n``
variables.
INPUT:
- ``condition`` -- a function on partitions with a boolean output,
selecting only certain terms (namely, only the items failing
the condition are being expanded)
- ``n`` -- a nonnegative integer
- ``alphabet`` -- (default: ``'x'``) a variable for the expansion
OUTPUT:
A monomial expansion of an instance of ``self`` in `n` variables.
EXAMPLES::
sage: p = SymmetricFunctions(QQ).p()
sage: a = p([2])+p([3])
sage: a._expand(lambda part: False, 3)
x0^3 + x1^3 + x2^3 + x0^2 + x1^2 + x2^2
sage: a._expand(lambda part: max(part)>2, 3)
x0^2 + x1^2 + x2^2
sage: p(0).expand(3)
0
sage: p([]).expand(3)
1
.. NOTE::
The term corresponding to the empty partition is always
selected, even if ``condition`` returns ``False`` or an
error when applied to the empty partition. This is in
order to simplify using the ``_expand`` method with
conditions like ``lambda part: max(part) < 3`` which
would require extra work to handle the empty partition.<|endoftext|>
|
4834db11b9cce49f14e6dc990927be6e9caf3ae96c622802d625559c1a2793fd
|
def is_schur_positive(self):
"\n Return ``True`` if and only if ``self`` is Schur positive.\n\n If `s` is the space of Schur functions over ``self``'s base ring, then\n this is the same as ``self._is_positive(s)``.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1]) + s([3])\n sage: a.is_schur_positive()\n True\n sage: a = s([2,1]) - s([3])\n sage: a.is_schur_positive()\n False\n\n ::\n\n sage: QQx = QQ['x']\n sage: s = SymmetricFunctions(QQx).s()\n sage: x = QQx.gen()\n sage: a = (1+x)*s([2,1])\n sage: a.is_schur_positive()\n True\n sage: a = (1-x)*s([2,1])\n sage: a.is_schur_positive()\n False\n sage: s(0).is_schur_positive()\n True\n sage: s(1+x).is_schur_positive()\n True\n "
return self._is_positive(self.parent().realization_of().schur())
|
Return ``True`` if and only if ``self`` is Schur positive.
If `s` is the space of Schur functions over ``self``'s base ring, then
this is the same as ``self._is_positive(s)``.
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1]) + s([3])
sage: a.is_schur_positive()
True
sage: a = s([2,1]) - s([3])
sage: a.is_schur_positive()
False
::
sage: QQx = QQ['x']
sage: s = SymmetricFunctions(QQx).s()
sage: x = QQx.gen()
sage: a = (1+x)*s([2,1])
sage: a.is_schur_positive()
True
sage: a = (1-x)*s([2,1])
sage: a.is_schur_positive()
False
sage: s(0).is_schur_positive()
True
sage: s(1+x).is_schur_positive()
True
|
src/sage/combinat/sf/sfa.py
|
is_schur_positive
|
bopopescu/sagesmc
| 5 |
python
|
def is_schur_positive(self):
"\n Return ``True`` if and only if ``self`` is Schur positive.\n\n If `s` is the space of Schur functions over ``self``'s base ring, then\n this is the same as ``self._is_positive(s)``.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1]) + s([3])\n sage: a.is_schur_positive()\n True\n sage: a = s([2,1]) - s([3])\n sage: a.is_schur_positive()\n False\n\n ::\n\n sage: QQx = QQ['x']\n sage: s = SymmetricFunctions(QQx).s()\n sage: x = QQx.gen()\n sage: a = (1+x)*s([2,1])\n sage: a.is_schur_positive()\n True\n sage: a = (1-x)*s([2,1])\n sage: a.is_schur_positive()\n False\n sage: s(0).is_schur_positive()\n True\n sage: s(1+x).is_schur_positive()\n True\n "
return self._is_positive(self.parent().realization_of().schur())
|
def is_schur_positive(self):
"\n Return ``True`` if and only if ``self`` is Schur positive.\n\n If `s` is the space of Schur functions over ``self``'s base ring, then\n this is the same as ``self._is_positive(s)``.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1]) + s([3])\n sage: a.is_schur_positive()\n True\n sage: a = s([2,1]) - s([3])\n sage: a.is_schur_positive()\n False\n\n ::\n\n sage: QQx = QQ['x']\n sage: s = SymmetricFunctions(QQx).s()\n sage: x = QQx.gen()\n sage: a = (1+x)*s([2,1])\n sage: a.is_schur_positive()\n True\n sage: a = (1-x)*s([2,1])\n sage: a.is_schur_positive()\n False\n sage: s(0).is_schur_positive()\n True\n sage: s(1+x).is_schur_positive()\n True\n "
return self._is_positive(self.parent().realization_of().schur())<|docstring|>Return ``True`` if and only if ``self`` is Schur positive.
If `s` is the space of Schur functions over ``self``'s base ring, then
this is the same as ``self._is_positive(s)``.
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1]) + s([3])
sage: a.is_schur_positive()
True
sage: a = s([2,1]) - s([3])
sage: a.is_schur_positive()
False
::
sage: QQx = QQ['x']
sage: s = SymmetricFunctions(QQx).s()
sage: x = QQx.gen()
sage: a = (1+x)*s([2,1])
sage: a.is_schur_positive()
True
sage: a = (1-x)*s([2,1])
sage: a.is_schur_positive()
False
sage: s(0).is_schur_positive()
True
sage: s(1+x).is_schur_positive()
True<|endoftext|>
|
6e6e2a5311f931bde5e9eadacb25ede375460ffd86c068bad67734af86bf1906
|
def _is_positive(self, s):
'\n Return ``True`` if and only if ``self`` has nonnegative coefficients\n in the basis `s`.\n\n INPUT:\n\n - ``s`` -- a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1]) + s([3])\n sage: a._is_positive(s)\n True\n sage: a = s([2,1]) - s([3])\n sage: a._is_positive(s)\n False\n\n sage: m = SymmetricFunctions(QQ).m()\n sage: a = s([2,1]) + s([3])\n sage: a._is_positive(m)\n True\n sage: a = -s[2,1]\n sage: a._is_positive(m)\n False\n\n sage: (s[2,1] - s[1,1,1])._is_positive(s)\n False\n sage: (s[2,1] - s[1,1,1])._is_positive(m)\n True\n '
s_self = s(self)
return all([_nonnegative_coefficients(c) for c in s_self.coefficients()])
|
Return ``True`` if and only if ``self`` has nonnegative coefficients
in the basis `s`.
INPUT:
- ``s`` -- a basis of the ring of symmetric functions
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1]) + s([3])
sage: a._is_positive(s)
True
sage: a = s([2,1]) - s([3])
sage: a._is_positive(s)
False
sage: m = SymmetricFunctions(QQ).m()
sage: a = s([2,1]) + s([3])
sage: a._is_positive(m)
True
sage: a = -s[2,1]
sage: a._is_positive(m)
False
sage: (s[2,1] - s[1,1,1])._is_positive(s)
False
sage: (s[2,1] - s[1,1,1])._is_positive(m)
True
|
src/sage/combinat/sf/sfa.py
|
_is_positive
|
bopopescu/sagesmc
| 5 |
python
|
def _is_positive(self, s):
'\n Return ``True`` if and only if ``self`` has nonnegative coefficients\n in the basis `s`.\n\n INPUT:\n\n - ``s`` -- a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1]) + s([3])\n sage: a._is_positive(s)\n True\n sage: a = s([2,1]) - s([3])\n sage: a._is_positive(s)\n False\n\n sage: m = SymmetricFunctions(QQ).m()\n sage: a = s([2,1]) + s([3])\n sage: a._is_positive(m)\n True\n sage: a = -s[2,1]\n sage: a._is_positive(m)\n False\n\n sage: (s[2,1] - s[1,1,1])._is_positive(s)\n False\n sage: (s[2,1] - s[1,1,1])._is_positive(m)\n True\n '
s_self = s(self)
return all([_nonnegative_coefficients(c) for c in s_self.coefficients()])
|
def _is_positive(self, s):
'\n Return ``True`` if and only if ``self`` has nonnegative coefficients\n in the basis `s`.\n\n INPUT:\n\n - ``s`` -- a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: a = s([2,1]) + s([3])\n sage: a._is_positive(s)\n True\n sage: a = s([2,1]) - s([3])\n sage: a._is_positive(s)\n False\n\n sage: m = SymmetricFunctions(QQ).m()\n sage: a = s([2,1]) + s([3])\n sage: a._is_positive(m)\n True\n sage: a = -s[2,1]\n sage: a._is_positive(m)\n False\n\n sage: (s[2,1] - s[1,1,1])._is_positive(s)\n False\n sage: (s[2,1] - s[1,1,1])._is_positive(m)\n True\n '
s_self = s(self)
return all([_nonnegative_coefficients(c) for c in s_self.coefficients()])<|docstring|>Return ``True`` if and only if ``self`` has nonnegative coefficients
in the basis `s`.
INPUT:
- ``s`` -- a basis of the ring of symmetric functions
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: a = s([2,1]) + s([3])
sage: a._is_positive(s)
True
sage: a = s([2,1]) - s([3])
sage: a._is_positive(s)
False
sage: m = SymmetricFunctions(QQ).m()
sage: a = s([2,1]) + s([3])
sage: a._is_positive(m)
True
sage: a = -s[2,1]
sage: a._is_positive(m)
False
sage: (s[2,1] - s[1,1,1])._is_positive(s)
False
sage: (s[2,1] - s[1,1,1])._is_positive(m)
True<|endoftext|>
|
5aff2ee6990164bd79043c9d152e77465a185e80513f94d2a69c2a96fbdce681
|
def degree(self):
'\n Return the degree of ``self`` (which is defined to be `0`\n for the zero element).\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1]) + 3\n sage: z.degree()\n 4\n sage: s(1).degree()\n 0\n sage: s(0).degree()\n 0\n '
return max((map(sum, self._monomial_coefficients) + [0]))
|
Return the degree of ``self`` (which is defined to be `0`
for the zero element).
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1]) + 3
sage: z.degree()
4
sage: s(1).degree()
0
sage: s(0).degree()
0
|
src/sage/combinat/sf/sfa.py
|
degree
|
bopopescu/sagesmc
| 5 |
python
|
def degree(self):
'\n Return the degree of ``self`` (which is defined to be `0`\n for the zero element).\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1]) + 3\n sage: z.degree()\n 4\n sage: s(1).degree()\n 0\n sage: s(0).degree()\n 0\n '
return max((map(sum, self._monomial_coefficients) + [0]))
|
def degree(self):
'\n Return the degree of ``self`` (which is defined to be `0`\n for the zero element).\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1]) + 3\n sage: z.degree()\n 4\n sage: s(1).degree()\n 0\n sage: s(0).degree()\n 0\n '
return max((map(sum, self._monomial_coefficients) + [0]))<|docstring|>Return the degree of ``self`` (which is defined to be `0`
for the zero element).
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1]) + 3
sage: z.degree()
4
sage: s(1).degree()
0
sage: s(0).degree()
0<|endoftext|>
|
afa8029488bf424e1aa619e0c8af5f06f38840385b13b57c63cda85754eb73d6
|
def restrict_degree(self, d, exact=True):
'\n Return the degree ``d`` component of ``self``.\n\n INPUT:\n\n - ``d`` -- positive integer, degree of the terms to be returned\n\n - ``exact`` -- boolean, if ``True``, returns the terms of degree\n exactly ``d``, otherwise returns all terms of degree less than\n or equal to ``d``\n\n OUTPUT:\n\n - the homogeneous component of ``self`` of degree ``d``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_degree(2)\n 0\n sage: z.restrict_degree(1)\n s[1]\n sage: z.restrict_degree(3)\n s[1, 1, 1] + s[2, 1]\n sage: z.restrict_degree(3, exact=False)\n s[1] + s[1, 1, 1] + s[2, 1]\n sage: z.restrict_degree(0)\n 0\n '
if exact:
res = dict(filter((lambda x: (sum(x[0]) == d)), self._monomial_coefficients.items()))
else:
res = dict(filter((lambda x: (sum(x[0]) <= d)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)
|
Return the degree ``d`` component of ``self``.
INPUT:
- ``d`` -- positive integer, degree of the terms to be returned
- ``exact`` -- boolean, if ``True``, returns the terms of degree
exactly ``d``, otherwise returns all terms of degree less than
or equal to ``d``
OUTPUT:
- the homogeneous component of ``self`` of degree ``d``
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
sage: z.restrict_degree(2)
0
sage: z.restrict_degree(1)
s[1]
sage: z.restrict_degree(3)
s[1, 1, 1] + s[2, 1]
sage: z.restrict_degree(3, exact=False)
s[1] + s[1, 1, 1] + s[2, 1]
sage: z.restrict_degree(0)
0
|
src/sage/combinat/sf/sfa.py
|
restrict_degree
|
bopopescu/sagesmc
| 5 |
python
|
def restrict_degree(self, d, exact=True):
'\n Return the degree ``d`` component of ``self``.\n\n INPUT:\n\n - ``d`` -- positive integer, degree of the terms to be returned\n\n - ``exact`` -- boolean, if ``True``, returns the terms of degree\n exactly ``d``, otherwise returns all terms of degree less than\n or equal to ``d``\n\n OUTPUT:\n\n - the homogeneous component of ``self`` of degree ``d``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_degree(2)\n 0\n sage: z.restrict_degree(1)\n s[1]\n sage: z.restrict_degree(3)\n s[1, 1, 1] + s[2, 1]\n sage: z.restrict_degree(3, exact=False)\n s[1] + s[1, 1, 1] + s[2, 1]\n sage: z.restrict_degree(0)\n 0\n '
if exact:
res = dict(filter((lambda x: (sum(x[0]) == d)), self._monomial_coefficients.items()))
else:
res = dict(filter((lambda x: (sum(x[0]) <= d)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)
|
def restrict_degree(self, d, exact=True):
'\n Return the degree ``d`` component of ``self``.\n\n INPUT:\n\n - ``d`` -- positive integer, degree of the terms to be returned\n\n - ``exact`` -- boolean, if ``True``, returns the terms of degree\n exactly ``d``, otherwise returns all terms of degree less than\n or equal to ``d``\n\n OUTPUT:\n\n - the homogeneous component of ``self`` of degree ``d``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_degree(2)\n 0\n sage: z.restrict_degree(1)\n s[1]\n sage: z.restrict_degree(3)\n s[1, 1, 1] + s[2, 1]\n sage: z.restrict_degree(3, exact=False)\n s[1] + s[1, 1, 1] + s[2, 1]\n sage: z.restrict_degree(0)\n 0\n '
if exact:
res = dict(filter((lambda x: (sum(x[0]) == d)), self._monomial_coefficients.items()))
else:
res = dict(filter((lambda x: (sum(x[0]) <= d)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)<|docstring|>Return the degree ``d`` component of ``self``.
INPUT:
- ``d`` -- positive integer, degree of the terms to be returned
- ``exact`` -- boolean, if ``True``, returns the terms of degree
exactly ``d``, otherwise returns all terms of degree less than
or equal to ``d``
OUTPUT:
- the homogeneous component of ``self`` of degree ``d``
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
sage: z.restrict_degree(2)
0
sage: z.restrict_degree(1)
s[1]
sage: z.restrict_degree(3)
s[1, 1, 1] + s[2, 1]
sage: z.restrict_degree(3, exact=False)
s[1] + s[1, 1, 1] + s[2, 1]
sage: z.restrict_degree(0)
0<|endoftext|>
|
1838a115eec37f24dfe0ee988f3e5e583c6a902d5dc731d9b66cbc0acc1fd17e
|
def restrict_partition_lengths(self, l, exact=True):
'\n Return the terms of ``self`` labelled by partitions of length ``l``.\n\n INPUT:\n\n - ``l`` -- nonnegative integer\n\n - ``exact`` -- boolean, defaulting to ``True``\n\n OUTPUT:\n\n - if ``True``, returns the terms labelled by\n partitions of length precisely ``l``; otherwise returns all terms\n labelled by partitions of length less than or equal to ``l``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_partition_lengths(2)\n s[2, 1]\n sage: z.restrict_partition_lengths(0)\n 0\n sage: z.restrict_partition_lengths(2, exact = False)\n s[1] + s[2, 1] + s[4]\n '
if exact:
res = dict(filter((lambda x: (len(x[0]) == l)), self._monomial_coefficients.items()))
else:
res = dict(filter((lambda x: (len(x[0]) <= l)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)
|
Return the terms of ``self`` labelled by partitions of length ``l``.
INPUT:
- ``l`` -- nonnegative integer
- ``exact`` -- boolean, defaulting to ``True``
OUTPUT:
- if ``True``, returns the terms labelled by
partitions of length precisely ``l``; otherwise returns all terms
labelled by partitions of length less than or equal to ``l``
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
sage: z.restrict_partition_lengths(2)
s[2, 1]
sage: z.restrict_partition_lengths(0)
0
sage: z.restrict_partition_lengths(2, exact = False)
s[1] + s[2, 1] + s[4]
|
src/sage/combinat/sf/sfa.py
|
restrict_partition_lengths
|
bopopescu/sagesmc
| 5 |
python
|
def restrict_partition_lengths(self, l, exact=True):
'\n Return the terms of ``self`` labelled by partitions of length ``l``.\n\n INPUT:\n\n - ``l`` -- nonnegative integer\n\n - ``exact`` -- boolean, defaulting to ``True``\n\n OUTPUT:\n\n - if ``True``, returns the terms labelled by\n partitions of length precisely ``l``; otherwise returns all terms\n labelled by partitions of length less than or equal to ``l``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_partition_lengths(2)\n s[2, 1]\n sage: z.restrict_partition_lengths(0)\n 0\n sage: z.restrict_partition_lengths(2, exact = False)\n s[1] + s[2, 1] + s[4]\n '
if exact:
res = dict(filter((lambda x: (len(x[0]) == l)), self._monomial_coefficients.items()))
else:
res = dict(filter((lambda x: (len(x[0]) <= l)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)
|
def restrict_partition_lengths(self, l, exact=True):
'\n Return the terms of ``self`` labelled by partitions of length ``l``.\n\n INPUT:\n\n - ``l`` -- nonnegative integer\n\n - ``exact`` -- boolean, defaulting to ``True``\n\n OUTPUT:\n\n - if ``True``, returns the terms labelled by\n partitions of length precisely ``l``; otherwise returns all terms\n labelled by partitions of length less than or equal to ``l``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_partition_lengths(2)\n s[2, 1]\n sage: z.restrict_partition_lengths(0)\n 0\n sage: z.restrict_partition_lengths(2, exact = False)\n s[1] + s[2, 1] + s[4]\n '
if exact:
res = dict(filter((lambda x: (len(x[0]) == l)), self._monomial_coefficients.items()))
else:
res = dict(filter((lambda x: (len(x[0]) <= l)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)<|docstring|>Return the terms of ``self`` labelled by partitions of length ``l``.
INPUT:
- ``l`` -- nonnegative integer
- ``exact`` -- boolean, defaulting to ``True``
OUTPUT:
- if ``True``, returns the terms labelled by
partitions of length precisely ``l``; otherwise returns all terms
labelled by partitions of length less than or equal to ``l``
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
sage: z.restrict_partition_lengths(2)
s[2, 1]
sage: z.restrict_partition_lengths(0)
0
sage: z.restrict_partition_lengths(2, exact = False)
s[1] + s[2, 1] + s[4]<|endoftext|>
|
87303d5ac3ecb9d62cf9a54dec9e8b0993fe5968efc533a5c30856c18fb45132
|
def restrict_parts(self, n):
'\n Return the terms of ``self`` labelled by partitions `\\lambda` with\n `\\lambda_1 \\leq n`.\n\n INPUT:\n\n - ``n`` -- positive integer, to restrict the parts of the partitions\n of the terms to be returned\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_parts(2)\n s[1] + s[1, 1, 1] + s[2, 1]\n sage: z.restrict_parts(1)\n s[1] + s[1, 1, 1]\n '
res = dict(filter((lambda x: (_lmax(x[0]) <= n)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)
|
Return the terms of ``self`` labelled by partitions `\lambda` with
`\lambda_1 \leq n`.
INPUT:
- ``n`` -- positive integer, to restrict the parts of the partitions
of the terms to be returned
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
sage: z.restrict_parts(2)
s[1] + s[1, 1, 1] + s[2, 1]
sage: z.restrict_parts(1)
s[1] + s[1, 1, 1]
|
src/sage/combinat/sf/sfa.py
|
restrict_parts
|
bopopescu/sagesmc
| 5 |
python
|
def restrict_parts(self, n):
'\n Return the terms of ``self`` labelled by partitions `\\lambda` with\n `\\lambda_1 \\leq n`.\n\n INPUT:\n\n - ``n`` -- positive integer, to restrict the parts of the partitions\n of the terms to be returned\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_parts(2)\n s[1] + s[1, 1, 1] + s[2, 1]\n sage: z.restrict_parts(1)\n s[1] + s[1, 1, 1]\n '
res = dict(filter((lambda x: (_lmax(x[0]) <= n)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)
|
def restrict_parts(self, n):
'\n Return the terms of ``self`` labelled by partitions `\\lambda` with\n `\\lambda_1 \\leq n`.\n\n INPUT:\n\n - ``n`` -- positive integer, to restrict the parts of the partitions\n of the terms to be returned\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])\n sage: z.restrict_parts(2)\n s[1] + s[1, 1, 1] + s[2, 1]\n sage: z.restrict_parts(1)\n s[1] + s[1, 1, 1]\n '
res = dict(filter((lambda x: (_lmax(x[0]) <= n)), self._monomial_coefficients.items()))
return self.parent()._from_dict(res)<|docstring|>Return the terms of ``self`` labelled by partitions `\lambda` with
`\lambda_1 \leq n`.
INPUT:
- ``n`` -- positive integer, to restrict the parts of the partitions
of the terms to be returned
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: z = s([4]) + s([2,1]) + s([1,1,1]) + s([1])
sage: z.restrict_parts(2)
s[1] + s[1, 1, 1] + s[2, 1]
sage: z.restrict_parts(1)
s[1] + s[1, 1, 1]<|endoftext|>
|
1bbbe6d0708227a96af868f10bdf3bf7769863e6f75161e0ef9858470ca7bb14
|
def expand(self, n, alphabet='x'):
"\n Expand the symmetric function as a symmetric polynomial in ``n``\n variables.\n\n INPUT:\n\n - ``n`` -- a nonnegative integer\n\n - ``alphabet`` -- (default: ``'x'``) a variable for the expansion\n\n OUTPUT:\n\n A monomial expansion of an instance of ``self`` in `n` variables.\n\n EXAMPLES::\n\n sage: J = SymmetricFunctions(QQ).jack(t=2).J()\n sage: J([2,1]).expand(3)\n 4*x0^2*x1 + 4*x0*x1^2 + 4*x0^2*x2 + 6*x0*x1*x2 + 4*x1^2*x2 + 4*x0*x2^2 + 4*x1*x2^2\n "
s = self.parent().realization_of().schur()
condition = (lambda part: (len(part) > n))
return s(self)._expand(condition, n, alphabet)
|
Expand the symmetric function as a symmetric polynomial in ``n``
variables.
INPUT:
- ``n`` -- a nonnegative integer
- ``alphabet`` -- (default: ``'x'``) a variable for the expansion
OUTPUT:
A monomial expansion of an instance of ``self`` in `n` variables.
EXAMPLES::
sage: J = SymmetricFunctions(QQ).jack(t=2).J()
sage: J([2,1]).expand(3)
4*x0^2*x1 + 4*x0*x1^2 + 4*x0^2*x2 + 6*x0*x1*x2 + 4*x1^2*x2 + 4*x0*x2^2 + 4*x1*x2^2
|
src/sage/combinat/sf/sfa.py
|
expand
|
bopopescu/sagesmc
| 5 |
python
|
def expand(self, n, alphabet='x'):
"\n Expand the symmetric function as a symmetric polynomial in ``n``\n variables.\n\n INPUT:\n\n - ``n`` -- a nonnegative integer\n\n - ``alphabet`` -- (default: ``'x'``) a variable for the expansion\n\n OUTPUT:\n\n A monomial expansion of an instance of ``self`` in `n` variables.\n\n EXAMPLES::\n\n sage: J = SymmetricFunctions(QQ).jack(t=2).J()\n sage: J([2,1]).expand(3)\n 4*x0^2*x1 + 4*x0*x1^2 + 4*x0^2*x2 + 6*x0*x1*x2 + 4*x1^2*x2 + 4*x0*x2^2 + 4*x1*x2^2\n "
s = self.parent().realization_of().schur()
condition = (lambda part: (len(part) > n))
return s(self)._expand(condition, n, alphabet)
|
def expand(self, n, alphabet='x'):
"\n Expand the symmetric function as a symmetric polynomial in ``n``\n variables.\n\n INPUT:\n\n - ``n`` -- a nonnegative integer\n\n - ``alphabet`` -- (default: ``'x'``) a variable for the expansion\n\n OUTPUT:\n\n A monomial expansion of an instance of ``self`` in `n` variables.\n\n EXAMPLES::\n\n sage: J = SymmetricFunctions(QQ).jack(t=2).J()\n sage: J([2,1]).expand(3)\n 4*x0^2*x1 + 4*x0*x1^2 + 4*x0^2*x2 + 6*x0*x1*x2 + 4*x1^2*x2 + 4*x0*x2^2 + 4*x1*x2^2\n "
s = self.parent().realization_of().schur()
condition = (lambda part: (len(part) > n))
return s(self)._expand(condition, n, alphabet)<|docstring|>Expand the symmetric function as a symmetric polynomial in ``n``
variables.
INPUT:
- ``n`` -- a nonnegative integer
- ``alphabet`` -- (default: ``'x'``) a variable for the expansion
OUTPUT:
A monomial expansion of an instance of ``self`` in `n` variables.
EXAMPLES::
sage: J = SymmetricFunctions(QQ).jack(t=2).J()
sage: J([2,1]).expand(3)
4*x0^2*x1 + 4*x0*x1^2 + 4*x0^2*x2 + 6*x0*x1*x2 + 4*x1^2*x2 + 4*x0*x2^2 + 4*x1*x2^2<|endoftext|>
|
fbc19ef3ef1a074ebcaec913339f865d939c40712a04873c52a4a44e7d652056
|
def skew_by(self, x):
'\n Return the result of skewing ``self`` by ``x``. (Skewing by ``x`` is\n the endomorphism (as additive group) of the ring of symmetric\n functions adjoint to multiplication by ``x`` with respect to the\n Hall inner product.)\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([3,2]).skew_by(s([2]))\n s[2, 1] + s[3]\n sage: s([3,2]).skew_by(s([1,1,1]))\n 0\n sage: s([3,2,1]).skew_by(s([2,1]))\n s[1, 1, 1] + 2*s[2, 1] + s[3]\n\n ::\n\n sage: p = SymmetricFunctions(QQ).powersum()\n sage: p([4,3,3,2,2,1]).skew_by(p([2,1]))\n 4*p[4, 3, 3, 2]\n sage: zee = sage.combinat.sf.sfa.zee\n sage: zee([4,3,3,2,2,1])/zee([4,3,3,2])\n 4\n sage: s(0).skew_by(s([1]))\n 0\n sage: s(1).skew_by(s([1]))\n 0\n sage: s([]).skew_by(s([]))\n s[]\n sage: s([]).skew_by(s[1])\n 0\n\n TESTS::\n\n sage: f=s[3,2]\n sage: f.skew_by([1])\n Traceback (most recent call last):\n ...\n ValueError: x needs to be a symmetric function\n '
if (x not in self.parent().realization_of()):
raise ValueError('x needs to be a symmetric function')
s = self.parent().realization_of().schur()
f = (lambda part1, part2: (s([part1, part2]) if part1.contains(part2) else 0))
return self.parent()(s._apply_multi_module_morphism(s(self), s(x), f))
|
Return the result of skewing ``self`` by ``x``. (Skewing by ``x`` is
the endomorphism (as additive group) of the ring of symmetric
functions adjoint to multiplication by ``x`` with respect to the
Hall inner product.)
INPUT:
- ``x`` -- element of the ring of symmetric functions over the same
base ring as ``self``
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s([3,2]).skew_by(s([2]))
s[2, 1] + s[3]
sage: s([3,2]).skew_by(s([1,1,1]))
0
sage: s([3,2,1]).skew_by(s([2,1]))
s[1, 1, 1] + 2*s[2, 1] + s[3]
::
sage: p = SymmetricFunctions(QQ).powersum()
sage: p([4,3,3,2,2,1]).skew_by(p([2,1]))
4*p[4, 3, 3, 2]
sage: zee = sage.combinat.sf.sfa.zee
sage: zee([4,3,3,2,2,1])/zee([4,3,3,2])
4
sage: s(0).skew_by(s([1]))
0
sage: s(1).skew_by(s([1]))
0
sage: s([]).skew_by(s([]))
s[]
sage: s([]).skew_by(s[1])
0
TESTS::
sage: f=s[3,2]
sage: f.skew_by([1])
Traceback (most recent call last):
...
ValueError: x needs to be a symmetric function
|
src/sage/combinat/sf/sfa.py
|
skew_by
|
bopopescu/sagesmc
| 5 |
python
|
def skew_by(self, x):
'\n Return the result of skewing ``self`` by ``x``. (Skewing by ``x`` is\n the endomorphism (as additive group) of the ring of symmetric\n functions adjoint to multiplication by ``x`` with respect to the\n Hall inner product.)\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([3,2]).skew_by(s([2]))\n s[2, 1] + s[3]\n sage: s([3,2]).skew_by(s([1,1,1]))\n 0\n sage: s([3,2,1]).skew_by(s([2,1]))\n s[1, 1, 1] + 2*s[2, 1] + s[3]\n\n ::\n\n sage: p = SymmetricFunctions(QQ).powersum()\n sage: p([4,3,3,2,2,1]).skew_by(p([2,1]))\n 4*p[4, 3, 3, 2]\n sage: zee = sage.combinat.sf.sfa.zee\n sage: zee([4,3,3,2,2,1])/zee([4,3,3,2])\n 4\n sage: s(0).skew_by(s([1]))\n 0\n sage: s(1).skew_by(s([1]))\n 0\n sage: s([]).skew_by(s([]))\n s[]\n sage: s([]).skew_by(s[1])\n 0\n\n TESTS::\n\n sage: f=s[3,2]\n sage: f.skew_by([1])\n Traceback (most recent call last):\n ...\n ValueError: x needs to be a symmetric function\n '
if (x not in self.parent().realization_of()):
raise ValueError('x needs to be a symmetric function')
s = self.parent().realization_of().schur()
f = (lambda part1, part2: (s([part1, part2]) if part1.contains(part2) else 0))
return self.parent()(s._apply_multi_module_morphism(s(self), s(x), f))
|
def skew_by(self, x):
'\n Return the result of skewing ``self`` by ``x``. (Skewing by ``x`` is\n the endomorphism (as additive group) of the ring of symmetric\n functions adjoint to multiplication by ``x`` with respect to the\n Hall inner product.)\n\n INPUT:\n\n - ``x`` -- element of the ring of symmetric functions over the same\n base ring as ``self``\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s([3,2]).skew_by(s([2]))\n s[2, 1] + s[3]\n sage: s([3,2]).skew_by(s([1,1,1]))\n 0\n sage: s([3,2,1]).skew_by(s([2,1]))\n s[1, 1, 1] + 2*s[2, 1] + s[3]\n\n ::\n\n sage: p = SymmetricFunctions(QQ).powersum()\n sage: p([4,3,3,2,2,1]).skew_by(p([2,1]))\n 4*p[4, 3, 3, 2]\n sage: zee = sage.combinat.sf.sfa.zee\n sage: zee([4,3,3,2,2,1])/zee([4,3,3,2])\n 4\n sage: s(0).skew_by(s([1]))\n 0\n sage: s(1).skew_by(s([1]))\n 0\n sage: s([]).skew_by(s([]))\n s[]\n sage: s([]).skew_by(s[1])\n 0\n\n TESTS::\n\n sage: f=s[3,2]\n sage: f.skew_by([1])\n Traceback (most recent call last):\n ...\n ValueError: x needs to be a symmetric function\n '
if (x not in self.parent().realization_of()):
raise ValueError('x needs to be a symmetric function')
s = self.parent().realization_of().schur()
f = (lambda part1, part2: (s([part1, part2]) if part1.contains(part2) else 0))
return self.parent()(s._apply_multi_module_morphism(s(self), s(x), f))<|docstring|>Return the result of skewing ``self`` by ``x``. (Skewing by ``x`` is
the endomorphism (as additive group) of the ring of symmetric
functions adjoint to multiplication by ``x`` with respect to the
Hall inner product.)
INPUT:
- ``x`` -- element of the ring of symmetric functions over the same
base ring as ``self``
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s([3,2]).skew_by(s([2]))
s[2, 1] + s[3]
sage: s([3,2]).skew_by(s([1,1,1]))
0
sage: s([3,2,1]).skew_by(s([2,1]))
s[1, 1, 1] + 2*s[2, 1] + s[3]
::
sage: p = SymmetricFunctions(QQ).powersum()
sage: p([4,3,3,2,2,1]).skew_by(p([2,1]))
4*p[4, 3, 3, 2]
sage: zee = sage.combinat.sf.sfa.zee
sage: zee([4,3,3,2,2,1])/zee([4,3,3,2])
4
sage: s(0).skew_by(s([1]))
0
sage: s(1).skew_by(s([1]))
0
sage: s([]).skew_by(s([]))
s[]
sage: s([]).skew_by(s[1])
0
TESTS::
sage: f=s[3,2]
sage: f.skew_by([1])
Traceback (most recent call last):
...
ValueError: x needs to be a symmetric function<|endoftext|>
|
c8a52ae3f633ad5e0a33dc22246faf8819c2694189783cd24a0088a502c146a7
|
def hl_creation_operator(self, nu, t=None):
"\n This is the vertex operator that generalizes Jing's operator.\n\n It is a linear operator that raises the degree by\n `|\\nu|`. This creation operator is a t-analogue of\n multiplication by ``s(nu)`` .\n\n .. SEEALSO:: Proposition 5 in [SZ2001]_.\n\n INPUT:\n\n - ``nu`` -- a partition\n\n - ``t`` -- (default: ``None``, in which case ``t`` is used) a parameter\n\n REFERENCES:\n\n .. [SZ2001] M. Shimozono, M. Zabrocki,\n Hall-Littlewood vertex operators and generalized Kostka polynomials.\n Adv. Math. 158 (2001), no. 1, 66-85.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ['t']).s()\n sage: s([2]).hl_creation_operator([3,2])\n s[3, 2, 2] + t*s[3, 3, 1] + t*s[4, 2, 1] + t^2*s[4, 3] + t^2*s[5, 2]\n\n sage: Sym = SymmetricFunctions(FractionField(QQ['t']))\n sage: HLQp = Sym.hall_littlewood().Qp()\n sage: s = Sym.s()\n sage: HLQp(s([2]).hl_creation_operator([2]).hl_creation_operator([3]))\n HLQp[3, 2, 2]\n sage: s([2,2]).hl_creation_operator([2,1])\n t*s[2, 2, 2, 1] + t^2*s[3, 2, 1, 1] + t^2*s[3, 2, 2] + t^3*s[3, 3, 1] + t^3*s[4, 2, 1] + t^4*s[4, 3]\n sage: s(1).hl_creation_operator([2,1,1])\n s[2, 1, 1]\n sage: s(0).hl_creation_operator([2,1,1])\n 0\n sage: s([3,2]).hl_creation_operator([2,1,1])\n (t^2-t)*s[2, 2, 2, 2, 1] + t^3*s[3, 2, 2, 1, 1] + (t^3-t^2)*s[3, 2, 2, 2] + t^3*s[3, 3, 1, 1, 1] + t^4*s[3, 3, 2, 1] + t^3*s[4, 2, 1, 1, 1] + t^4*s[4, 2, 2, 1] + 2*t^4*s[4, 3, 1, 1] + t^5*s[4, 3, 2] + t^5*s[4, 4, 1] + t^4*s[5, 2, 1, 1] + t^5*s[5, 3, 1]\n\n TESTS::\n\n sage: s(0).hl_creation_operator([1])\n 0\n "
s = self.parent().realization_of().schur()
if (t is None):
if hasattr(self.parent(), 't'):
t = self.parent().t
else:
t = QQ['t'].gen()
P = self.parent()
self = s(self)
return P(((self * s(nu)) + s.sum(((s.sum_of_terms(((lam, c) for (lam, c) in (s(mu) * s(nu)) if (len(lam) <= len(nu)))) * self.skew_by(s(mu).plethysm(((t - 1) * s([1]))))) for d in range(self.degree()) for mu in Partitions((d + 1), max_length=len(nu))))))
|
This is the vertex operator that generalizes Jing's operator.
It is a linear operator that raises the degree by
`|\nu|`. This creation operator is a t-analogue of
multiplication by ``s(nu)`` .
.. SEEALSO:: Proposition 5 in [SZ2001]_.
INPUT:
- ``nu`` -- a partition
- ``t`` -- (default: ``None``, in which case ``t`` is used) a parameter
REFERENCES:
.. [SZ2001] M. Shimozono, M. Zabrocki,
Hall-Littlewood vertex operators and generalized Kostka polynomials.
Adv. Math. 158 (2001), no. 1, 66-85.
EXAMPLES::
sage: s = SymmetricFunctions(QQ['t']).s()
sage: s([2]).hl_creation_operator([3,2])
s[3, 2, 2] + t*s[3, 3, 1] + t*s[4, 2, 1] + t^2*s[4, 3] + t^2*s[5, 2]
sage: Sym = SymmetricFunctions(FractionField(QQ['t']))
sage: HLQp = Sym.hall_littlewood().Qp()
sage: s = Sym.s()
sage: HLQp(s([2]).hl_creation_operator([2]).hl_creation_operator([3]))
HLQp[3, 2, 2]
sage: s([2,2]).hl_creation_operator([2,1])
t*s[2, 2, 2, 1] + t^2*s[3, 2, 1, 1] + t^2*s[3, 2, 2] + t^3*s[3, 3, 1] + t^3*s[4, 2, 1] + t^4*s[4, 3]
sage: s(1).hl_creation_operator([2,1,1])
s[2, 1, 1]
sage: s(0).hl_creation_operator([2,1,1])
0
sage: s([3,2]).hl_creation_operator([2,1,1])
(t^2-t)*s[2, 2, 2, 2, 1] + t^3*s[3, 2, 2, 1, 1] + (t^3-t^2)*s[3, 2, 2, 2] + t^3*s[3, 3, 1, 1, 1] + t^4*s[3, 3, 2, 1] + t^3*s[4, 2, 1, 1, 1] + t^4*s[4, 2, 2, 1] + 2*t^4*s[4, 3, 1, 1] + t^5*s[4, 3, 2] + t^5*s[4, 4, 1] + t^4*s[5, 2, 1, 1] + t^5*s[5, 3, 1]
TESTS::
sage: s(0).hl_creation_operator([1])
0
|
src/sage/combinat/sf/sfa.py
|
hl_creation_operator
|
bopopescu/sagesmc
| 5 |
python
|
def hl_creation_operator(self, nu, t=None):
"\n This is the vertex operator that generalizes Jing's operator.\n\n It is a linear operator that raises the degree by\n `|\\nu|`. This creation operator is a t-analogue of\n multiplication by ``s(nu)`` .\n\n .. SEEALSO:: Proposition 5 in [SZ2001]_.\n\n INPUT:\n\n - ``nu`` -- a partition\n\n - ``t`` -- (default: ``None``, in which case ``t`` is used) a parameter\n\n REFERENCES:\n\n .. [SZ2001] M. Shimozono, M. Zabrocki,\n Hall-Littlewood vertex operators and generalized Kostka polynomials.\n Adv. Math. 158 (2001), no. 1, 66-85.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ['t']).s()\n sage: s([2]).hl_creation_operator([3,2])\n s[3, 2, 2] + t*s[3, 3, 1] + t*s[4, 2, 1] + t^2*s[4, 3] + t^2*s[5, 2]\n\n sage: Sym = SymmetricFunctions(FractionField(QQ['t']))\n sage: HLQp = Sym.hall_littlewood().Qp()\n sage: s = Sym.s()\n sage: HLQp(s([2]).hl_creation_operator([2]).hl_creation_operator([3]))\n HLQp[3, 2, 2]\n sage: s([2,2]).hl_creation_operator([2,1])\n t*s[2, 2, 2, 1] + t^2*s[3, 2, 1, 1] + t^2*s[3, 2, 2] + t^3*s[3, 3, 1] + t^3*s[4, 2, 1] + t^4*s[4, 3]\n sage: s(1).hl_creation_operator([2,1,1])\n s[2, 1, 1]\n sage: s(0).hl_creation_operator([2,1,1])\n 0\n sage: s([3,2]).hl_creation_operator([2,1,1])\n (t^2-t)*s[2, 2, 2, 2, 1] + t^3*s[3, 2, 2, 1, 1] + (t^3-t^2)*s[3, 2, 2, 2] + t^3*s[3, 3, 1, 1, 1] + t^4*s[3, 3, 2, 1] + t^3*s[4, 2, 1, 1, 1] + t^4*s[4, 2, 2, 1] + 2*t^4*s[4, 3, 1, 1] + t^5*s[4, 3, 2] + t^5*s[4, 4, 1] + t^4*s[5, 2, 1, 1] + t^5*s[5, 3, 1]\n\n TESTS::\n\n sage: s(0).hl_creation_operator([1])\n 0\n "
s = self.parent().realization_of().schur()
if (t is None):
if hasattr(self.parent(), 't'):
t = self.parent().t
else:
t = QQ['t'].gen()
P = self.parent()
self = s(self)
return P(((self * s(nu)) + s.sum(((s.sum_of_terms(((lam, c) for (lam, c) in (s(mu) * s(nu)) if (len(lam) <= len(nu)))) * self.skew_by(s(mu).plethysm(((t - 1) * s([1]))))) for d in range(self.degree()) for mu in Partitions((d + 1), max_length=len(nu))))))
|
def hl_creation_operator(self, nu, t=None):
"\n This is the vertex operator that generalizes Jing's operator.\n\n It is a linear operator that raises the degree by\n `|\\nu|`. This creation operator is a t-analogue of\n multiplication by ``s(nu)`` .\n\n .. SEEALSO:: Proposition 5 in [SZ2001]_.\n\n INPUT:\n\n - ``nu`` -- a partition\n\n - ``t`` -- (default: ``None``, in which case ``t`` is used) a parameter\n\n REFERENCES:\n\n .. [SZ2001] M. Shimozono, M. Zabrocki,\n Hall-Littlewood vertex operators and generalized Kostka polynomials.\n Adv. Math. 158 (2001), no. 1, 66-85.\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ['t']).s()\n sage: s([2]).hl_creation_operator([3,2])\n s[3, 2, 2] + t*s[3, 3, 1] + t*s[4, 2, 1] + t^2*s[4, 3] + t^2*s[5, 2]\n\n sage: Sym = SymmetricFunctions(FractionField(QQ['t']))\n sage: HLQp = Sym.hall_littlewood().Qp()\n sage: s = Sym.s()\n sage: HLQp(s([2]).hl_creation_operator([2]).hl_creation_operator([3]))\n HLQp[3, 2, 2]\n sage: s([2,2]).hl_creation_operator([2,1])\n t*s[2, 2, 2, 1] + t^2*s[3, 2, 1, 1] + t^2*s[3, 2, 2] + t^3*s[3, 3, 1] + t^3*s[4, 2, 1] + t^4*s[4, 3]\n sage: s(1).hl_creation_operator([2,1,1])\n s[2, 1, 1]\n sage: s(0).hl_creation_operator([2,1,1])\n 0\n sage: s([3,2]).hl_creation_operator([2,1,1])\n (t^2-t)*s[2, 2, 2, 2, 1] + t^3*s[3, 2, 2, 1, 1] + (t^3-t^2)*s[3, 2, 2, 2] + t^3*s[3, 3, 1, 1, 1] + t^4*s[3, 3, 2, 1] + t^3*s[4, 2, 1, 1, 1] + t^4*s[4, 2, 2, 1] + 2*t^4*s[4, 3, 1, 1] + t^5*s[4, 3, 2] + t^5*s[4, 4, 1] + t^4*s[5, 2, 1, 1] + t^5*s[5, 3, 1]\n\n TESTS::\n\n sage: s(0).hl_creation_operator([1])\n 0\n "
s = self.parent().realization_of().schur()
if (t is None):
if hasattr(self.parent(), 't'):
t = self.parent().t
else:
t = QQ['t'].gen()
P = self.parent()
self = s(self)
return P(((self * s(nu)) + s.sum(((s.sum_of_terms(((lam, c) for (lam, c) in (s(mu) * s(nu)) if (len(lam) <= len(nu)))) * self.skew_by(s(mu).plethysm(((t - 1) * s([1]))))) for d in range(self.degree()) for mu in Partitions((d + 1), max_length=len(nu))))))<|docstring|>This is the vertex operator that generalizes Jing's operator.
It is a linear operator that raises the degree by
`|\nu|`. This creation operator is a t-analogue of
multiplication by ``s(nu)`` .
.. SEEALSO:: Proposition 5 in [SZ2001]_.
INPUT:
- ``nu`` -- a partition
- ``t`` -- (default: ``None``, in which case ``t`` is used) a parameter
REFERENCES:
.. [SZ2001] M. Shimozono, M. Zabrocki,
Hall-Littlewood vertex operators and generalized Kostka polynomials.
Adv. Math. 158 (2001), no. 1, 66-85.
EXAMPLES::
sage: s = SymmetricFunctions(QQ['t']).s()
sage: s([2]).hl_creation_operator([3,2])
s[3, 2, 2] + t*s[3, 3, 1] + t*s[4, 2, 1] + t^2*s[4, 3] + t^2*s[5, 2]
sage: Sym = SymmetricFunctions(FractionField(QQ['t']))
sage: HLQp = Sym.hall_littlewood().Qp()
sage: s = Sym.s()
sage: HLQp(s([2]).hl_creation_operator([2]).hl_creation_operator([3]))
HLQp[3, 2, 2]
sage: s([2,2]).hl_creation_operator([2,1])
t*s[2, 2, 2, 1] + t^2*s[3, 2, 1, 1] + t^2*s[3, 2, 2] + t^3*s[3, 3, 1] + t^3*s[4, 2, 1] + t^4*s[4, 3]
sage: s(1).hl_creation_operator([2,1,1])
s[2, 1, 1]
sage: s(0).hl_creation_operator([2,1,1])
0
sage: s([3,2]).hl_creation_operator([2,1,1])
(t^2-t)*s[2, 2, 2, 2, 1] + t^3*s[3, 2, 2, 1, 1] + (t^3-t^2)*s[3, 2, 2, 2] + t^3*s[3, 3, 1, 1, 1] + t^4*s[3, 3, 2, 1] + t^3*s[4, 2, 1, 1, 1] + t^4*s[4, 2, 2, 1] + 2*t^4*s[4, 3, 1, 1] + t^5*s[4, 3, 2] + t^5*s[4, 4, 1] + t^4*s[5, 2, 1, 1] + t^5*s[5, 3, 1]
TESTS::
sage: s(0).hl_creation_operator([1])
0<|endoftext|>
|
3d8fa118d41054cf32e963b0598a0baeed982acc64d386f3db295a959ad43b3e
|
def is_integral_domain(self, proof=True):
'\n Return whether ``self`` is an integral domain. (It is if\n and only if the base ring is an integral domain.)\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``proof`` -- an optional argument (default value: ``True``)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_integral_domain()\n True\n\n The following doctest is disabled pending :trac:`10963`::\n\n sage: s = SymmetricFunctions(Zmod(14)).s() # not tested\n sage: s.is_integral_domain() # not tested\n False\n '
return self.base_ring().is_integral_domain()
|
Return whether ``self`` is an integral domain. (It is if
and only if the base ring is an integral domain.)
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``proof`` -- an optional argument (default value: ``True``)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s.is_integral_domain()
True
The following doctest is disabled pending :trac:`10963`::
sage: s = SymmetricFunctions(Zmod(14)).s() # not tested
sage: s.is_integral_domain() # not tested
False
|
src/sage/combinat/sf/sfa.py
|
is_integral_domain
|
bopopescu/sagesmc
| 5 |
python
|
def is_integral_domain(self, proof=True):
'\n Return whether ``self`` is an integral domain. (It is if\n and only if the base ring is an integral domain.)\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``proof`` -- an optional argument (default value: ``True``)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_integral_domain()\n True\n\n The following doctest is disabled pending :trac:`10963`::\n\n sage: s = SymmetricFunctions(Zmod(14)).s() # not tested\n sage: s.is_integral_domain() # not tested\n False\n '
return self.base_ring().is_integral_domain()
|
def is_integral_domain(self, proof=True):
'\n Return whether ``self`` is an integral domain. (It is if\n and only if the base ring is an integral domain.)\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``proof`` -- an optional argument (default value: ``True``)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_integral_domain()\n True\n\n The following doctest is disabled pending :trac:`10963`::\n\n sage: s = SymmetricFunctions(Zmod(14)).s() # not tested\n sage: s.is_integral_domain() # not tested\n False\n '
return self.base_ring().is_integral_domain()<|docstring|>Return whether ``self`` is an integral domain. (It is if
and only if the base ring is an integral domain.)
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``proof`` -- an optional argument (default value: ``True``)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s.is_integral_domain()
True
The following doctest is disabled pending :trac:`10963`::
sage: s = SymmetricFunctions(Zmod(14)).s() # not tested
sage: s.is_integral_domain() # not tested
False<|endoftext|>
|
3c649586bb6875f1b8d6dd972c4f6faf72143348e3b6541a97eed873c3c24ac6
|
def is_field(self, proof=True):
'\n Return whether ``self`` is a field. (It is not.)\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``proof`` -- an optional argument (default value: ``True``)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_field()\n False\n '
return False
|
Return whether ``self`` is a field. (It is not.)
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``proof`` -- an optional argument (default value: ``True``)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s.is_field()
False
|
src/sage/combinat/sf/sfa.py
|
is_field
|
bopopescu/sagesmc
| 5 |
python
|
def is_field(self, proof=True):
'\n Return whether ``self`` is a field. (It is not.)\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``proof`` -- an optional argument (default value: ``True``)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_field()\n False\n '
return False
|
def is_field(self, proof=True):
'\n Return whether ``self`` is a field. (It is not.)\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``proof`` -- an optional argument (default value: ``True``)\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_field()\n False\n '
return False<|docstring|>Return whether ``self`` is a field. (It is not.)
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``proof`` -- an optional argument (default value: ``True``)
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s.is_field()
False<|endoftext|>
|
7698d217483a5760dd84d96c78b2e7db8cb59e78063492ce43397e7ea05d7e04
|
def is_commutative(self):
'\n Returns whether this symmetric function algebra is commutative.\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_commutative()\n True\n '
return self.base_ring().is_commutative()
|
Returns whether this symmetric function algebra is commutative.
INPUT:
- ``self`` -- a basis of the symmetric functions
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s.is_commutative()
True
|
src/sage/combinat/sf/sfa.py
|
is_commutative
|
bopopescu/sagesmc
| 5 |
python
|
def is_commutative(self):
'\n Returns whether this symmetric function algebra is commutative.\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_commutative()\n True\n '
return self.base_ring().is_commutative()
|
def is_commutative(self):
'\n Returns whether this symmetric function algebra is commutative.\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n\n EXAMPLES::\n\n sage: s = SymmetricFunctions(QQ).s()\n sage: s.is_commutative()\n True\n '
return self.base_ring().is_commutative()<|docstring|>Returns whether this symmetric function algebra is commutative.
INPUT:
- ``self`` -- a basis of the symmetric functions
EXAMPLES::
sage: s = SymmetricFunctions(QQ).s()
sage: s.is_commutative()
True<|endoftext|>
|
86e4e1e109f4be4593978dccff5517bed67d9958f547b2276d55c483410fa241
|
def _repr_(self):
'\n Text representation of this basis of symmetric functions\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(FractionField(QQ[\'q,t\'])); Sym\n Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field\n sage: Sym.p()\n Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the powersum basis\n\n In the following examples, we rename {{{Sym}}} for brevity::\n\n sage: Sym.rename("Sym"); Sym\n Sym\n\n Classical bases::\n\n sage: Sym.s()\n Sym in the Schur basis\n sage: Sym.p()\n Sym in the powersum basis\n sage: Sym.m()\n Sym in the monomial basis\n sage: Sym.e()\n Sym in the elementary basis\n sage: Sym.h()\n Sym in the homogeneous basis\n sage: Sym.f()\n Sym in the forgotten basis\n\n Macdonald polynomials::\n\n sage: Sym.macdonald().P()\n Sym in the Macdonald P basis\n sage: Sym.macdonald().Q()\n Sym in the Macdonald Q basis\n sage: Sym.macdonald().J()\n Sym in the Macdonald J basis\n sage: Sym.macdonald().H()\n Sym in the Macdonald H basis\n sage: Sym.macdonald().Ht()\n Sym in the Macdonald Ht basis\n sage: Sym.macdonald().S()\n Sym in the Macdonald S basis\n\n Macdonald polynomials, with specialized parameters::\n\n sage: Sym.macdonald(q=1).S()\n Sym in the Macdonald S with q=1 basis\n sage: Sym.macdonald(q=1,t=3).P()\n Sym in the Macdonald P with q=1 and t=3 basis\n\n Hall-Littlewood polynomials:\n\n sage: Sym.hall_littlewood().P()\n Sym in the Hall-Littlewood P basis\n sage: Sym.hall_littlewood().Q()\n Sym in the Hall-Littlewood Q basis\n sage: Sym.hall_littlewood().Qp()\n Sym in the Hall-Littlewood Qp basis\n\n Hall-Littlewood polynomials, with specialized parameter::\n\n sage: Sym.hall_littlewood(t=1).P()\n Sym in the Hall-Littlewood P with t=1 basis\n\n Jack polynomials::\n\n sage: Sym.jack().J()\n Sym in the Jack J basis\n sage: Sym.jack().P()\n Sym in the Jack P basis\n sage: Sym.jack().Q()\n Sym in the Jack Q basis\n sage: Sym.jack().Qp()\n Sym in the Jack Qp basis\n\n Jack polynomials, with specialized parameter::\n\n sage: Sym.jack(t=1).J()\n Sym in the Jack J with t=1 basis\n\n Zonal polynomials::\n\n sage: Sym.zonal()\n Sym in the zonal basis\n\n LLT polynomials::\n\n sage: Sym.llt(3).hspin()\n Sym in the level 3 LLT spin basis\n sage: Sym.llt(3).hcospin()\n Sym in the level 3 LLT cospin basis\n\n LLT polynomials, with specialized parameter::\n\n sage: Sym.llt(3, t=1).hspin()\n Sym in the level 3 LLT spin with t=1 basis\n sage: Sym.llt(3, t=1).hcospin()\n Sym in the level 3 LLT cospin with t=1 basis\n\n TESTS::\n\n sage: Sym.s()._repr_()\n \'Sym in the Schur basis\'\n sage: Sym.s()._repr_.__module__\n \'sage.combinat.sf.sfa\'\n\n ::\n\n sage: Sym.rename()\n '
return ('%s in the %s basis' % (self.realization_of(), self.basis_name()))
|
Text representation of this basis of symmetric functions
INPUT:
- ``self`` -- a basis of the symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(FractionField(QQ['q,t'])); Sym
Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field
sage: Sym.p()
Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the powersum basis
In the following examples, we rename {{{Sym}}} for brevity::
sage: Sym.rename("Sym"); Sym
Sym
Classical bases::
sage: Sym.s()
Sym in the Schur basis
sage: Sym.p()
Sym in the powersum basis
sage: Sym.m()
Sym in the monomial basis
sage: Sym.e()
Sym in the elementary basis
sage: Sym.h()
Sym in the homogeneous basis
sage: Sym.f()
Sym in the forgotten basis
Macdonald polynomials::
sage: Sym.macdonald().P()
Sym in the Macdonald P basis
sage: Sym.macdonald().Q()
Sym in the Macdonald Q basis
sage: Sym.macdonald().J()
Sym in the Macdonald J basis
sage: Sym.macdonald().H()
Sym in the Macdonald H basis
sage: Sym.macdonald().Ht()
Sym in the Macdonald Ht basis
sage: Sym.macdonald().S()
Sym in the Macdonald S basis
Macdonald polynomials, with specialized parameters::
sage: Sym.macdonald(q=1).S()
Sym in the Macdonald S with q=1 basis
sage: Sym.macdonald(q=1,t=3).P()
Sym in the Macdonald P with q=1 and t=3 basis
Hall-Littlewood polynomials:
sage: Sym.hall_littlewood().P()
Sym in the Hall-Littlewood P basis
sage: Sym.hall_littlewood().Q()
Sym in the Hall-Littlewood Q basis
sage: Sym.hall_littlewood().Qp()
Sym in the Hall-Littlewood Qp basis
Hall-Littlewood polynomials, with specialized parameter::
sage: Sym.hall_littlewood(t=1).P()
Sym in the Hall-Littlewood P with t=1 basis
Jack polynomials::
sage: Sym.jack().J()
Sym in the Jack J basis
sage: Sym.jack().P()
Sym in the Jack P basis
sage: Sym.jack().Q()
Sym in the Jack Q basis
sage: Sym.jack().Qp()
Sym in the Jack Qp basis
Jack polynomials, with specialized parameter::
sage: Sym.jack(t=1).J()
Sym in the Jack J with t=1 basis
Zonal polynomials::
sage: Sym.zonal()
Sym in the zonal basis
LLT polynomials::
sage: Sym.llt(3).hspin()
Sym in the level 3 LLT spin basis
sage: Sym.llt(3).hcospin()
Sym in the level 3 LLT cospin basis
LLT polynomials, with specialized parameter::
sage: Sym.llt(3, t=1).hspin()
Sym in the level 3 LLT spin with t=1 basis
sage: Sym.llt(3, t=1).hcospin()
Sym in the level 3 LLT cospin with t=1 basis
TESTS::
sage: Sym.s()._repr_()
'Sym in the Schur basis'
sage: Sym.s()._repr_.__module__
'sage.combinat.sf.sfa'
::
sage: Sym.rename()
|
src/sage/combinat/sf/sfa.py
|
_repr_
|
bopopescu/sagesmc
| 5 |
python
|
def _repr_(self):
'\n Text representation of this basis of symmetric functions\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(FractionField(QQ[\'q,t\'])); Sym\n Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field\n sage: Sym.p()\n Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the powersum basis\n\n In the following examples, we rename {{{Sym}}} for brevity::\n\n sage: Sym.rename("Sym"); Sym\n Sym\n\n Classical bases::\n\n sage: Sym.s()\n Sym in the Schur basis\n sage: Sym.p()\n Sym in the powersum basis\n sage: Sym.m()\n Sym in the monomial basis\n sage: Sym.e()\n Sym in the elementary basis\n sage: Sym.h()\n Sym in the homogeneous basis\n sage: Sym.f()\n Sym in the forgotten basis\n\n Macdonald polynomials::\n\n sage: Sym.macdonald().P()\n Sym in the Macdonald P basis\n sage: Sym.macdonald().Q()\n Sym in the Macdonald Q basis\n sage: Sym.macdonald().J()\n Sym in the Macdonald J basis\n sage: Sym.macdonald().H()\n Sym in the Macdonald H basis\n sage: Sym.macdonald().Ht()\n Sym in the Macdonald Ht basis\n sage: Sym.macdonald().S()\n Sym in the Macdonald S basis\n\n Macdonald polynomials, with specialized parameters::\n\n sage: Sym.macdonald(q=1).S()\n Sym in the Macdonald S with q=1 basis\n sage: Sym.macdonald(q=1,t=3).P()\n Sym in the Macdonald P with q=1 and t=3 basis\n\n Hall-Littlewood polynomials:\n\n sage: Sym.hall_littlewood().P()\n Sym in the Hall-Littlewood P basis\n sage: Sym.hall_littlewood().Q()\n Sym in the Hall-Littlewood Q basis\n sage: Sym.hall_littlewood().Qp()\n Sym in the Hall-Littlewood Qp basis\n\n Hall-Littlewood polynomials, with specialized parameter::\n\n sage: Sym.hall_littlewood(t=1).P()\n Sym in the Hall-Littlewood P with t=1 basis\n\n Jack polynomials::\n\n sage: Sym.jack().J()\n Sym in the Jack J basis\n sage: Sym.jack().P()\n Sym in the Jack P basis\n sage: Sym.jack().Q()\n Sym in the Jack Q basis\n sage: Sym.jack().Qp()\n Sym in the Jack Qp basis\n\n Jack polynomials, with specialized parameter::\n\n sage: Sym.jack(t=1).J()\n Sym in the Jack J with t=1 basis\n\n Zonal polynomials::\n\n sage: Sym.zonal()\n Sym in the zonal basis\n\n LLT polynomials::\n\n sage: Sym.llt(3).hspin()\n Sym in the level 3 LLT spin basis\n sage: Sym.llt(3).hcospin()\n Sym in the level 3 LLT cospin basis\n\n LLT polynomials, with specialized parameter::\n\n sage: Sym.llt(3, t=1).hspin()\n Sym in the level 3 LLT spin with t=1 basis\n sage: Sym.llt(3, t=1).hcospin()\n Sym in the level 3 LLT cospin with t=1 basis\n\n TESTS::\n\n sage: Sym.s()._repr_()\n \'Sym in the Schur basis\'\n sage: Sym.s()._repr_.__module__\n \'sage.combinat.sf.sfa\'\n\n ::\n\n sage: Sym.rename()\n '
return ('%s in the %s basis' % (self.realization_of(), self.basis_name()))
|
def _repr_(self):
'\n Text representation of this basis of symmetric functions\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(FractionField(QQ[\'q,t\'])); Sym\n Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field\n sage: Sym.p()\n Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the powersum basis\n\n In the following examples, we rename {{{Sym}}} for brevity::\n\n sage: Sym.rename("Sym"); Sym\n Sym\n\n Classical bases::\n\n sage: Sym.s()\n Sym in the Schur basis\n sage: Sym.p()\n Sym in the powersum basis\n sage: Sym.m()\n Sym in the monomial basis\n sage: Sym.e()\n Sym in the elementary basis\n sage: Sym.h()\n Sym in the homogeneous basis\n sage: Sym.f()\n Sym in the forgotten basis\n\n Macdonald polynomials::\n\n sage: Sym.macdonald().P()\n Sym in the Macdonald P basis\n sage: Sym.macdonald().Q()\n Sym in the Macdonald Q basis\n sage: Sym.macdonald().J()\n Sym in the Macdonald J basis\n sage: Sym.macdonald().H()\n Sym in the Macdonald H basis\n sage: Sym.macdonald().Ht()\n Sym in the Macdonald Ht basis\n sage: Sym.macdonald().S()\n Sym in the Macdonald S basis\n\n Macdonald polynomials, with specialized parameters::\n\n sage: Sym.macdonald(q=1).S()\n Sym in the Macdonald S with q=1 basis\n sage: Sym.macdonald(q=1,t=3).P()\n Sym in the Macdonald P with q=1 and t=3 basis\n\n Hall-Littlewood polynomials:\n\n sage: Sym.hall_littlewood().P()\n Sym in the Hall-Littlewood P basis\n sage: Sym.hall_littlewood().Q()\n Sym in the Hall-Littlewood Q basis\n sage: Sym.hall_littlewood().Qp()\n Sym in the Hall-Littlewood Qp basis\n\n Hall-Littlewood polynomials, with specialized parameter::\n\n sage: Sym.hall_littlewood(t=1).P()\n Sym in the Hall-Littlewood P with t=1 basis\n\n Jack polynomials::\n\n sage: Sym.jack().J()\n Sym in the Jack J basis\n sage: Sym.jack().P()\n Sym in the Jack P basis\n sage: Sym.jack().Q()\n Sym in the Jack Q basis\n sage: Sym.jack().Qp()\n Sym in the Jack Qp basis\n\n Jack polynomials, with specialized parameter::\n\n sage: Sym.jack(t=1).J()\n Sym in the Jack J with t=1 basis\n\n Zonal polynomials::\n\n sage: Sym.zonal()\n Sym in the zonal basis\n\n LLT polynomials::\n\n sage: Sym.llt(3).hspin()\n Sym in the level 3 LLT spin basis\n sage: Sym.llt(3).hcospin()\n Sym in the level 3 LLT cospin basis\n\n LLT polynomials, with specialized parameter::\n\n sage: Sym.llt(3, t=1).hspin()\n Sym in the level 3 LLT spin with t=1 basis\n sage: Sym.llt(3, t=1).hcospin()\n Sym in the level 3 LLT cospin with t=1 basis\n\n TESTS::\n\n sage: Sym.s()._repr_()\n \'Sym in the Schur basis\'\n sage: Sym.s()._repr_.__module__\n \'sage.combinat.sf.sfa\'\n\n ::\n\n sage: Sym.rename()\n '
return ('%s in the %s basis' % (self.realization_of(), self.basis_name()))<|docstring|>Text representation of this basis of symmetric functions
INPUT:
- ``self`` -- a basis of the symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(FractionField(QQ['q,t'])); Sym
Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field
sage: Sym.p()
Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the powersum basis
In the following examples, we rename {{{Sym}}} for brevity::
sage: Sym.rename("Sym"); Sym
Sym
Classical bases::
sage: Sym.s()
Sym in the Schur basis
sage: Sym.p()
Sym in the powersum basis
sage: Sym.m()
Sym in the monomial basis
sage: Sym.e()
Sym in the elementary basis
sage: Sym.h()
Sym in the homogeneous basis
sage: Sym.f()
Sym in the forgotten basis
Macdonald polynomials::
sage: Sym.macdonald().P()
Sym in the Macdonald P basis
sage: Sym.macdonald().Q()
Sym in the Macdonald Q basis
sage: Sym.macdonald().J()
Sym in the Macdonald J basis
sage: Sym.macdonald().H()
Sym in the Macdonald H basis
sage: Sym.macdonald().Ht()
Sym in the Macdonald Ht basis
sage: Sym.macdonald().S()
Sym in the Macdonald S basis
Macdonald polynomials, with specialized parameters::
sage: Sym.macdonald(q=1).S()
Sym in the Macdonald S with q=1 basis
sage: Sym.macdonald(q=1,t=3).P()
Sym in the Macdonald P with q=1 and t=3 basis
Hall-Littlewood polynomials:
sage: Sym.hall_littlewood().P()
Sym in the Hall-Littlewood P basis
sage: Sym.hall_littlewood().Q()
Sym in the Hall-Littlewood Q basis
sage: Sym.hall_littlewood().Qp()
Sym in the Hall-Littlewood Qp basis
Hall-Littlewood polynomials, with specialized parameter::
sage: Sym.hall_littlewood(t=1).P()
Sym in the Hall-Littlewood P with t=1 basis
Jack polynomials::
sage: Sym.jack().J()
Sym in the Jack J basis
sage: Sym.jack().P()
Sym in the Jack P basis
sage: Sym.jack().Q()
Sym in the Jack Q basis
sage: Sym.jack().Qp()
Sym in the Jack Qp basis
Jack polynomials, with specialized parameter::
sage: Sym.jack(t=1).J()
Sym in the Jack J with t=1 basis
Zonal polynomials::
sage: Sym.zonal()
Sym in the zonal basis
LLT polynomials::
sage: Sym.llt(3).hspin()
Sym in the level 3 LLT spin basis
sage: Sym.llt(3).hcospin()
Sym in the level 3 LLT cospin basis
LLT polynomials, with specialized parameter::
sage: Sym.llt(3, t=1).hspin()
Sym in the level 3 LLT spin with t=1 basis
sage: Sym.llt(3, t=1).hcospin()
Sym in the level 3 LLT cospin with t=1 basis
TESTS::
sage: Sym.s()._repr_()
'Sym in the Schur basis'
sage: Sym.s()._repr_.__module__
'sage.combinat.sf.sfa'
::
sage: Sym.rename()<|endoftext|>
|
455d85ee84b496740547a999ee082052bda2e59405d8af5f3f52dff91f205f4a
|
@cached_method
def one_basis(self):
"\n Returns the empty partition, as per ``AlgebrasWithBasis.ParentMethods.one_basis``\n\n INPUT:\n\n - ``self`` -- a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ['t'].fraction_field())\n sage: s = Sym.s()\n sage: s.one_basis()\n []\n sage: Q = Sym.hall_littlewood().Q()\n sage: Q.one_basis()\n []\n\n .. TODO:: generalize to Modules.Graded.Connected.ParentMethods\n "
return sage.combinat.partition.Partition([])
|
Returns the empty partition, as per ``AlgebrasWithBasis.ParentMethods.one_basis``
INPUT:
- ``self`` -- a basis of the ring of symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ['t'].fraction_field())
sage: s = Sym.s()
sage: s.one_basis()
[]
sage: Q = Sym.hall_littlewood().Q()
sage: Q.one_basis()
[]
.. TODO:: generalize to Modules.Graded.Connected.ParentMethods
|
src/sage/combinat/sf/sfa.py
|
one_basis
|
bopopescu/sagesmc
| 5 |
python
|
@cached_method
def one_basis(self):
"\n Returns the empty partition, as per ``AlgebrasWithBasis.ParentMethods.one_basis``\n\n INPUT:\n\n - ``self`` -- a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ['t'].fraction_field())\n sage: s = Sym.s()\n sage: s.one_basis()\n []\n sage: Q = Sym.hall_littlewood().Q()\n sage: Q.one_basis()\n []\n\n .. TODO:: generalize to Modules.Graded.Connected.ParentMethods\n "
return sage.combinat.partition.Partition([])
|
@cached_method
def one_basis(self):
"\n Returns the empty partition, as per ``AlgebrasWithBasis.ParentMethods.one_basis``\n\n INPUT:\n\n - ``self`` -- a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ['t'].fraction_field())\n sage: s = Sym.s()\n sage: s.one_basis()\n []\n sage: Q = Sym.hall_littlewood().Q()\n sage: Q.one_basis()\n []\n\n .. TODO:: generalize to Modules.Graded.Connected.ParentMethods\n "
return sage.combinat.partition.Partition([])<|docstring|>Returns the empty partition, as per ``AlgebrasWithBasis.ParentMethods.one_basis``
INPUT:
- ``self`` -- a basis of the ring of symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ['t'].fraction_field())
sage: s = Sym.s()
sage: s.one_basis()
[]
sage: Q = Sym.hall_littlewood().Q()
sage: Q.one_basis()
[]
.. TODO:: generalize to Modules.Graded.Connected.ParentMethods<|endoftext|>
|
f1fff864658267ca5096e1f88043861ae387d36f1be3ebcabc50d1b62978a76c
|
def degree_on_basis(self, b):
"\n Return the degree of the basis element indexed by ``b``.\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``b`` -- a partition\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ['q,t'].fraction_field())\n sage: m = Sym.monomial()\n sage: m.degree_on_basis(Partition([3,2]))\n 5\n sage: P = Sym.macdonald().P()\n sage: P.degree_on_basis(Partition([]))\n 0\n "
return sum(b)
|
Return the degree of the basis element indexed by ``b``.
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``b`` -- a partition
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ['q,t'].fraction_field())
sage: m = Sym.monomial()
sage: m.degree_on_basis(Partition([3,2]))
5
sage: P = Sym.macdonald().P()
sage: P.degree_on_basis(Partition([]))
0
|
src/sage/combinat/sf/sfa.py
|
degree_on_basis
|
bopopescu/sagesmc
| 5 |
python
|
def degree_on_basis(self, b):
"\n Return the degree of the basis element indexed by ``b``.\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``b`` -- a partition\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ['q,t'].fraction_field())\n sage: m = Sym.monomial()\n sage: m.degree_on_basis(Partition([3,2]))\n 5\n sage: P = Sym.macdonald().P()\n sage: P.degree_on_basis(Partition([]))\n 0\n "
return sum(b)
|
def degree_on_basis(self, b):
"\n Return the degree of the basis element indexed by ``b``.\n\n INPUT:\n\n - ``self`` -- a basis of the symmetric functions\n - ``b`` -- a partition\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ['q,t'].fraction_field())\n sage: m = Sym.monomial()\n sage: m.degree_on_basis(Partition([3,2]))\n 5\n sage: P = Sym.macdonald().P()\n sage: P.degree_on_basis(Partition([]))\n 0\n "
return sum(b)<|docstring|>Return the degree of the basis element indexed by ``b``.
INPUT:
- ``self`` -- a basis of the symmetric functions
- ``b`` -- a partition
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ['q,t'].fraction_field())
sage: m = Sym.monomial()
sage: m.degree_on_basis(Partition([3,2]))
5
sage: P = Sym.macdonald().P()
sage: P.degree_on_basis(Partition([]))
0<|endoftext|>
|
c430f0e6606ddbe4b87606750e4e1818a1ff58a5e839b9528cbfbd184d0447f5
|
def antipode_by_coercion(self, element):
'\n The antipode of ``element``.\n\n INPUT:\n\n - ``element`` -- element in a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: p = Sym.p()\n sage: s = Sym.s()\n sage: e = Sym.e()\n sage: h = Sym.h()\n sage: (h([]) + h([1])).antipode() # indirect doctest\n h[] - h[1]\n sage: (s([]) + s([1]) + s[2]).antipode()\n s[] - s[1] + s[1, 1]\n sage: (p([2]) + p([3])).antipode()\n -p[2] - p[3]\n sage: (e([2]) + e([3])).antipode()\n e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]\n sage: f = Sym.f()\n sage: f([3,2,1]).antipode()\n -f[3, 2, 1] - 4*f[3, 3] - 2*f[4, 2] - 2*f[5, 1] - 6*f[6]\n\n The antipode is an involution::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: s = Sym.s()\n sage: all( s[u].antipode().antipode() == s[u] for u in Partitions(4) )\n True\n\n The antipode is an algebra homomorphism::\n\n sage: Sym = SymmetricFunctions(FiniteField(23))\n sage: h = Sym.h()\n sage: all( all( (s[u] * s[v]).antipode() == s[u].antipode() * s[v].antipode()\n ....: for u in Partitions(3) )\n ....: for v in Partitions(3) )\n True\n\n TESTS:\n\n Everything works over `\\ZZ`::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: s = Sym.s()\n sage: e = Sym.e()\n sage: h = Sym.h()\n sage: (h([]) + h([1])).antipode() # indirect doctest\n h[] - h[1]\n sage: (s([]) + s([1]) + s[2]).antipode()\n s[] - s[1] + s[1, 1]\n sage: (p([2]) + p([3])).antipode()\n -p[2] - p[3]\n sage: (e([2]) + e([3])).antipode()\n e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]\n '
return self.degree_negation(element.omega())
|
The antipode of ``element``.
INPUT:
- ``element`` -- element in a basis of the ring of symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: p = Sym.p()
sage: s = Sym.s()
sage: e = Sym.e()
sage: h = Sym.h()
sage: (h([]) + h([1])).antipode() # indirect doctest
h[] - h[1]
sage: (s([]) + s([1]) + s[2]).antipode()
s[] - s[1] + s[1, 1]
sage: (p([2]) + p([3])).antipode()
-p[2] - p[3]
sage: (e([2]) + e([3])).antipode()
e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]
sage: f = Sym.f()
sage: f([3,2,1]).antipode()
-f[3, 2, 1] - 4*f[3, 3] - 2*f[4, 2] - 2*f[5, 1] - 6*f[6]
The antipode is an involution::
sage: Sym = SymmetricFunctions(ZZ)
sage: s = Sym.s()
sage: all( s[u].antipode().antipode() == s[u] for u in Partitions(4) )
True
The antipode is an algebra homomorphism::
sage: Sym = SymmetricFunctions(FiniteField(23))
sage: h = Sym.h()
sage: all( all( (s[u] * s[v]).antipode() == s[u].antipode() * s[v].antipode()
....: for u in Partitions(3) )
....: for v in Partitions(3) )
True
TESTS:
Everything works over `\ZZ`::
sage: Sym = SymmetricFunctions(ZZ)
sage: p = Sym.p()
sage: s = Sym.s()
sage: e = Sym.e()
sage: h = Sym.h()
sage: (h([]) + h([1])).antipode() # indirect doctest
h[] - h[1]
sage: (s([]) + s([1]) + s[2]).antipode()
s[] - s[1] + s[1, 1]
sage: (p([2]) + p([3])).antipode()
-p[2] - p[3]
sage: (e([2]) + e([3])).antipode()
e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]
|
src/sage/combinat/sf/sfa.py
|
antipode_by_coercion
|
bopopescu/sagesmc
| 5 |
python
|
def antipode_by_coercion(self, element):
'\n The antipode of ``element``.\n\n INPUT:\n\n - ``element`` -- element in a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: p = Sym.p()\n sage: s = Sym.s()\n sage: e = Sym.e()\n sage: h = Sym.h()\n sage: (h([]) + h([1])).antipode() # indirect doctest\n h[] - h[1]\n sage: (s([]) + s([1]) + s[2]).antipode()\n s[] - s[1] + s[1, 1]\n sage: (p([2]) + p([3])).antipode()\n -p[2] - p[3]\n sage: (e([2]) + e([3])).antipode()\n e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]\n sage: f = Sym.f()\n sage: f([3,2,1]).antipode()\n -f[3, 2, 1] - 4*f[3, 3] - 2*f[4, 2] - 2*f[5, 1] - 6*f[6]\n\n The antipode is an involution::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: s = Sym.s()\n sage: all( s[u].antipode().antipode() == s[u] for u in Partitions(4) )\n True\n\n The antipode is an algebra homomorphism::\n\n sage: Sym = SymmetricFunctions(FiniteField(23))\n sage: h = Sym.h()\n sage: all( all( (s[u] * s[v]).antipode() == s[u].antipode() * s[v].antipode()\n ....: for u in Partitions(3) )\n ....: for v in Partitions(3) )\n True\n\n TESTS:\n\n Everything works over `\\ZZ`::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: s = Sym.s()\n sage: e = Sym.e()\n sage: h = Sym.h()\n sage: (h([]) + h([1])).antipode() # indirect doctest\n h[] - h[1]\n sage: (s([]) + s([1]) + s[2]).antipode()\n s[] - s[1] + s[1, 1]\n sage: (p([2]) + p([3])).antipode()\n -p[2] - p[3]\n sage: (e([2]) + e([3])).antipode()\n e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]\n '
return self.degree_negation(element.omega())
|
def antipode_by_coercion(self, element):
'\n The antipode of ``element``.\n\n INPUT:\n\n - ``element`` -- element in a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: p = Sym.p()\n sage: s = Sym.s()\n sage: e = Sym.e()\n sage: h = Sym.h()\n sage: (h([]) + h([1])).antipode() # indirect doctest\n h[] - h[1]\n sage: (s([]) + s([1]) + s[2]).antipode()\n s[] - s[1] + s[1, 1]\n sage: (p([2]) + p([3])).antipode()\n -p[2] - p[3]\n sage: (e([2]) + e([3])).antipode()\n e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]\n sage: f = Sym.f()\n sage: f([3,2,1]).antipode()\n -f[3, 2, 1] - 4*f[3, 3] - 2*f[4, 2] - 2*f[5, 1] - 6*f[6]\n\n The antipode is an involution::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: s = Sym.s()\n sage: all( s[u].antipode().antipode() == s[u] for u in Partitions(4) )\n True\n\n The antipode is an algebra homomorphism::\n\n sage: Sym = SymmetricFunctions(FiniteField(23))\n sage: h = Sym.h()\n sage: all( all( (s[u] * s[v]).antipode() == s[u].antipode() * s[v].antipode()\n ....: for u in Partitions(3) )\n ....: for v in Partitions(3) )\n True\n\n TESTS:\n\n Everything works over `\\ZZ`::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: p = Sym.p()\n sage: s = Sym.s()\n sage: e = Sym.e()\n sage: h = Sym.h()\n sage: (h([]) + h([1])).antipode() # indirect doctest\n h[] - h[1]\n sage: (s([]) + s([1]) + s[2]).antipode()\n s[] - s[1] + s[1, 1]\n sage: (p([2]) + p([3])).antipode()\n -p[2] - p[3]\n sage: (e([2]) + e([3])).antipode()\n e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]\n '
return self.degree_negation(element.omega())<|docstring|>The antipode of ``element``.
INPUT:
- ``element`` -- element in a basis of the ring of symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: p = Sym.p()
sage: s = Sym.s()
sage: e = Sym.e()
sage: h = Sym.h()
sage: (h([]) + h([1])).antipode() # indirect doctest
h[] - h[1]
sage: (s([]) + s([1]) + s[2]).antipode()
s[] - s[1] + s[1, 1]
sage: (p([2]) + p([3])).antipode()
-p[2] - p[3]
sage: (e([2]) + e([3])).antipode()
e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]
sage: f = Sym.f()
sage: f([3,2,1]).antipode()
-f[3, 2, 1] - 4*f[3, 3] - 2*f[4, 2] - 2*f[5, 1] - 6*f[6]
The antipode is an involution::
sage: Sym = SymmetricFunctions(ZZ)
sage: s = Sym.s()
sage: all( s[u].antipode().antipode() == s[u] for u in Partitions(4) )
True
The antipode is an algebra homomorphism::
sage: Sym = SymmetricFunctions(FiniteField(23))
sage: h = Sym.h()
sage: all( all( (s[u] * s[v]).antipode() == s[u].antipode() * s[v].antipode()
....: for u in Partitions(3) )
....: for v in Partitions(3) )
True
TESTS:
Everything works over `\ZZ`::
sage: Sym = SymmetricFunctions(ZZ)
sage: p = Sym.p()
sage: s = Sym.s()
sage: e = Sym.e()
sage: h = Sym.h()
sage: (h([]) + h([1])).antipode() # indirect doctest
h[] - h[1]
sage: (s([]) + s([1]) + s[2]).antipode()
s[] - s[1] + s[1, 1]
sage: (p([2]) + p([3])).antipode()
-p[2] - p[3]
sage: (e([2]) + e([3])).antipode()
e[1, 1] - e[1, 1, 1] - e[2] + 2*e[2, 1] - e[3]<|endoftext|>
|
057ed0a534cfceb6b06f0557d3fea8fb827d3f43ea74718f97b8cab74c62172c
|
def counit(self, element):
'\n Return the counit of ``element``.\n\n The counit is the constant term of ``element``.\n\n INPUT:\n\n - ``element`` -- element in a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 3*m[[]]\n sage: f.counit()\n 3\n '
return element.degree_zero_coefficient()
|
Return the counit of ``element``.
The counit is the constant term of ``element``.
INPUT:
- ``element`` -- element in a basis of the ring of symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.monomial()
sage: f = 2*m[2,1] + 3*m[[]]
sage: f.counit()
3
|
src/sage/combinat/sf/sfa.py
|
counit
|
bopopescu/sagesmc
| 5 |
python
|
def counit(self, element):
'\n Return the counit of ``element``.\n\n The counit is the constant term of ``element``.\n\n INPUT:\n\n - ``element`` -- element in a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 3*m[[]]\n sage: f.counit()\n 3\n '
return element.degree_zero_coefficient()
|
def counit(self, element):
'\n Return the counit of ``element``.\n\n The counit is the constant term of ``element``.\n\n INPUT:\n\n - ``element`` -- element in a basis of the ring of symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 3*m[[]]\n sage: f.counit()\n 3\n '
return element.degree_zero_coefficient()<|docstring|>Return the counit of ``element``.
The counit is the constant term of ``element``.
INPUT:
- ``element`` -- element in a basis of the ring of symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.monomial()
sage: f = 2*m[2,1] + 3*m[[]]
sage: f.counit()
3<|endoftext|>
|
c28e40547dda9449a0aceb7a79860173525af91ed9a58da3239ad1c4ba6c70fb
|
def degree_negation(self, element):
'\n Return the image of ``element`` under the degree negation\n automorphism of the ring of symmetric functions.\n\n The degree negation is the automorphism which scales every\n homogeneous element of degree `k` by `(-1)^k` (for all `k`).\n\n INPUT:\n\n - ``element`` -- symmetric function written in ``self``\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 4*m[1,1] - 5*m[1] - 3*m[[]]\n sage: m.degree_negation(f)\n -3*m[] + 5*m[1] + 4*m[1, 1] - 2*m[2, 1]\n\n TESTS:\n\n Using :meth:`degree_negation` on an element of a different\n basis works correctly::\n\n sage: e = Sym.elementary()\n sage: m.degree_negation(e[3])\n -m[1, 1, 1]\n sage: m.degree_negation(m(e[3]))\n -m[1, 1, 1]\n '
return self.sum_of_terms([(lam, (((- 1) ** (sum(lam) % 2)) * a)) for (lam, a) in self(element)])
|
Return the image of ``element`` under the degree negation
automorphism of the ring of symmetric functions.
The degree negation is the automorphism which scales every
homogeneous element of degree `k` by `(-1)^k` (for all `k`).
INPUT:
- ``element`` -- symmetric function written in ``self``
EXAMPLES::
sage: Sym = SymmetricFunctions(ZZ)
sage: m = Sym.monomial()
sage: f = 2*m[2,1] + 4*m[1,1] - 5*m[1] - 3*m[[]]
sage: m.degree_negation(f)
-3*m[] + 5*m[1] + 4*m[1, 1] - 2*m[2, 1]
TESTS:
Using :meth:`degree_negation` on an element of a different
basis works correctly::
sage: e = Sym.elementary()
sage: m.degree_negation(e[3])
-m[1, 1, 1]
sage: m.degree_negation(m(e[3]))
-m[1, 1, 1]
|
src/sage/combinat/sf/sfa.py
|
degree_negation
|
bopopescu/sagesmc
| 5 |
python
|
def degree_negation(self, element):
'\n Return the image of ``element`` under the degree negation\n automorphism of the ring of symmetric functions.\n\n The degree negation is the automorphism which scales every\n homogeneous element of degree `k` by `(-1)^k` (for all `k`).\n\n INPUT:\n\n - ``element`` -- symmetric function written in ``self``\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 4*m[1,1] - 5*m[1] - 3*m[[]]\n sage: m.degree_negation(f)\n -3*m[] + 5*m[1] + 4*m[1, 1] - 2*m[2, 1]\n\n TESTS:\n\n Using :meth:`degree_negation` on an element of a different\n basis works correctly::\n\n sage: e = Sym.elementary()\n sage: m.degree_negation(e[3])\n -m[1, 1, 1]\n sage: m.degree_negation(m(e[3]))\n -m[1, 1, 1]\n '
return self.sum_of_terms([(lam, (((- 1) ** (sum(lam) % 2)) * a)) for (lam, a) in self(element)])
|
def degree_negation(self, element):
'\n Return the image of ``element`` under the degree negation\n automorphism of the ring of symmetric functions.\n\n The degree negation is the automorphism which scales every\n homogeneous element of degree `k` by `(-1)^k` (for all `k`).\n\n INPUT:\n\n - ``element`` -- symmetric function written in ``self``\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(ZZ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 4*m[1,1] - 5*m[1] - 3*m[[]]\n sage: m.degree_negation(f)\n -3*m[] + 5*m[1] + 4*m[1, 1] - 2*m[2, 1]\n\n TESTS:\n\n Using :meth:`degree_negation` on an element of a different\n basis works correctly::\n\n sage: e = Sym.elementary()\n sage: m.degree_negation(e[3])\n -m[1, 1, 1]\n sage: m.degree_negation(m(e[3]))\n -m[1, 1, 1]\n '
return self.sum_of_terms([(lam, (((- 1) ** (sum(lam) % 2)) * a)) for (lam, a) in self(element)])<|docstring|>Return the image of ``element`` under the degree negation
automorphism of the ring of symmetric functions.
The degree negation is the automorphism which scales every
homogeneous element of degree `k` by `(-1)^k` (for all `k`).
INPUT:
- ``element`` -- symmetric function written in ``self``
EXAMPLES::
sage: Sym = SymmetricFunctions(ZZ)
sage: m = Sym.monomial()
sage: f = 2*m[2,1] + 4*m[1,1] - 5*m[1] - 3*m[[]]
sage: m.degree_negation(f)
-3*m[] + 5*m[1] + 4*m[1, 1] - 2*m[2, 1]
TESTS:
Using :meth:`degree_negation` on an element of a different
basis works correctly::
sage: e = Sym.elementary()
sage: m.degree_negation(e[3])
-m[1, 1, 1]
sage: m.degree_negation(m(e[3]))
-m[1, 1, 1]<|endoftext|>
|
e26d5a55608c2912c3efa6790f646e9e9283e64fcff48fa77b72a1fcd4a4f3a0
|
def corresponding_basis_over(self, R):
"\n Return the realization of symmetric functions corresponding to\n ``self`` but over the base ring ``R``. Only works when ``self``\n is one of the classical bases, not one of the `q,t`-dependent\n ones. In the latter case, ``None`` is returned instead.\n\n INPUT:\n\n - ``R`` -- a commutative ring\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: m.corresponding_basis_over(ZZ)\n Symmetric Functions over Integer Ring in the monomial basis\n\n sage: Sym = SymmetricFunctions(CyclotomicField())\n sage: s = Sym.schur()\n sage: s.corresponding_basis_over(Integers(13))\n Symmetric Functions over Ring of integers modulo 13 in the Schur basis\n\n sage: P = ZZ['q','t']\n sage: Sym = SymmetricFunctions(P)\n sage: mj = Sym.macdonald().J()\n sage: mj.corresponding_basis_over(Integers(13))\n\n TESTS:\n\n Let's check that this handles each of the bases properly::\n\n sage: P = QQ['q','t']\n sage: Sym = SymmetricFunctions(P)\n sage: Q = CyclotomicField()['q','t']\n sage: Sym.s().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the Schur basis\n sage: Sym.p().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the powersum basis\n sage: Sym.m().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the monomial basis\n sage: Sym.e().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the elementary basis\n sage: Sym.h().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the homogeneous basis\n sage: Sym.f().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the forgotten basis\n sage: Sym.w().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the Witt basis\n sage: Sym.macdonald().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().J().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().H().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().Ht().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().S().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald(q=1).S().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald(q=1,t=3).P().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().Qp().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood(t=1).P().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().J().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().Qp().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack(t=1).J().corresponding_basis_over(CyclotomicField())\n sage: Sym.zonal().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the zonal basis\n sage: Sym.llt(3).hspin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3).hcospin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3, t=1).hspin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3, t=1).hcospin().corresponding_basis_over(CyclotomicField())\n\n .. TODO::\n\n This function is an ugly hack using strings. It should be\n rewritten as soon as the bases of ``SymmetricFunctions`` are\n put on a more robust and systematic footing.\n "
from sage.combinat.sf.sf import SymmetricFunctions
from sage.misc.misc import attrcall
try:
return attrcall(self._basis)(SymmetricFunctions(R))
except AttributeError:
return None
|
Return the realization of symmetric functions corresponding to
``self`` but over the base ring ``R``. Only works when ``self``
is one of the classical bases, not one of the `q,t`-dependent
ones. In the latter case, ``None`` is returned instead.
INPUT:
- ``R`` -- a commutative ring
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.monomial()
sage: m.corresponding_basis_over(ZZ)
Symmetric Functions over Integer Ring in the monomial basis
sage: Sym = SymmetricFunctions(CyclotomicField())
sage: s = Sym.schur()
sage: s.corresponding_basis_over(Integers(13))
Symmetric Functions over Ring of integers modulo 13 in the Schur basis
sage: P = ZZ['q','t']
sage: Sym = SymmetricFunctions(P)
sage: mj = Sym.macdonald().J()
sage: mj.corresponding_basis_over(Integers(13))
TESTS:
Let's check that this handles each of the bases properly::
sage: P = QQ['q','t']
sage: Sym = SymmetricFunctions(P)
sage: Q = CyclotomicField()['q','t']
sage: Sym.s().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the Schur basis
sage: Sym.p().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the powersum basis
sage: Sym.m().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the monomial basis
sage: Sym.e().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the elementary basis
sage: Sym.h().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the homogeneous basis
sage: Sym.f().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the forgotten basis
sage: Sym.w().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the Witt basis
sage: Sym.macdonald().P().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().Q().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().J().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().H().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().Ht().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().S().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald(q=1).S().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald(q=1,t=3).P().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood().P().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood().Q().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood().Qp().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood(t=1).P().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().J().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().P().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().Q().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().Qp().corresponding_basis_over(CyclotomicField())
sage: Sym.jack(t=1).J().corresponding_basis_over(CyclotomicField())
sage: Sym.zonal().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the zonal basis
sage: Sym.llt(3).hspin().corresponding_basis_over(CyclotomicField())
sage: Sym.llt(3).hcospin().corresponding_basis_over(CyclotomicField())
sage: Sym.llt(3, t=1).hspin().corresponding_basis_over(CyclotomicField())
sage: Sym.llt(3, t=1).hcospin().corresponding_basis_over(CyclotomicField())
.. TODO::
This function is an ugly hack using strings. It should be
rewritten as soon as the bases of ``SymmetricFunctions`` are
put on a more robust and systematic footing.
|
src/sage/combinat/sf/sfa.py
|
corresponding_basis_over
|
bopopescu/sagesmc
| 5 |
python
|
def corresponding_basis_over(self, R):
"\n Return the realization of symmetric functions corresponding to\n ``self`` but over the base ring ``R``. Only works when ``self``\n is one of the classical bases, not one of the `q,t`-dependent\n ones. In the latter case, ``None`` is returned instead.\n\n INPUT:\n\n - ``R`` -- a commutative ring\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: m.corresponding_basis_over(ZZ)\n Symmetric Functions over Integer Ring in the monomial basis\n\n sage: Sym = SymmetricFunctions(CyclotomicField())\n sage: s = Sym.schur()\n sage: s.corresponding_basis_over(Integers(13))\n Symmetric Functions over Ring of integers modulo 13 in the Schur basis\n\n sage: P = ZZ['q','t']\n sage: Sym = SymmetricFunctions(P)\n sage: mj = Sym.macdonald().J()\n sage: mj.corresponding_basis_over(Integers(13))\n\n TESTS:\n\n Let's check that this handles each of the bases properly::\n\n sage: P = QQ['q','t']\n sage: Sym = SymmetricFunctions(P)\n sage: Q = CyclotomicField()['q','t']\n sage: Sym.s().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the Schur basis\n sage: Sym.p().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the powersum basis\n sage: Sym.m().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the monomial basis\n sage: Sym.e().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the elementary basis\n sage: Sym.h().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the homogeneous basis\n sage: Sym.f().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the forgotten basis\n sage: Sym.w().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the Witt basis\n sage: Sym.macdonald().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().J().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().H().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().Ht().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().S().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald(q=1).S().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald(q=1,t=3).P().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().Qp().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood(t=1).P().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().J().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().Qp().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack(t=1).J().corresponding_basis_over(CyclotomicField())\n sage: Sym.zonal().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the zonal basis\n sage: Sym.llt(3).hspin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3).hcospin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3, t=1).hspin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3, t=1).hcospin().corresponding_basis_over(CyclotomicField())\n\n .. TODO::\n\n This function is an ugly hack using strings. It should be\n rewritten as soon as the bases of ``SymmetricFunctions`` are\n put on a more robust and systematic footing.\n "
from sage.combinat.sf.sf import SymmetricFunctions
from sage.misc.misc import attrcall
try:
return attrcall(self._basis)(SymmetricFunctions(R))
except AttributeError:
return None
|
def corresponding_basis_over(self, R):
"\n Return the realization of symmetric functions corresponding to\n ``self`` but over the base ring ``R``. Only works when ``self``\n is one of the classical bases, not one of the `q,t`-dependent\n ones. In the latter case, ``None`` is returned instead.\n\n INPUT:\n\n - ``R`` -- a commutative ring\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: m.corresponding_basis_over(ZZ)\n Symmetric Functions over Integer Ring in the monomial basis\n\n sage: Sym = SymmetricFunctions(CyclotomicField())\n sage: s = Sym.schur()\n sage: s.corresponding_basis_over(Integers(13))\n Symmetric Functions over Ring of integers modulo 13 in the Schur basis\n\n sage: P = ZZ['q','t']\n sage: Sym = SymmetricFunctions(P)\n sage: mj = Sym.macdonald().J()\n sage: mj.corresponding_basis_over(Integers(13))\n\n TESTS:\n\n Let's check that this handles each of the bases properly::\n\n sage: P = QQ['q','t']\n sage: Sym = SymmetricFunctions(P)\n sage: Q = CyclotomicField()['q','t']\n sage: Sym.s().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the Schur basis\n sage: Sym.p().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the powersum basis\n sage: Sym.m().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the monomial basis\n sage: Sym.e().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the elementary basis\n sage: Sym.h().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the homogeneous basis\n sage: Sym.f().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the forgotten basis\n sage: Sym.w().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the Witt basis\n sage: Sym.macdonald().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().J().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().H().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().Ht().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald().S().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald(q=1).S().corresponding_basis_over(CyclotomicField())\n sage: Sym.macdonald(q=1,t=3).P().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood().Qp().corresponding_basis_over(CyclotomicField())\n sage: Sym.hall_littlewood(t=1).P().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().J().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().P().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().Q().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack().Qp().corresponding_basis_over(CyclotomicField())\n sage: Sym.jack(t=1).J().corresponding_basis_over(CyclotomicField())\n sage: Sym.zonal().corresponding_basis_over(CyclotomicField())\n Symmetric Functions over Universal Cyclotomic Field in the zonal basis\n sage: Sym.llt(3).hspin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3).hcospin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3, t=1).hspin().corresponding_basis_over(CyclotomicField())\n sage: Sym.llt(3, t=1).hcospin().corresponding_basis_over(CyclotomicField())\n\n .. TODO::\n\n This function is an ugly hack using strings. It should be\n rewritten as soon as the bases of ``SymmetricFunctions`` are\n put on a more robust and systematic footing.\n "
from sage.combinat.sf.sf import SymmetricFunctions
from sage.misc.misc import attrcall
try:
return attrcall(self._basis)(SymmetricFunctions(R))
except AttributeError:
return None<|docstring|>Return the realization of symmetric functions corresponding to
``self`` but over the base ring ``R``. Only works when ``self``
is one of the classical bases, not one of the `q,t`-dependent
ones. In the latter case, ``None`` is returned instead.
INPUT:
- ``R`` -- a commutative ring
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.monomial()
sage: m.corresponding_basis_over(ZZ)
Symmetric Functions over Integer Ring in the monomial basis
sage: Sym = SymmetricFunctions(CyclotomicField())
sage: s = Sym.schur()
sage: s.corresponding_basis_over(Integers(13))
Symmetric Functions over Ring of integers modulo 13 in the Schur basis
sage: P = ZZ['q','t']
sage: Sym = SymmetricFunctions(P)
sage: mj = Sym.macdonald().J()
sage: mj.corresponding_basis_over(Integers(13))
TESTS:
Let's check that this handles each of the bases properly::
sage: P = QQ['q','t']
sage: Sym = SymmetricFunctions(P)
sage: Q = CyclotomicField()['q','t']
sage: Sym.s().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the Schur basis
sage: Sym.p().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the powersum basis
sage: Sym.m().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the monomial basis
sage: Sym.e().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the elementary basis
sage: Sym.h().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the homogeneous basis
sage: Sym.f().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the forgotten basis
sage: Sym.w().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the Witt basis
sage: Sym.macdonald().P().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().Q().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().J().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().H().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().Ht().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald().S().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald(q=1).S().corresponding_basis_over(CyclotomicField())
sage: Sym.macdonald(q=1,t=3).P().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood().P().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood().Q().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood().Qp().corresponding_basis_over(CyclotomicField())
sage: Sym.hall_littlewood(t=1).P().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().J().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().P().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().Q().corresponding_basis_over(CyclotomicField())
sage: Sym.jack().Qp().corresponding_basis_over(CyclotomicField())
sage: Sym.jack(t=1).J().corresponding_basis_over(CyclotomicField())
sage: Sym.zonal().corresponding_basis_over(CyclotomicField())
Symmetric Functions over Universal Cyclotomic Field in the zonal basis
sage: Sym.llt(3).hspin().corresponding_basis_over(CyclotomicField())
sage: Sym.llt(3).hcospin().corresponding_basis_over(CyclotomicField())
sage: Sym.llt(3, t=1).hspin().corresponding_basis_over(CyclotomicField())
sage: Sym.llt(3, t=1).hcospin().corresponding_basis_over(CyclotomicField())
.. TODO::
This function is an ugly hack using strings. It should be
rewritten as soon as the bases of ``SymmetricFunctions`` are
put on a more robust and systematic footing.<|endoftext|>
|
7ef852eda1ee410a57b39eb2e6cd71a41ba87375266bdeb8e3d34ea659937001
|
def Eulerian(self, n, j, k=None):
'\n Return the Eulerian symmetric function `Q_{n,j}` (with `n`\n either an integer or a partition) or `Q_{n,j,k}` (if the\n optional argument ``k`` is specified) in terms of the basis\n ``self``.\n\n It is known that the Eulerian quasisymmetric functions are\n in fact symmetric functions [SW2010]_. For more information,\n see :meth:`QuasiSymmetricFunctions.Fundamental.Eulerian()`,\n which accepts the same syntax as this method.\n\n INPUT:\n\n - ``n`` -- the nonnegative integer `n` or a partition\n - ``j`` -- the number of excedances\n - ``k`` -- (optional) if specified, determines the number of fixed\n points of the permutations which are being summed over\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.m()\n sage: m.Eulerian(3, 1)\n 4*m[1, 1, 1] + 3*m[2, 1] + 2*m[3]\n sage: h = Sym.h()\n sage: h.Eulerian(4, 2)\n h[2, 2] + h[3, 1] + h[4]\n sage: s = Sym.s()\n sage: s.Eulerian(5, 2)\n s[2, 2, 1] + s[3, 1, 1] + 5*s[3, 2] + 6*s[4, 1] + 6*s[5]\n sage: s.Eulerian([2,2,1], 2)\n s[2, 2, 1] + s[3, 2] + s[4, 1] + s[5]\n sage: s.Eulerian(5, 2, 2)\n s[3, 2] + s[4, 1] + s[5]\n\n We check Equation (5.4) in [SW2010]_::\n\n sage: h.Eulerian([6], 3)\n h[3, 2, 1] - h[4, 1, 1] + 2*h[4, 2] + h[5, 1]\n sage: s.Eulerian([6], 3)\n s[3, 2, 1] + s[3, 3] + 3*s[4, 2] + 3*s[5, 1] + 3*s[6]\n '
from sage.combinat.ncsf_qsym.qsym import QuasiSymmetricFunctions
F = QuasiSymmetricFunctions(self.base_ring()).F()
if (n in _Partitions):
n = _Partitions(n)
return self(F.Eulerian(n, j, k).to_symmetric_function())
|
Return the Eulerian symmetric function `Q_{n,j}` (with `n`
either an integer or a partition) or `Q_{n,j,k}` (if the
optional argument ``k`` is specified) in terms of the basis
``self``.
It is known that the Eulerian quasisymmetric functions are
in fact symmetric functions [SW2010]_. For more information,
see :meth:`QuasiSymmetricFunctions.Fundamental.Eulerian()`,
which accepts the same syntax as this method.
INPUT:
- ``n`` -- the nonnegative integer `n` or a partition
- ``j`` -- the number of excedances
- ``k`` -- (optional) if specified, determines the number of fixed
points of the permutations which are being summed over
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.m()
sage: m.Eulerian(3, 1)
4*m[1, 1, 1] + 3*m[2, 1] + 2*m[3]
sage: h = Sym.h()
sage: h.Eulerian(4, 2)
h[2, 2] + h[3, 1] + h[4]
sage: s = Sym.s()
sage: s.Eulerian(5, 2)
s[2, 2, 1] + s[3, 1, 1] + 5*s[3, 2] + 6*s[4, 1] + 6*s[5]
sage: s.Eulerian([2,2,1], 2)
s[2, 2, 1] + s[3, 2] + s[4, 1] + s[5]
sage: s.Eulerian(5, 2, 2)
s[3, 2] + s[4, 1] + s[5]
We check Equation (5.4) in [SW2010]_::
sage: h.Eulerian([6], 3)
h[3, 2, 1] - h[4, 1, 1] + 2*h[4, 2] + h[5, 1]
sage: s.Eulerian([6], 3)
s[3, 2, 1] + s[3, 3] + 3*s[4, 2] + 3*s[5, 1] + 3*s[6]
|
src/sage/combinat/sf/sfa.py
|
Eulerian
|
bopopescu/sagesmc
| 5 |
python
|
def Eulerian(self, n, j, k=None):
'\n Return the Eulerian symmetric function `Q_{n,j}` (with `n`\n either an integer or a partition) or `Q_{n,j,k}` (if the\n optional argument ``k`` is specified) in terms of the basis\n ``self``.\n\n It is known that the Eulerian quasisymmetric functions are\n in fact symmetric functions [SW2010]_. For more information,\n see :meth:`QuasiSymmetricFunctions.Fundamental.Eulerian()`,\n which accepts the same syntax as this method.\n\n INPUT:\n\n - ``n`` -- the nonnegative integer `n` or a partition\n - ``j`` -- the number of excedances\n - ``k`` -- (optional) if specified, determines the number of fixed\n points of the permutations which are being summed over\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.m()\n sage: m.Eulerian(3, 1)\n 4*m[1, 1, 1] + 3*m[2, 1] + 2*m[3]\n sage: h = Sym.h()\n sage: h.Eulerian(4, 2)\n h[2, 2] + h[3, 1] + h[4]\n sage: s = Sym.s()\n sage: s.Eulerian(5, 2)\n s[2, 2, 1] + s[3, 1, 1] + 5*s[3, 2] + 6*s[4, 1] + 6*s[5]\n sage: s.Eulerian([2,2,1], 2)\n s[2, 2, 1] + s[3, 2] + s[4, 1] + s[5]\n sage: s.Eulerian(5, 2, 2)\n s[3, 2] + s[4, 1] + s[5]\n\n We check Equation (5.4) in [SW2010]_::\n\n sage: h.Eulerian([6], 3)\n h[3, 2, 1] - h[4, 1, 1] + 2*h[4, 2] + h[5, 1]\n sage: s.Eulerian([6], 3)\n s[3, 2, 1] + s[3, 3] + 3*s[4, 2] + 3*s[5, 1] + 3*s[6]\n '
from sage.combinat.ncsf_qsym.qsym import QuasiSymmetricFunctions
F = QuasiSymmetricFunctions(self.base_ring()).F()
if (n in _Partitions):
n = _Partitions(n)
return self(F.Eulerian(n, j, k).to_symmetric_function())
|
def Eulerian(self, n, j, k=None):
'\n Return the Eulerian symmetric function `Q_{n,j}` (with `n`\n either an integer or a partition) or `Q_{n,j,k}` (if the\n optional argument ``k`` is specified) in terms of the basis\n ``self``.\n\n It is known that the Eulerian quasisymmetric functions are\n in fact symmetric functions [SW2010]_. For more information,\n see :meth:`QuasiSymmetricFunctions.Fundamental.Eulerian()`,\n which accepts the same syntax as this method.\n\n INPUT:\n\n - ``n`` -- the nonnegative integer `n` or a partition\n - ``j`` -- the number of excedances\n - ``k`` -- (optional) if specified, determines the number of fixed\n points of the permutations which are being summed over\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.m()\n sage: m.Eulerian(3, 1)\n 4*m[1, 1, 1] + 3*m[2, 1] + 2*m[3]\n sage: h = Sym.h()\n sage: h.Eulerian(4, 2)\n h[2, 2] + h[3, 1] + h[4]\n sage: s = Sym.s()\n sage: s.Eulerian(5, 2)\n s[2, 2, 1] + s[3, 1, 1] + 5*s[3, 2] + 6*s[4, 1] + 6*s[5]\n sage: s.Eulerian([2,2,1], 2)\n s[2, 2, 1] + s[3, 2] + s[4, 1] + s[5]\n sage: s.Eulerian(5, 2, 2)\n s[3, 2] + s[4, 1] + s[5]\n\n We check Equation (5.4) in [SW2010]_::\n\n sage: h.Eulerian([6], 3)\n h[3, 2, 1] - h[4, 1, 1] + 2*h[4, 2] + h[5, 1]\n sage: s.Eulerian([6], 3)\n s[3, 2, 1] + s[3, 3] + 3*s[4, 2] + 3*s[5, 1] + 3*s[6]\n '
from sage.combinat.ncsf_qsym.qsym import QuasiSymmetricFunctions
F = QuasiSymmetricFunctions(self.base_ring()).F()
if (n in _Partitions):
n = _Partitions(n)
return self(F.Eulerian(n, j, k).to_symmetric_function())<|docstring|>Return the Eulerian symmetric function `Q_{n,j}` (with `n`
either an integer or a partition) or `Q_{n,j,k}` (if the
optional argument ``k`` is specified) in terms of the basis
``self``.
It is known that the Eulerian quasisymmetric functions are
in fact symmetric functions [SW2010]_. For more information,
see :meth:`QuasiSymmetricFunctions.Fundamental.Eulerian()`,
which accepts the same syntax as this method.
INPUT:
- ``n`` -- the nonnegative integer `n` or a partition
- ``j`` -- the number of excedances
- ``k`` -- (optional) if specified, determines the number of fixed
points of the permutations which are being summed over
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.m()
sage: m.Eulerian(3, 1)
4*m[1, 1, 1] + 3*m[2, 1] + 2*m[3]
sage: h = Sym.h()
sage: h.Eulerian(4, 2)
h[2, 2] + h[3, 1] + h[4]
sage: s = Sym.s()
sage: s.Eulerian(5, 2)
s[2, 2, 1] + s[3, 1, 1] + 5*s[3, 2] + 6*s[4, 1] + 6*s[5]
sage: s.Eulerian([2,2,1], 2)
s[2, 2, 1] + s[3, 2] + s[4, 1] + s[5]
sage: s.Eulerian(5, 2, 2)
s[3, 2] + s[4, 1] + s[5]
We check Equation (5.4) in [SW2010]_::
sage: h.Eulerian([6], 3)
h[3, 2, 1] - h[4, 1, 1] + 2*h[4, 2] + h[5, 1]
sage: s.Eulerian([6], 3)
s[3, 2, 1] + s[3, 3] + 3*s[4, 2] + 3*s[5, 1] + 3*s[6]<|endoftext|>
|
4722b9ae7a49163b6812d8c0b283905fb18eee8e1f202404d6accbfeea6255d1
|
def degree_zero_coefficient(self):
'\n Returns the degree zero coefficient of ``self``.\n\n INPUT:\n\n - ``self`` -- an element of the symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 3*m[[]]\n sage: f.degree_zero_coefficient()\n 3\n '
return self.coefficient([])
|
Returns the degree zero coefficient of ``self``.
INPUT:
- ``self`` -- an element of the symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.monomial()
sage: f = 2*m[2,1] + 3*m[[]]
sage: f.degree_zero_coefficient()
3
|
src/sage/combinat/sf/sfa.py
|
degree_zero_coefficient
|
bopopescu/sagesmc
| 5 |
python
|
def degree_zero_coefficient(self):
'\n Returns the degree zero coefficient of ``self``.\n\n INPUT:\n\n - ``self`` -- an element of the symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 3*m[[]]\n sage: f.degree_zero_coefficient()\n 3\n '
return self.coefficient([])
|
def degree_zero_coefficient(self):
'\n Returns the degree zero coefficient of ``self``.\n\n INPUT:\n\n - ``self`` -- an element of the symmetric functions\n\n EXAMPLES::\n\n sage: Sym = SymmetricFunctions(QQ)\n sage: m = Sym.monomial()\n sage: f = 2*m[2,1] + 3*m[[]]\n sage: f.degree_zero_coefficient()\n 3\n '
return self.coefficient([])<|docstring|>Returns the degree zero coefficient of ``self``.
INPUT:
- ``self`` -- an element of the symmetric functions
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: m = Sym.monomial()
sage: f = 2*m[2,1] + 3*m[[]]
sage: f.degree_zero_coefficient()
3<|endoftext|>
|
8d3334a75b2b0eeaa9ce931efa84ea20ca57faf25937e1d702d20b276fdeab40
|
@classmethod
def guiStart(self, parent=None):
'Graphical interface for starting this class'
(kwargs, independent) = common._SimplePluginStart('Mapper').startDisplay()
kwargs['parent'] = parent
return (self(**kwargs), independent)
|
Graphical interface for starting this class
|
artview/components/mapper.py
|
guiStart
|
savelov/artview
| 40 |
python
|
@classmethod
def guiStart(self, parent=None):
(kwargs, independent) = common._SimplePluginStart('Mapper').startDisplay()
kwargs['parent'] = parent
return (self(**kwargs), independent)
|
@classmethod
def guiStart(self, parent=None):
(kwargs, independent) = common._SimplePluginStart('Mapper').startDisplay()
kwargs['parent'] = parent
return (self(**kwargs), independent)<|docstring|>Graphical interface for starting this class<|endoftext|>
|
b19d76fc12e0368f0f56d7af04928c5585cdb7e2571ce99b99ba5f44e7f15bec
|
def __init__(self, Vradar=None, Vgrid=None, name='Mapper', parent=None):
'Initialize the class to create the interface.\n\n Parameters\n ----------\n [Optional]\n Vradar : :py:class:`~artview.core.core.Variable` instance\n Radar signal variable.\n A value of None initializes an empty Variable.\n Vgrid : :py:class:`~artview.core.core.Variable` instance\n Grid signal variable.\n A value of None initializes an empty Variable.\n name : string\n Field Radiobutton window name.\n parent : PyQt instance\n Parent instance to associate to this class.\n If None, then Qt owns, otherwise associated w/ parent PyQt instance\n '
super(Mapper, self).__init__(name=name, parent=parent)
self.central_widget = QtWidgets.QWidget()
self.setCentralWidget(self.central_widget)
self.layout = QtWidgets.QGridLayout(self.central_widget)
self.mountUI()
self.parameters = {'radars': None, 'gridshape': (1, 500, 500), 'grid_limits': ((2000, 3000), ((- 250000), 250000), ((- 250000), 250000)), 'grid_origin': (0, 0), 'grid_origin_lat': 0, 'grid_origin_lon': 0, 'grid_origin_alt': 0, 'gridding_algo': 'map_gates_to_grid', 'fields': [], 'refl_filter_flag': True, 'refl_field': get_field_name('reflectivity'), 'max_refl': 100, 'map_roi': True, 'weighting_function': 'Barnes', 'toa': 17000, 'roi_func': 'dist_beam', 'constant_roi': 500, 'z_factor': 0.05, 'xy_factor': 0.02, 'min_radius': 500, 'bsp': 1, 'copy_field_data': True, 'algorithm': 'kd_tree', 'leafsize': 10}
self.general_parameters_type = [('grid_origin_lat', float), ('grid_origin_lon', float), ('grid_origin_alt', float), ('gridding_algo', ('map_to_grid', 'map_gates_to_grid')), ('refl_filter_flag', bool), ('refl_field', str), ('max_refl', float), ('map_roi', bool), ('weighting_function', ('Barnes', 'Cressman')), ('toa', float)]
self.roi_parameters_type = [('roi_func', ('constant', 'dist', 'dist_beam')), ('constant_roi', float), ('z_factor', float), ('xy_factor', float), ('min_radius', float), ('bsp', float)]
self.gridding_parameters_type = [('copy_field_data', bool), ('algorithm', ('kd_tree', 'ball_tree')), ('leafsize', int)]
if (Vradar is None):
self.Vradar = Variable(None)
else:
self.Vradar = Vradar
if (Vgrid is None):
self.Vgrid = Variable(None)
else:
self.Vgrid = Vgrid
self.sharedVariables = {'Vradar': self.NewRadar, 'Vgrid': None}
self.connectAllVariables()
self.NewRadar(None, True)
self.show()
|
Initialize the class to create the interface.
Parameters
----------
[Optional]
Vradar : :py:class:`~artview.core.core.Variable` instance
Radar signal variable.
A value of None initializes an empty Variable.
Vgrid : :py:class:`~artview.core.core.Variable` instance
Grid signal variable.
A value of None initializes an empty Variable.
name : string
Field Radiobutton window name.
parent : PyQt instance
Parent instance to associate to this class.
If None, then Qt owns, otherwise associated w/ parent PyQt instance
|
artview/components/mapper.py
|
__init__
|
savelov/artview
| 40 |
python
|
def __init__(self, Vradar=None, Vgrid=None, name='Mapper', parent=None):
'Initialize the class to create the interface.\n\n Parameters\n ----------\n [Optional]\n Vradar : :py:class:`~artview.core.core.Variable` instance\n Radar signal variable.\n A value of None initializes an empty Variable.\n Vgrid : :py:class:`~artview.core.core.Variable` instance\n Grid signal variable.\n A value of None initializes an empty Variable.\n name : string\n Field Radiobutton window name.\n parent : PyQt instance\n Parent instance to associate to this class.\n If None, then Qt owns, otherwise associated w/ parent PyQt instance\n '
super(Mapper, self).__init__(name=name, parent=parent)
self.central_widget = QtWidgets.QWidget()
self.setCentralWidget(self.central_widget)
self.layout = QtWidgets.QGridLayout(self.central_widget)
self.mountUI()
self.parameters = {'radars': None, 'gridshape': (1, 500, 500), 'grid_limits': ((2000, 3000), ((- 250000), 250000), ((- 250000), 250000)), 'grid_origin': (0, 0), 'grid_origin_lat': 0, 'grid_origin_lon': 0, 'grid_origin_alt': 0, 'gridding_algo': 'map_gates_to_grid', 'fields': [], 'refl_filter_flag': True, 'refl_field': get_field_name('reflectivity'), 'max_refl': 100, 'map_roi': True, 'weighting_function': 'Barnes', 'toa': 17000, 'roi_func': 'dist_beam', 'constant_roi': 500, 'z_factor': 0.05, 'xy_factor': 0.02, 'min_radius': 500, 'bsp': 1, 'copy_field_data': True, 'algorithm': 'kd_tree', 'leafsize': 10}
self.general_parameters_type = [('grid_origin_lat', float), ('grid_origin_lon', float), ('grid_origin_alt', float), ('gridding_algo', ('map_to_grid', 'map_gates_to_grid')), ('refl_filter_flag', bool), ('refl_field', str), ('max_refl', float), ('map_roi', bool), ('weighting_function', ('Barnes', 'Cressman')), ('toa', float)]
self.roi_parameters_type = [('roi_func', ('constant', 'dist', 'dist_beam')), ('constant_roi', float), ('z_factor', float), ('xy_factor', float), ('min_radius', float), ('bsp', float)]
self.gridding_parameters_type = [('copy_field_data', bool), ('algorithm', ('kd_tree', 'ball_tree')), ('leafsize', int)]
if (Vradar is None):
self.Vradar = Variable(None)
else:
self.Vradar = Vradar
if (Vgrid is None):
self.Vgrid = Variable(None)
else:
self.Vgrid = Vgrid
self.sharedVariables = {'Vradar': self.NewRadar, 'Vgrid': None}
self.connectAllVariables()
self.NewRadar(None, True)
self.show()
|
def __init__(self, Vradar=None, Vgrid=None, name='Mapper', parent=None):
'Initialize the class to create the interface.\n\n Parameters\n ----------\n [Optional]\n Vradar : :py:class:`~artview.core.core.Variable` instance\n Radar signal variable.\n A value of None initializes an empty Variable.\n Vgrid : :py:class:`~artview.core.core.Variable` instance\n Grid signal variable.\n A value of None initializes an empty Variable.\n name : string\n Field Radiobutton window name.\n parent : PyQt instance\n Parent instance to associate to this class.\n If None, then Qt owns, otherwise associated w/ parent PyQt instance\n '
super(Mapper, self).__init__(name=name, parent=parent)
self.central_widget = QtWidgets.QWidget()
self.setCentralWidget(self.central_widget)
self.layout = QtWidgets.QGridLayout(self.central_widget)
self.mountUI()
self.parameters = {'radars': None, 'gridshape': (1, 500, 500), 'grid_limits': ((2000, 3000), ((- 250000), 250000), ((- 250000), 250000)), 'grid_origin': (0, 0), 'grid_origin_lat': 0, 'grid_origin_lon': 0, 'grid_origin_alt': 0, 'gridding_algo': 'map_gates_to_grid', 'fields': [], 'refl_filter_flag': True, 'refl_field': get_field_name('reflectivity'), 'max_refl': 100, 'map_roi': True, 'weighting_function': 'Barnes', 'toa': 17000, 'roi_func': 'dist_beam', 'constant_roi': 500, 'z_factor': 0.05, 'xy_factor': 0.02, 'min_radius': 500, 'bsp': 1, 'copy_field_data': True, 'algorithm': 'kd_tree', 'leafsize': 10}
self.general_parameters_type = [('grid_origin_lat', float), ('grid_origin_lon', float), ('grid_origin_alt', float), ('gridding_algo', ('map_to_grid', 'map_gates_to_grid')), ('refl_filter_flag', bool), ('refl_field', str), ('max_refl', float), ('map_roi', bool), ('weighting_function', ('Barnes', 'Cressman')), ('toa', float)]
self.roi_parameters_type = [('roi_func', ('constant', 'dist', 'dist_beam')), ('constant_roi', float), ('z_factor', float), ('xy_factor', float), ('min_radius', float), ('bsp', float)]
self.gridding_parameters_type = [('copy_field_data', bool), ('algorithm', ('kd_tree', 'ball_tree')), ('leafsize', int)]
if (Vradar is None):
self.Vradar = Variable(None)
else:
self.Vradar = Vradar
if (Vgrid is None):
self.Vgrid = Variable(None)
else:
self.Vgrid = Vgrid
self.sharedVariables = {'Vradar': self.NewRadar, 'Vgrid': None}
self.connectAllVariables()
self.NewRadar(None, True)
self.show()<|docstring|>Initialize the class to create the interface.
Parameters
----------
[Optional]
Vradar : :py:class:`~artview.core.core.Variable` instance
Radar signal variable.
A value of None initializes an empty Variable.
Vgrid : :py:class:`~artview.core.core.Variable` instance
Grid signal variable.
A value of None initializes an empty Variable.
name : string
Field Radiobutton window name.
parent : PyQt instance
Parent instance to associate to this class.
If None, then Qt owns, otherwise associated w/ parent PyQt instance<|endoftext|>
|
bcd7797f13a2bf77d9f0e5d7bdb7a08c315b1d3806cf856254240a8568213020
|
def mountUI(self):
'Mount Options Layout.'
self.despeckleButton = QtWidgets.QPushButton('Map')
self.despeckleButton.clicked.connect(self.grid_from_radars)
self.layout.addWidget(self.despeckleButton, 7, 0, 1, 2)
parentdir = os.path.abspath(os.path.join(os.path.dirname(__file__), os.pardir))
config_icon = QtGui.QIcon(os.sep.join([parentdir, 'icons', 'categories-applications-system-icon.png']))
self.configButton = QtWidgets.QPushButton(config_icon, '')
self.layout.addWidget(self.configButton, 7, 2)
self.configMenu = QtWidgets.QMenu(self)
self.configButton.setMenu(self.configMenu)
self.configMenu.addAction(QtWidgets.QAction('Set General Parameters', self, triggered=self.setParameters))
self.configMenu.addAction(QtWidgets.QAction('Set Radius of Influence Parameters', self, triggered=self.setRoiParameters))
self.configMenu.addAction(QtWidgets.QAction('Set map_to_grid Parameters', self, triggered=self.setGriddingParameters))
self.fieldMenu = self.configMenu.addMenu('Fields')
self.configMenu.addAction(QtWidgets.QAction('Help', self, triggered=self._displayHelp))
self.layout.addWidget(QtWidgets.QLabel('Z'), 1, 0, 2, 1)
self.layout.addWidget(QtWidgets.QLabel('Y'), 3, 0, 2, 1)
self.layout.addWidget(QtWidgets.QLabel('X'), 5, 0, 2, 1)
self.gridShapeZ = QtWidgets.QSpinBox()
self.gridShapeZ.setRange(0, 1000000)
self.gridShapeZ.setValue(1)
self.gridShapeY = QtWidgets.QSpinBox()
self.gridShapeY.setRange(0, 1000000)
self.gridShapeY.setValue(500)
self.gridShapeX = QtWidgets.QSpinBox()
self.gridShapeX.setRange(0, 1000000)
self.gridShapeX.setValue(500)
self.layout.addWidget(QtWidgets.QLabel('grid_shape'), 0, 1)
self.layout.addWidget(self.gridShapeZ, 1, 1, 2, 1)
self.layout.addWidget(self.gridShapeY, 3, 1, 2, 1)
self.layout.addWidget(self.gridShapeX, 5, 1, 2, 1)
self.gridLimitsZmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsZmin.setRange((- 41000000), 41000000)
self.gridLimitsZmin.setSingleStep(1000)
self.gridLimitsZmin.setValue(2000)
self.gridLimitsZmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsZmax.setRange((- 41000000), 41000000)
self.gridLimitsZmax.setSingleStep(1000)
self.gridLimitsZmax.setValue(3000)
self.gridLimitsYmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsYmin.setRange((- 41000000), 41000000)
self.gridLimitsYmin.setSingleStep(1000)
self.gridLimitsYmin.setValue((- 250000))
self.gridLimitsYmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsYmax.setRange((- 41000000), 41000000)
self.gridLimitsYmax.setSingleStep(1000)
self.gridLimitsYmax.setValue(250000)
self.gridLimitsXmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsXmin.setRange((- 41000000), 41000000)
self.gridLimitsXmin.setSingleStep(1000)
self.gridLimitsXmin.setValue((- 250000))
self.gridLimitsXmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsXmax.setRange((- 41000000), 41000000)
self.gridLimitsXmax.setSingleStep(1000)
self.gridLimitsXmax.setValue(250000)
self.layout.addWidget(QtWidgets.QLabel('grid_limits (m)'), 0, 2)
self.layout.addWidget(self.gridLimitsZmin, 1, 2)
self.layout.addWidget(self.gridLimitsZmax, 2, 2)
self.layout.addWidget(self.gridLimitsYmin, 3, 2)
self.layout.addWidget(self.gridLimitsYmax, 4, 2)
self.layout.addWidget(self.gridLimitsXmin, 5, 2)
self.layout.addWidget(self.gridLimitsXmax, 6, 2)
self.layout.setRowStretch(8, 1)
self.layout.setColumnStretch(1, 1)
self.layout.setColumnStretch(2, 1)
|
Mount Options Layout.
|
artview/components/mapper.py
|
mountUI
|
savelov/artview
| 40 |
python
|
def mountUI(self):
self.despeckleButton = QtWidgets.QPushButton('Map')
self.despeckleButton.clicked.connect(self.grid_from_radars)
self.layout.addWidget(self.despeckleButton, 7, 0, 1, 2)
parentdir = os.path.abspath(os.path.join(os.path.dirname(__file__), os.pardir))
config_icon = QtGui.QIcon(os.sep.join([parentdir, 'icons', 'categories-applications-system-icon.png']))
self.configButton = QtWidgets.QPushButton(config_icon, )
self.layout.addWidget(self.configButton, 7, 2)
self.configMenu = QtWidgets.QMenu(self)
self.configButton.setMenu(self.configMenu)
self.configMenu.addAction(QtWidgets.QAction('Set General Parameters', self, triggered=self.setParameters))
self.configMenu.addAction(QtWidgets.QAction('Set Radius of Influence Parameters', self, triggered=self.setRoiParameters))
self.configMenu.addAction(QtWidgets.QAction('Set map_to_grid Parameters', self, triggered=self.setGriddingParameters))
self.fieldMenu = self.configMenu.addMenu('Fields')
self.configMenu.addAction(QtWidgets.QAction('Help', self, triggered=self._displayHelp))
self.layout.addWidget(QtWidgets.QLabel('Z'), 1, 0, 2, 1)
self.layout.addWidget(QtWidgets.QLabel('Y'), 3, 0, 2, 1)
self.layout.addWidget(QtWidgets.QLabel('X'), 5, 0, 2, 1)
self.gridShapeZ = QtWidgets.QSpinBox()
self.gridShapeZ.setRange(0, 1000000)
self.gridShapeZ.setValue(1)
self.gridShapeY = QtWidgets.QSpinBox()
self.gridShapeY.setRange(0, 1000000)
self.gridShapeY.setValue(500)
self.gridShapeX = QtWidgets.QSpinBox()
self.gridShapeX.setRange(0, 1000000)
self.gridShapeX.setValue(500)
self.layout.addWidget(QtWidgets.QLabel('grid_shape'), 0, 1)
self.layout.addWidget(self.gridShapeZ, 1, 1, 2, 1)
self.layout.addWidget(self.gridShapeY, 3, 1, 2, 1)
self.layout.addWidget(self.gridShapeX, 5, 1, 2, 1)
self.gridLimitsZmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsZmin.setRange((- 41000000), 41000000)
self.gridLimitsZmin.setSingleStep(1000)
self.gridLimitsZmin.setValue(2000)
self.gridLimitsZmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsZmax.setRange((- 41000000), 41000000)
self.gridLimitsZmax.setSingleStep(1000)
self.gridLimitsZmax.setValue(3000)
self.gridLimitsYmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsYmin.setRange((- 41000000), 41000000)
self.gridLimitsYmin.setSingleStep(1000)
self.gridLimitsYmin.setValue((- 250000))
self.gridLimitsYmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsYmax.setRange((- 41000000), 41000000)
self.gridLimitsYmax.setSingleStep(1000)
self.gridLimitsYmax.setValue(250000)
self.gridLimitsXmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsXmin.setRange((- 41000000), 41000000)
self.gridLimitsXmin.setSingleStep(1000)
self.gridLimitsXmin.setValue((- 250000))
self.gridLimitsXmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsXmax.setRange((- 41000000), 41000000)
self.gridLimitsXmax.setSingleStep(1000)
self.gridLimitsXmax.setValue(250000)
self.layout.addWidget(QtWidgets.QLabel('grid_limits (m)'), 0, 2)
self.layout.addWidget(self.gridLimitsZmin, 1, 2)
self.layout.addWidget(self.gridLimitsZmax, 2, 2)
self.layout.addWidget(self.gridLimitsYmin, 3, 2)
self.layout.addWidget(self.gridLimitsYmax, 4, 2)
self.layout.addWidget(self.gridLimitsXmin, 5, 2)
self.layout.addWidget(self.gridLimitsXmax, 6, 2)
self.layout.setRowStretch(8, 1)
self.layout.setColumnStretch(1, 1)
self.layout.setColumnStretch(2, 1)
|
def mountUI(self):
self.despeckleButton = QtWidgets.QPushButton('Map')
self.despeckleButton.clicked.connect(self.grid_from_radars)
self.layout.addWidget(self.despeckleButton, 7, 0, 1, 2)
parentdir = os.path.abspath(os.path.join(os.path.dirname(__file__), os.pardir))
config_icon = QtGui.QIcon(os.sep.join([parentdir, 'icons', 'categories-applications-system-icon.png']))
self.configButton = QtWidgets.QPushButton(config_icon, )
self.layout.addWidget(self.configButton, 7, 2)
self.configMenu = QtWidgets.QMenu(self)
self.configButton.setMenu(self.configMenu)
self.configMenu.addAction(QtWidgets.QAction('Set General Parameters', self, triggered=self.setParameters))
self.configMenu.addAction(QtWidgets.QAction('Set Radius of Influence Parameters', self, triggered=self.setRoiParameters))
self.configMenu.addAction(QtWidgets.QAction('Set map_to_grid Parameters', self, triggered=self.setGriddingParameters))
self.fieldMenu = self.configMenu.addMenu('Fields')
self.configMenu.addAction(QtWidgets.QAction('Help', self, triggered=self._displayHelp))
self.layout.addWidget(QtWidgets.QLabel('Z'), 1, 0, 2, 1)
self.layout.addWidget(QtWidgets.QLabel('Y'), 3, 0, 2, 1)
self.layout.addWidget(QtWidgets.QLabel('X'), 5, 0, 2, 1)
self.gridShapeZ = QtWidgets.QSpinBox()
self.gridShapeZ.setRange(0, 1000000)
self.gridShapeZ.setValue(1)
self.gridShapeY = QtWidgets.QSpinBox()
self.gridShapeY.setRange(0, 1000000)
self.gridShapeY.setValue(500)
self.gridShapeX = QtWidgets.QSpinBox()
self.gridShapeX.setRange(0, 1000000)
self.gridShapeX.setValue(500)
self.layout.addWidget(QtWidgets.QLabel('grid_shape'), 0, 1)
self.layout.addWidget(self.gridShapeZ, 1, 1, 2, 1)
self.layout.addWidget(self.gridShapeY, 3, 1, 2, 1)
self.layout.addWidget(self.gridShapeX, 5, 1, 2, 1)
self.gridLimitsZmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsZmin.setRange((- 41000000), 41000000)
self.gridLimitsZmin.setSingleStep(1000)
self.gridLimitsZmin.setValue(2000)
self.gridLimitsZmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsZmax.setRange((- 41000000), 41000000)
self.gridLimitsZmax.setSingleStep(1000)
self.gridLimitsZmax.setValue(3000)
self.gridLimitsYmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsYmin.setRange((- 41000000), 41000000)
self.gridLimitsYmin.setSingleStep(1000)
self.gridLimitsYmin.setValue((- 250000))
self.gridLimitsYmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsYmax.setRange((- 41000000), 41000000)
self.gridLimitsYmax.setSingleStep(1000)
self.gridLimitsYmax.setValue(250000)
self.gridLimitsXmin = QtWidgets.QDoubleSpinBox()
self.gridLimitsXmin.setRange((- 41000000), 41000000)
self.gridLimitsXmin.setSingleStep(1000)
self.gridLimitsXmin.setValue((- 250000))
self.gridLimitsXmax = QtWidgets.QDoubleSpinBox()
self.gridLimitsXmax.setRange((- 41000000), 41000000)
self.gridLimitsXmax.setSingleStep(1000)
self.gridLimitsXmax.setValue(250000)
self.layout.addWidget(QtWidgets.QLabel('grid_limits (m)'), 0, 2)
self.layout.addWidget(self.gridLimitsZmin, 1, 2)
self.layout.addWidget(self.gridLimitsZmax, 2, 2)
self.layout.addWidget(self.gridLimitsYmin, 3, 2)
self.layout.addWidget(self.gridLimitsYmax, 4, 2)
self.layout.addWidget(self.gridLimitsXmin, 5, 2)
self.layout.addWidget(self.gridLimitsXmax, 6, 2)
self.layout.setRowStretch(8, 1)
self.layout.setColumnStretch(1, 1)
self.layout.setColumnStretch(2, 1)<|docstring|>Mount Options Layout.<|endoftext|>
|
bc873acd130e91f2efe1461b984fa78b142b8f99583aae609293af6880e0b1d1
|
def grid_from_radars(self):
'Mount Options and execute :py:func:`~pyart.correct.grid_from_radars`.\n The resulting grid is update in Vgrid.\n '
if (self.Vradar.value is None):
common.ShowWarning('Radar is None, can not perform correction')
return
self.parameters['radars'] = (self.Vradar.value,)
self.parameters['fields'] = []
for field in self.field_actions.keys():
if self.field_actions[field].isChecked():
self.parameters['fields'].append(field)
self.parameters['grid_shape'] = (self.gridShapeZ.value(), self.gridShapeY.value(), self.gridShapeX.value())
self.parameters['grid_limits'] = ((self.gridLimitsZmin.value(), self.gridLimitsZmax.value()), (self.gridLimitsYmin.value(), self.gridLimitsYmax.value()), (self.gridLimitsXmin.value(), self.gridLimitsXmax.value()))
self.parameters['grid_origin'] = (self.parameters['grid_origin_lat'], self.parameters['grid_origin_lon'])
print('mapping ..', file=log.debug)
t0 = time.time()
try:
grid = pyart.map.grid_from_radars(**self.parameters)
except:
import traceback
error = traceback.format_exc()
common.ShowLongText(('Py-ART fails with following error\n\n' + error))
t1 = time.time()
print(('Mapping took %fs' % (t1 - t0)), file=log.debug)
self.Vgrid.change(grid)
|
Mount Options and execute :py:func:`~pyart.correct.grid_from_radars`.
The resulting grid is update in Vgrid.
|
artview/components/mapper.py
|
grid_from_radars
|
savelov/artview
| 40 |
python
|
def grid_from_radars(self):
'Mount Options and execute :py:func:`~pyart.correct.grid_from_radars`.\n The resulting grid is update in Vgrid.\n '
if (self.Vradar.value is None):
common.ShowWarning('Radar is None, can not perform correction')
return
self.parameters['radars'] = (self.Vradar.value,)
self.parameters['fields'] = []
for field in self.field_actions.keys():
if self.field_actions[field].isChecked():
self.parameters['fields'].append(field)
self.parameters['grid_shape'] = (self.gridShapeZ.value(), self.gridShapeY.value(), self.gridShapeX.value())
self.parameters['grid_limits'] = ((self.gridLimitsZmin.value(), self.gridLimitsZmax.value()), (self.gridLimitsYmin.value(), self.gridLimitsYmax.value()), (self.gridLimitsXmin.value(), self.gridLimitsXmax.value()))
self.parameters['grid_origin'] = (self.parameters['grid_origin_lat'], self.parameters['grid_origin_lon'])
print('mapping ..', file=log.debug)
t0 = time.time()
try:
grid = pyart.map.grid_from_radars(**self.parameters)
except:
import traceback
error = traceback.format_exc()
common.ShowLongText(('Py-ART fails with following error\n\n' + error))
t1 = time.time()
print(('Mapping took %fs' % (t1 - t0)), file=log.debug)
self.Vgrid.change(grid)
|
def grid_from_radars(self):
'Mount Options and execute :py:func:`~pyart.correct.grid_from_radars`.\n The resulting grid is update in Vgrid.\n '
if (self.Vradar.value is None):
common.ShowWarning('Radar is None, can not perform correction')
return
self.parameters['radars'] = (self.Vradar.value,)
self.parameters['fields'] = []
for field in self.field_actions.keys():
if self.field_actions[field].isChecked():
self.parameters['fields'].append(field)
self.parameters['grid_shape'] = (self.gridShapeZ.value(), self.gridShapeY.value(), self.gridShapeX.value())
self.parameters['grid_limits'] = ((self.gridLimitsZmin.value(), self.gridLimitsZmax.value()), (self.gridLimitsYmin.value(), self.gridLimitsYmax.value()), (self.gridLimitsXmin.value(), self.gridLimitsXmax.value()))
self.parameters['grid_origin'] = (self.parameters['grid_origin_lat'], self.parameters['grid_origin_lon'])
print('mapping ..', file=log.debug)
t0 = time.time()
try:
grid = pyart.map.grid_from_radars(**self.parameters)
except:
import traceback
error = traceback.format_exc()
common.ShowLongText(('Py-ART fails with following error\n\n' + error))
t1 = time.time()
print(('Mapping took %fs' % (t1 - t0)), file=log.debug)
self.Vgrid.change(grid)<|docstring|>Mount Options and execute :py:func:`~pyart.correct.grid_from_radars`.
The resulting grid is update in Vgrid.<|endoftext|>
|
3643288cf3ff60ea7cc71ca5323c800e4325190b73f9b9ab11a66093a7f1f3ae
|
def setParameters(self):
'Open set parameters dialog.'
parm = common.get_options(self.general_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]
|
Open set parameters dialog.
|
artview/components/mapper.py
|
setParameters
|
savelov/artview
| 40 |
python
|
def setParameters(self):
parm = common.get_options(self.general_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]
|
def setParameters(self):
parm = common.get_options(self.general_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]<|docstring|>Open set parameters dialog.<|endoftext|>
|
0ec45bb566c6f5ad92aae36786facfb6715727189d4826fe739ebe82870179d4
|
def setGriddingParameters(self):
'Open set parameters dialog.'
parm = common.get_options(self.gridding_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]
|
Open set parameters dialog.
|
artview/components/mapper.py
|
setGriddingParameters
|
savelov/artview
| 40 |
python
|
def setGriddingParameters(self):
parm = common.get_options(self.gridding_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]
|
def setGriddingParameters(self):
parm = common.get_options(self.gridding_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]<|docstring|>Open set parameters dialog.<|endoftext|>
|
dec7f5e00d6548992108c9a2fec27c6b86951dc46d34e45f8efe39e1a58fcd9b
|
def setRoiParameters(self):
'Open set parameters dialog.'
parm = common.get_options(self.roi_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]
|
Open set parameters dialog.
|
artview/components/mapper.py
|
setRoiParameters
|
savelov/artview
| 40 |
python
|
def setRoiParameters(self):
parm = common.get_options(self.roi_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]
|
def setRoiParameters(self):
parm = common.get_options(self.roi_parameters_type, self.parameters)
for key in parm.keys():
self.parameters[key] = parm[key]<|docstring|>Open set parameters dialog.<|endoftext|>
|
30c09696e89e096bfb9a7eacdde3fb9aabe6013e1e347a840a02e3be699d14ef
|
def _displayHelp(self):
"Display Py-Art's docstring for help."
common.ShowLongText(pyart.map.grid_from_radars.__doc__)
|
Display Py-Art's docstring for help.
|
artview/components/mapper.py
|
_displayHelp
|
savelov/artview
| 40 |
python
|
def _displayHelp(self):
common.ShowLongText(pyart.map.grid_from_radars.__doc__)
|
def _displayHelp(self):
common.ShowLongText(pyart.map.grid_from_radars.__doc__)<|docstring|>Display Py-Art's docstring for help.<|endoftext|>
|
b3aec951552fcb2e0d51436bf77eb25ebefd87f8f7ce75909956bc565ceb7127
|
def NewRadar(self, variable, strong):
"Display Py-Art's docstring for help."
if (self.Vradar.value is None):
return
fields = self.Vradar.value.fields.keys()
self.field_radio_group = QtWidgets.QActionGroup(self, exclusive=False)
self.field_actions = {}
self.fieldMenu.clear()
for field in fields:
action = self.field_radio_group.addAction(field)
action.setCheckable(True)
action.setChecked(True)
self.fieldMenu.addAction(action)
self.field_actions[field] = action
lat = float(self.Vradar.value.latitude['data'])
lon = float(self.Vradar.value.longitude['data'])
alt = float(self.Vradar.value.altitude['data'])
self.parameters['grid_origin_lat'] = lat
self.parameters['grid_origin_lon'] = lon
self.parameters['grid_origin_alt'] = alt
|
Display Py-Art's docstring for help.
|
artview/components/mapper.py
|
NewRadar
|
savelov/artview
| 40 |
python
|
def NewRadar(self, variable, strong):
if (self.Vradar.value is None):
return
fields = self.Vradar.value.fields.keys()
self.field_radio_group = QtWidgets.QActionGroup(self, exclusive=False)
self.field_actions = {}
self.fieldMenu.clear()
for field in fields:
action = self.field_radio_group.addAction(field)
action.setCheckable(True)
action.setChecked(True)
self.fieldMenu.addAction(action)
self.field_actions[field] = action
lat = float(self.Vradar.value.latitude['data'])
lon = float(self.Vradar.value.longitude['data'])
alt = float(self.Vradar.value.altitude['data'])
self.parameters['grid_origin_lat'] = lat
self.parameters['grid_origin_lon'] = lon
self.parameters['grid_origin_alt'] = alt
|
def NewRadar(self, variable, strong):
if (self.Vradar.value is None):
return
fields = self.Vradar.value.fields.keys()
self.field_radio_group = QtWidgets.QActionGroup(self, exclusive=False)
self.field_actions = {}
self.fieldMenu.clear()
for field in fields:
action = self.field_radio_group.addAction(field)
action.setCheckable(True)
action.setChecked(True)
self.fieldMenu.addAction(action)
self.field_actions[field] = action
lat = float(self.Vradar.value.latitude['data'])
lon = float(self.Vradar.value.longitude['data'])
alt = float(self.Vradar.value.altitude['data'])
self.parameters['grid_origin_lat'] = lat
self.parameters['grid_origin_lon'] = lon
self.parameters['grid_origin_alt'] = alt<|docstring|>Display Py-Art's docstring for help.<|endoftext|>
|
1614d193934143c2b4e15ab4fa455bb091da2158072e852990ed0cb52130fc7c
|
@Profiler.profile
def test_flush_no_pk(n):
'Individual INSERT statements via the ORM, calling upon last row id'
session = Session(bind=engine)
for chunk in range(0, n, 1000):
session.add_all([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(chunk, (chunk + 1000))])
session.flush()
session.commit()
|
Individual INSERT statements via the ORM, calling upon last row id
|
examples/performance/bulk_inserts.py
|
test_flush_no_pk
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_flush_no_pk(n):
session = Session(bind=engine)
for chunk in range(0, n, 1000):
session.add_all([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(chunk, (chunk + 1000))])
session.flush()
session.commit()
|
@Profiler.profile
def test_flush_no_pk(n):
session = Session(bind=engine)
for chunk in range(0, n, 1000):
session.add_all([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(chunk, (chunk + 1000))])
session.flush()
session.commit()<|docstring|>Individual INSERT statements via the ORM, calling upon last row id<|endoftext|>
|
5036234609bdb51ed02b81f6b723fbb2f4967b043d8ad240c14839b35deb21af
|
@Profiler.profile
def test_bulk_save_return_pks(n):
'Individual INSERT statements in "bulk", but calling upon last row id'
session = Session(bind=engine)
session.bulk_save_objects([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)], return_defaults=True)
session.commit()
|
Individual INSERT statements in "bulk", but calling upon last row id
|
examples/performance/bulk_inserts.py
|
test_bulk_save_return_pks
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_bulk_save_return_pks(n):
session = Session(bind=engine)
session.bulk_save_objects([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)], return_defaults=True)
session.commit()
|
@Profiler.profile
def test_bulk_save_return_pks(n):
session = Session(bind=engine)
session.bulk_save_objects([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)], return_defaults=True)
session.commit()<|docstring|>Individual INSERT statements in "bulk", but calling upon last row id<|endoftext|>
|
26e338d5a303f236b9c7706212a62be2fd18d3592aecf0b2b031e0602a6093eb
|
@Profiler.profile
def test_flush_pk_given(n):
'Batched INSERT statements via the ORM, PKs already defined'
session = Session(bind=engine)
for chunk in range(0, n, 1000):
session.add_all([Customer(id=(i + 1), name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(chunk, (chunk + 1000))])
session.flush()
session.commit()
|
Batched INSERT statements via the ORM, PKs already defined
|
examples/performance/bulk_inserts.py
|
test_flush_pk_given
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_flush_pk_given(n):
session = Session(bind=engine)
for chunk in range(0, n, 1000):
session.add_all([Customer(id=(i + 1), name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(chunk, (chunk + 1000))])
session.flush()
session.commit()
|
@Profiler.profile
def test_flush_pk_given(n):
session = Session(bind=engine)
for chunk in range(0, n, 1000):
session.add_all([Customer(id=(i + 1), name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(chunk, (chunk + 1000))])
session.flush()
session.commit()<|docstring|>Batched INSERT statements via the ORM, PKs already defined<|endoftext|>
|
5256f6f336d98ccfd118d25da6f66039045d5fd50d2ad9cca7d384f09b76528b
|
@Profiler.profile
def test_bulk_save(n):
'Batched INSERT statements via the ORM in "bulk", discarding PKs.'
session = Session(bind=engine)
session.bulk_save_objects([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
session.commit()
|
Batched INSERT statements via the ORM in "bulk", discarding PKs.
|
examples/performance/bulk_inserts.py
|
test_bulk_save
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_bulk_save(n):
session = Session(bind=engine)
session.bulk_save_objects([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
session.commit()
|
@Profiler.profile
def test_bulk_save(n):
session = Session(bind=engine)
session.bulk_save_objects([Customer(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
session.commit()<|docstring|>Batched INSERT statements via the ORM in "bulk", discarding PKs.<|endoftext|>
|
876e8ef2f73e053d3ddfe8d69a3354cbe6b34e1bd3f00259ba807bb3d5b8da55
|
@Profiler.profile
def test_bulk_insert_mappings(n):
'Batched INSERT statements via the ORM "bulk", using dictionaries.'
session = Session(bind=engine)
session.bulk_insert_mappings(Customer, [dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
session.commit()
|
Batched INSERT statements via the ORM "bulk", using dictionaries.
|
examples/performance/bulk_inserts.py
|
test_bulk_insert_mappings
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_bulk_insert_mappings(n):
session = Session(bind=engine)
session.bulk_insert_mappings(Customer, [dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
session.commit()
|
@Profiler.profile
def test_bulk_insert_mappings(n):
session = Session(bind=engine)
session.bulk_insert_mappings(Customer, [dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
session.commit()<|docstring|>Batched INSERT statements via the ORM "bulk", using dictionaries.<|endoftext|>
|
931b9508319c147ec2985046caa76cdb7ec277a51fad011d17d9a213d7b9e7b7
|
@Profiler.profile
def test_core_insert(n):
'A single Core INSERT construct inserting mappings in bulk.'
conn = engine.connect()
conn.execute(Customer.__table__.insert(), [dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
|
A single Core INSERT construct inserting mappings in bulk.
|
examples/performance/bulk_inserts.py
|
test_core_insert
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_core_insert(n):
conn = engine.connect()
conn.execute(Customer.__table__.insert(), [dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])
|
@Profiler.profile
def test_core_insert(n):
conn = engine.connect()
conn.execute(Customer.__table__.insert(), [dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n)])<|docstring|>A single Core INSERT construct inserting mappings in bulk.<|endoftext|>
|
ce110adea04024e911b1ff5b3734d9e61aa5dceba97ede1b435e95240c2634e2
|
@Profiler.profile
def test_dbapi_raw(n):
"The DBAPI's API inserting rows in bulk."
conn = engine.pool._creator()
cursor = conn.cursor()
compiled = Customer.__table__.insert().values(name=bindparam('name'), description=bindparam('description')).compile(dialect=engine.dialect)
if compiled.positional:
args = ((('customer name %d' % i), ('customer description %d' % i)) for i in range(n))
else:
args = (dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n))
cursor.executemany(str(compiled), list(args))
conn.commit()
conn.close()
|
The DBAPI's API inserting rows in bulk.
|
examples/performance/bulk_inserts.py
|
test_dbapi_raw
|
NickKush/sqlalchemy
| 5,383 |
python
|
@Profiler.profile
def test_dbapi_raw(n):
conn = engine.pool._creator()
cursor = conn.cursor()
compiled = Customer.__table__.insert().values(name=bindparam('name'), description=bindparam('description')).compile(dialect=engine.dialect)
if compiled.positional:
args = ((('customer name %d' % i), ('customer description %d' % i)) for i in range(n))
else:
args = (dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n))
cursor.executemany(str(compiled), list(args))
conn.commit()
conn.close()
|
@Profiler.profile
def test_dbapi_raw(n):
conn = engine.pool._creator()
cursor = conn.cursor()
compiled = Customer.__table__.insert().values(name=bindparam('name'), description=bindparam('description')).compile(dialect=engine.dialect)
if compiled.positional:
args = ((('customer name %d' % i), ('customer description %d' % i)) for i in range(n))
else:
args = (dict(name=('customer name %d' % i), description=('customer description %d' % i)) for i in range(n))
cursor.executemany(str(compiled), list(args))
conn.commit()
conn.close()<|docstring|>The DBAPI's API inserting rows in bulk.<|endoftext|>
|
3f38675d125afd3c289f08306f3c5fa707cb76c17ae195e3fbf22c3dc6e06c87
|
@contextlib.contextmanager
def change_directory(path):
'Changes working directory and returns to previous on exit.'
previous = Path.cwd()
os.chdir(path)
try:
(yield)
finally:
os.chdir(previous)
|
Changes working directory and returns to previous on exit.
|
tests/support.py
|
change_directory
|
akashdhruv/FlashKit
| 2 |
python
|
@contextlib.contextmanager
def change_directory(path):
previous = Path.cwd()
os.chdir(path)
try:
(yield)
finally:
os.chdir(previous)
|
@contextlib.contextmanager
def change_directory(path):
previous = Path.cwd()
os.chdir(path)
try:
(yield)
finally:
os.chdir(previous)<|docstring|>Changes working directory and returns to previous on exit.<|endoftext|>
|
310fc428cef5ea675261879e92a4c5ccf63268a9eee949bed45068a3e03f1e43
|
def exclude(path: str):
'Does the path meet any rules for exclusion?'
EXCLUDES = {'__.*__', '/\\.'}
NO_LINKS = {'\\.xmf', '\\.h5', 'run'}
return any((re.search(exclude, str(path)) for exclude in EXCLUDES.union(NO_LINKS)))
|
Does the path meet any rules for exclusion?
|
tests/support.py
|
exclude
|
akashdhruv/FlashKit
| 2 |
python
|
def exclude(path: str):
EXCLUDES = {'__.*__', '/\\.'}
NO_LINKS = {'\\.xmf', '\\.h5', 'run'}
return any((re.search(exclude, str(path)) for exclude in EXCLUDES.union(NO_LINKS)))
|
def exclude(path: str):
EXCLUDES = {'__.*__', '/\\.'}
NO_LINKS = {'\\.xmf', '\\.h5', 'run'}
return any((re.search(exclude, str(path)) for exclude in EXCLUDES.union(NO_LINKS)))<|docstring|>Does the path meet any rules for exclusion?<|endoftext|>
|
c236343d4d3cd4b264104909bd32b9f481e612f68ee0ff182f44fa0ee845d8a6
|
def selectStack(self, parent_trace):
'\n Called as part of setting up each integration test case. It chooses and provisions the stack that should\n be used by this test case.\n '
self._stack = ShutilStoreTestStack(parent_trace, self.a6i_config)
|
Called as part of setting up each integration test case. It chooses and provisions the stack that should
be used by this test case.
|
src/apodeixi/knowledge_base/tests_integration/post_update_skeleton.py
|
selectStack
|
ChateauClaudia-Labs/apodeixi
| 0 |
python
|
def selectStack(self, parent_trace):
'\n Called as part of setting up each integration test case. It chooses and provisions the stack that should\n be used by this test case.\n '
self._stack = ShutilStoreTestStack(parent_trace, self.a6i_config)
|
def selectStack(self, parent_trace):
'\n Called as part of setting up each integration test case. It chooses and provisions the stack that should\n be used by this test case.\n '
self._stack = ShutilStoreTestStack(parent_trace, self.a6i_config)<|docstring|>Called as part of setting up each integration test case. It chooses and provisions the stack that should
be used by this test case.<|endoftext|>
|
67b889af2c82ae5692acba976423562d248d1d7262c726bcb7ca0fbc05e15b37
|
def setup_static_data(self, parent_trace):
'\n Sets up the static data that is generally needed by flow tests\n '
EXCEL_FILES = ['products.static-data.admin.a6i.xlsx', 'scoring-cycles.static-data.admin.a6i.xlsx']
my_trace = parent_trace.doing('Setting up static data')
for file in EXCEL_FILES:
loop_trace = my_trace.doing((("Posting file '" + str(file)) + "'"))
posting_path = ((((self.getInputDataFolder(loop_trace) + '/') + self.scenario()) + '/') + file)
(response, log_txt) = self.stack().kb().postByFile(parent_trace=loop_trace, path_of_file_being_posted=posting_path, excel_sheet='Posting Label')
|
Sets up the static data that is generally needed by flow tests
|
src/apodeixi/knowledge_base/tests_integration/post_update_skeleton.py
|
setup_static_data
|
ChateauClaudia-Labs/apodeixi
| 0 |
python
|
def setup_static_data(self, parent_trace):
'\n \n '
EXCEL_FILES = ['products.static-data.admin.a6i.xlsx', 'scoring-cycles.static-data.admin.a6i.xlsx']
my_trace = parent_trace.doing('Setting up static data')
for file in EXCEL_FILES:
loop_trace = my_trace.doing((("Posting file '" + str(file)) + "'"))
posting_path = ((((self.getInputDataFolder(loop_trace) + '/') + self.scenario()) + '/') + file)
(response, log_txt) = self.stack().kb().postByFile(parent_trace=loop_trace, path_of_file_being_posted=posting_path, excel_sheet='Posting Label')
|
def setup_static_data(self, parent_trace):
'\n \n '
EXCEL_FILES = ['products.static-data.admin.a6i.xlsx', 'scoring-cycles.static-data.admin.a6i.xlsx']
my_trace = parent_trace.doing('Setting up static data')
for file in EXCEL_FILES:
loop_trace = my_trace.doing((("Posting file '" + str(file)) + "'"))
posting_path = ((((self.getInputDataFolder(loop_trace) + '/') + self.scenario()) + '/') + file)
(response, log_txt) = self.stack().kb().postByFile(parent_trace=loop_trace, path_of_file_being_posted=posting_path, excel_sheet='Posting Label')<|docstring|>Sets up the static data that is generally needed by flow tests<|endoftext|>
|
ad97078d248855e0ccfad897eebeb4ae144225afb9e3b4a889bea909f91c0deb
|
def setup_reference_data(self, parent_trace):
'\n Sets up any reference data (such as other manifests) that are assumed as pre-conditions by this test. \n '
if (self.scenario() == 'basic_posting_flows.milestones'):
EXCEL_FILE = 'for_mls.big-rocks.journeys.a6i.xlsx'
EXCEL_FOLDER = ((self.getInputDataFolder(parent_trace) + '/') + self.scenario())
my_trace = self.trace_environment(parent_trace, 'Creating big-rocks dependency')
if True:
clientURL = self.stack().store().current_environment(my_trace).clientURL(my_trace)
posting_path = ((EXCEL_FOLDER + '/') + EXCEL_FILE)
(response, log_txt) = self.stack().kb().postByFile(parent_trace=my_trace, path_of_file_being_posted=posting_path, excel_sheet='Posting Label')
self.check_environment_contents(parent_trace=my_trace)
else:
return
|
Sets up any reference data (such as other manifests) that are assumed as pre-conditions by this test.
|
src/apodeixi/knowledge_base/tests_integration/post_update_skeleton.py
|
setup_reference_data
|
ChateauClaudia-Labs/apodeixi
| 0 |
python
|
def setup_reference_data(self, parent_trace):
'\n \n '
if (self.scenario() == 'basic_posting_flows.milestones'):
EXCEL_FILE = 'for_mls.big-rocks.journeys.a6i.xlsx'
EXCEL_FOLDER = ((self.getInputDataFolder(parent_trace) + '/') + self.scenario())
my_trace = self.trace_environment(parent_trace, 'Creating big-rocks dependency')
if True:
clientURL = self.stack().store().current_environment(my_trace).clientURL(my_trace)
posting_path = ((EXCEL_FOLDER + '/') + EXCEL_FILE)
(response, log_txt) = self.stack().kb().postByFile(parent_trace=my_trace, path_of_file_being_posted=posting_path, excel_sheet='Posting Label')
self.check_environment_contents(parent_trace=my_trace)
else:
return
|
def setup_reference_data(self, parent_trace):
'\n \n '
if (self.scenario() == 'basic_posting_flows.milestones'):
EXCEL_FILE = 'for_mls.big-rocks.journeys.a6i.xlsx'
EXCEL_FOLDER = ((self.getInputDataFolder(parent_trace) + '/') + self.scenario())
my_trace = self.trace_environment(parent_trace, 'Creating big-rocks dependency')
if True:
clientURL = self.stack().store().current_environment(my_trace).clientURL(my_trace)
posting_path = ((EXCEL_FOLDER + '/') + EXCEL_FILE)
(response, log_txt) = self.stack().kb().postByFile(parent_trace=my_trace, path_of_file_being_posted=posting_path, excel_sheet='Posting Label')
self.check_environment_contents(parent_trace=my_trace)
else:
return<|docstring|>Sets up any reference data (such as other manifests) that are assumed as pre-conditions by this test.<|endoftext|>
|
a8f4be543135430936fd5890917a0ef00d869fed952d00fd832aaf6f676124bd
|
def is_palindrome(text):
'A string of characters is a palindrome if it reads the same forwards and\n backwards, ignoring punctuation, whitespace, and letter casing.'
assert isinstance(text, str), 'input is not a string: {}'.format(text)
return is_palindrome_recursive(text, 0, (len(text) - 1))
|
A string of characters is a palindrome if it reads the same forwards and
backwards, ignoring punctuation, whitespace, and letter casing.
|
Src-Code/palindromes-and-strings/palindromes.py
|
is_palindrome
|
KingGenius5/CS13-Core-Data-Structures
| 0 |
python
|
def is_palindrome(text):
'A string of characters is a palindrome if it reads the same forwards and\n backwards, ignoring punctuation, whitespace, and letter casing.'
assert isinstance(text, str), 'input is not a string: {}'.format(text)
return is_palindrome_recursive(text, 0, (len(text) - 1))
|
def is_palindrome(text):
'A string of characters is a palindrome if it reads the same forwards and\n backwards, ignoring punctuation, whitespace, and letter casing.'
assert isinstance(text, str), 'input is not a string: {}'.format(text)
return is_palindrome_recursive(text, 0, (len(text) - 1))<|docstring|>A string of characters is a palindrome if it reads the same forwards and
backwards, ignoring punctuation, whitespace, and letter casing.<|endoftext|>
|
3feab423bf657c5fdd817568c518c266ef78608297cc93dbcd88bdfe49f14bd5
|
def set_soc_variables(self):
'Set variables relating to the state of charge.'
z = pybamm.standard_spatial_vars.z
soc = (pybamm.Integral(self.variables['X-averaged electrolyte concentration'], z) * 100)
self.variables.update({'State of Charge': soc, 'Depth of Discharge': (100 - soc)})
if ('Fractional Charge Input' not in self.variables):
fci = pybamm.Variable('Fractional Charge Input', domain='current collector')
self.variables['Fractional Charge Input'] = fci
self.rhs[fci] = ((- self.variables['Total current density']) * 100)
self.initial_conditions[fci] = (self.param.q_init * 100)
|
Set variables relating to the state of charge.
|
pybamm/models/full_battery_models/lead_acid/base_lead_acid_model.py
|
set_soc_variables
|
DrSOKane/PyBaMM
| 1 |
python
|
def set_soc_variables(self):
z = pybamm.standard_spatial_vars.z
soc = (pybamm.Integral(self.variables['X-averaged electrolyte concentration'], z) * 100)
self.variables.update({'State of Charge': soc, 'Depth of Discharge': (100 - soc)})
if ('Fractional Charge Input' not in self.variables):
fci = pybamm.Variable('Fractional Charge Input', domain='current collector')
self.variables['Fractional Charge Input'] = fci
self.rhs[fci] = ((- self.variables['Total current density']) * 100)
self.initial_conditions[fci] = (self.param.q_init * 100)
|
def set_soc_variables(self):
z = pybamm.standard_spatial_vars.z
soc = (pybamm.Integral(self.variables['X-averaged electrolyte concentration'], z) * 100)
self.variables.update({'State of Charge': soc, 'Depth of Discharge': (100 - soc)})
if ('Fractional Charge Input' not in self.variables):
fci = pybamm.Variable('Fractional Charge Input', domain='current collector')
self.variables['Fractional Charge Input'] = fci
self.rhs[fci] = ((- self.variables['Total current density']) * 100)
self.initial_conditions[fci] = (self.param.q_init * 100)<|docstring|>Set variables relating to the state of charge.<|endoftext|>
|
19c01b3b8fb084a3942e2a132551dcf972e8d2f25fba8c2adc115e9768969dc4
|
def Update(self, level: Map, dt: int, movingAIGroup: pygame.sprite.Group):
'Update the AI. Brain and needs'
self.time += dt
if (self.time > 500):
self.time = 0
self.needs.stepNeeds()
self.movingCreatures = movingAIGroup
self.brain.update(level)
|
Update the AI. Brain and needs
|
ClergyRobotClasses/ClergyRobot.py
|
Update
|
FearlessClock/RobotFactory
| 0 |
python
|
def Update(self, level: Map, dt: int, movingAIGroup: pygame.sprite.Group):
self.time += dt
if (self.time > 500):
self.time = 0
self.needs.stepNeeds()
self.movingCreatures = movingAIGroup
self.brain.update(level)
|
def Update(self, level: Map, dt: int, movingAIGroup: pygame.sprite.Group):
self.time += dt
if (self.time > 500):
self.time = 0
self.needs.stepNeeds()
self.movingCreatures = movingAIGroup
self.brain.update(level)<|docstring|>Update the AI. Brain and needs<|endoftext|>
|
d3b4188f2ab2f5585dc9ddd9e67cfd6727edcbe33cdf9c57ce22855191733ad7
|
@staticmethod
def _distance(token_from: str, token_to: str) -> float:
'\n Calculates distance between two cell centers in KMs based on Earth radius 6373 KM\n :param cell_a: first cell\n :param cell_b: second cell\n :return: distance in KMs\n '
r = 6373.0
cell_from = s2sphere.CellId.from_token(token_from)
cell_to = s2sphere.CellId.from_token(token_to)
return (cell_from.to_lat_lng().get_distance(cell_to.to_lat_lng()).radians * r)
|
Calculates distance between two cell centers in KMs based on Earth radius 6373 KM
:param cell_a: first cell
:param cell_b: second cell
:return: distance in KMs
|
src/pipeline_oriented_analytics/transformer/sphere_distance.py
|
_distance
|
bbiletskyy/pipeline-oriented-analytics
| 8 |
python
|
@staticmethod
def _distance(token_from: str, token_to: str) -> float:
'\n Calculates distance between two cell centers in KMs based on Earth radius 6373 KM\n :param cell_a: first cell\n :param cell_b: second cell\n :return: distance in KMs\n '
r = 6373.0
cell_from = s2sphere.CellId.from_token(token_from)
cell_to = s2sphere.CellId.from_token(token_to)
return (cell_from.to_lat_lng().get_distance(cell_to.to_lat_lng()).radians * r)
|
@staticmethod
def _distance(token_from: str, token_to: str) -> float:
'\n Calculates distance between two cell centers in KMs based on Earth radius 6373 KM\n :param cell_a: first cell\n :param cell_b: second cell\n :return: distance in KMs\n '
r = 6373.0
cell_from = s2sphere.CellId.from_token(token_from)
cell_to = s2sphere.CellId.from_token(token_to)
return (cell_from.to_lat_lng().get_distance(cell_to.to_lat_lng()).radians * r)<|docstring|>Calculates distance between two cell centers in KMs based on Earth radius 6373 KM
:param cell_a: first cell
:param cell_b: second cell
:return: distance in KMs<|endoftext|>
|
27f3124b5ff5776e6040d3491fc3dc9d6246ee0dddf6b8bc22855a6973da9bbe
|
@command('install')
def install(config):
'install elasticsearch from zip right here, mostly used for testing'
package = 'elasticsearch'
version = '6.3.2'
filename = '{}-{}.zip'.format(package, version)
if (not exists(filename)):
url = ('https://artifacts.elastic.co/downloads/elasticsearch/' + filename)
logger.info('Downloading %s', url)
r = requests.get(url)
with open(filename, 'wb') as output:
for chunk in r.iter_content(chunk_size=(512 * 1024)):
output.write(chunk)
logger.info('Extracting %s', filename)
import zipfile
zip_ref = MyZipFile(filename, 'r')
zip_ref.extractall('.')
zip_ref.close()
|
install elasticsearch from zip right here, mostly used for testing
|
elastico/cli_old.py
|
install
|
klorenz/python-elastico
| 0 |
python
|
@command('install')
def install(config):
package = 'elasticsearch'
version = '6.3.2'
filename = '{}-{}.zip'.format(package, version)
if (not exists(filename)):
url = ('https://artifacts.elastic.co/downloads/elasticsearch/' + filename)
logger.info('Downloading %s', url)
r = requests.get(url)
with open(filename, 'wb') as output:
for chunk in r.iter_content(chunk_size=(512 * 1024)):
output.write(chunk)
logger.info('Extracting %s', filename)
import zipfile
zip_ref = MyZipFile(filename, 'r')
zip_ref.extractall('.')
zip_ref.close()
|
@command('install')
def install(config):
package = 'elasticsearch'
version = '6.3.2'
filename = '{}-{}.zip'.format(package, version)
if (not exists(filename)):
url = ('https://artifacts.elastic.co/downloads/elasticsearch/' + filename)
logger.info('Downloading %s', url)
r = requests.get(url)
with open(filename, 'wb') as output:
for chunk in r.iter_content(chunk_size=(512 * 1024)):
output.write(chunk)
logger.info('Extracting %s', filename)
import zipfile
zip_ref = MyZipFile(filename, 'r')
zip_ref.extractall('.')
zip_ref.close()<|docstring|>install elasticsearch from zip right here, mostly used for testing<|endoftext|>
|
e4bd6a27174e7deb5534bd94c62a6aa4cc7b49d83d2e8d864a94b9872cb2d79e
|
@command('run')
def install(config):
'run elastic search in current directory'
package = 'elasticsearch'
version = '6.3.2'
executable = '{}-{}/bin/elasticsearch'.format(package, version)
os.execl(executable, executable)
|
run elastic search in current directory
|
elastico/cli_old.py
|
install
|
klorenz/python-elastico
| 0 |
python
|
@command('run')
def install(config):
package = 'elasticsearch'
version = '6.3.2'
executable = '{}-{}/bin/elasticsearch'.format(package, version)
os.execl(executable, executable)
|
@command('run')
def install(config):
package = 'elasticsearch'
version = '6.3.2'
executable = '{}-{}/bin/elasticsearch'.format(package, version)
os.execl(executable, executable)<|docstring|>run elastic search in current directory<|endoftext|>
|
9933556e61ead66d089cabf3df2f1029f3335d6246aeacce9f74803d17c21b40
|
@command('export', arg('--format', choices=('zip', 'dir'), default='dir'), arg('index_name', help='name of index to export'))
def cmd_export(config):
'Export indices into your working directory\n '
from .connection import elasticsearch
es = elasticsearch(config)
from elasticsearch.helpers import scan
index_name = config.get('export.index_name')
result = es.indices.get(index_name)
for (idx_name, idx_data) in result.items():
if (config.get('export.format') == 'dir'):
os.makedirs(idx_name)
with open(join(idx_name, 'mappings.json'), 'w') as f:
json.dump(result[idx_name]['mappings'], f)
log.info('exporting %s to %s/', idx_name, idx_name)
with open(join(idx_name, 'data.json'), 'w') as f:
for data in scan(es, query={'query': {'match_all': {}}}, index=index_name):
json.dump(data, f)
f.write('\n')
elif (config.get('export.format') == 'zip'):
pass
|
Export indices into your working directory
|
elastico/cli_old.py
|
cmd_export
|
klorenz/python-elastico
| 0 |
python
|
@command('export', arg('--format', choices=('zip', 'dir'), default='dir'), arg('index_name', help='name of index to export'))
def cmd_export(config):
'\n '
from .connection import elasticsearch
es = elasticsearch(config)
from elasticsearch.helpers import scan
index_name = config.get('export.index_name')
result = es.indices.get(index_name)
for (idx_name, idx_data) in result.items():
if (config.get('export.format') == 'dir'):
os.makedirs(idx_name)
with open(join(idx_name, 'mappings.json'), 'w') as f:
json.dump(result[idx_name]['mappings'], f)
log.info('exporting %s to %s/', idx_name, idx_name)
with open(join(idx_name, 'data.json'), 'w') as f:
for data in scan(es, query={'query': {'match_all': {}}}, index=index_name):
json.dump(data, f)
f.write('\n')
elif (config.get('export.format') == 'zip'):
pass
|
@command('export', arg('--format', choices=('zip', 'dir'), default='dir'), arg('index_name', help='name of index to export'))
def cmd_export(config):
'\n '
from .connection import elasticsearch
es = elasticsearch(config)
from elasticsearch.helpers import scan
index_name = config.get('export.index_name')
result = es.indices.get(index_name)
for (idx_name, idx_data) in result.items():
if (config.get('export.format') == 'dir'):
os.makedirs(idx_name)
with open(join(idx_name, 'mappings.json'), 'w') as f:
json.dump(result[idx_name]['mappings'], f)
log.info('exporting %s to %s/', idx_name, idx_name)
with open(join(idx_name, 'data.json'), 'w') as f:
for data in scan(es, query={'query': {'match_all': {}}}, index=index_name):
json.dump(data, f)
f.write('\n')
elif (config.get('export.format') == 'zip'):
pass<|docstring|>Export indices into your working directory<|endoftext|>
|
24a070d4af075fecc39c3b3538087b0e76ec6af04ad74bc8a4fa5b1a9288c701
|
def main():
'Main entry point for script.'
parser = argparse.ArgumentParser(description='Find a RSA private key collision.')
parser.add_argument('cipher_path', help='Cipher')
parser.add_argument('message_path', help='Message')
parser.add_argument('secretkey_path', help='Secret Key in pem format')
parser.add_argument('--log_path', type=str, help='Create a log in given path')
args = parser.parse_args()
mfile = open(args.message_path, 'r')
message = mfile.read()
mfile.close()
cfile = open(args.cipher_path, 'r')
cipher = cfile.read()
cfile.close()
kfile = open(args.publickey_path, 'r')
publickey = kfile.read()
kfile.close()
if (args.log_path is not None):
path = (args.log_path + '/latency.log')
basicConfig(filename=path, level=DEBUG)
start = time()
print(collision_finder(message, cipher, publickey))
debug('%s: collision_finder: %s [s]', asctime(localtime(time())), (time() - start))
|
Main entry point for script.
|
deniable/scripts/deniablecollision.py
|
main
|
victormn/deniable-encryption
| 3 |
python
|
def main():
parser = argparse.ArgumentParser(description='Find a RSA private key collision.')
parser.add_argument('cipher_path', help='Cipher')
parser.add_argument('message_path', help='Message')
parser.add_argument('secretkey_path', help='Secret Key in pem format')
parser.add_argument('--log_path', type=str, help='Create a log in given path')
args = parser.parse_args()
mfile = open(args.message_path, 'r')
message = mfile.read()
mfile.close()
cfile = open(args.cipher_path, 'r')
cipher = cfile.read()
cfile.close()
kfile = open(args.publickey_path, 'r')
publickey = kfile.read()
kfile.close()
if (args.log_path is not None):
path = (args.log_path + '/latency.log')
basicConfig(filename=path, level=DEBUG)
start = time()
print(collision_finder(message, cipher, publickey))
debug('%s: collision_finder: %s [s]', asctime(localtime(time())), (time() - start))
|
def main():
parser = argparse.ArgumentParser(description='Find a RSA private key collision.')
parser.add_argument('cipher_path', help='Cipher')
parser.add_argument('message_path', help='Message')
parser.add_argument('secretkey_path', help='Secret Key in pem format')
parser.add_argument('--log_path', type=str, help='Create a log in given path')
args = parser.parse_args()
mfile = open(args.message_path, 'r')
message = mfile.read()
mfile.close()
cfile = open(args.cipher_path, 'r')
cipher = cfile.read()
cfile.close()
kfile = open(args.publickey_path, 'r')
publickey = kfile.read()
kfile.close()
if (args.log_path is not None):
path = (args.log_path + '/latency.log')
basicConfig(filename=path, level=DEBUG)
start = time()
print(collision_finder(message, cipher, publickey))
debug('%s: collision_finder: %s [s]', asctime(localtime(time())), (time() - start))<|docstring|>Main entry point for script.<|endoftext|>
|
0189b881444f6d000c78aa07515d0bc7bbc8b9216c52807d32a5431fe4ac4de9
|
def clean_word(to_clean):
'Normalizes and cleans a non-ascii string.\n\n Args:\n to_clean (string): the string to clean and normalize.\n\n Returns:\n A cleaned and normalized string\n '
import string
import unicodedata
return unicodedata.normalize('NFKD', to_clean).encode('ASCII', 'ignore').lower().strip().replace(' ', '').translate(None, string.punctuation)
|
Normalizes and cleans a non-ascii string.
Args:
to_clean (string): the string to clean and normalize.
Returns:
A cleaned and normalized string
|
9. is_anagram/anagram.py
|
clean_word
|
jeury301/python-morsels
| 2 |
python
|
def clean_word(to_clean):
'Normalizes and cleans a non-ascii string.\n\n Args:\n to_clean (string): the string to clean and normalize.\n\n Returns:\n A cleaned and normalized string\n '
import string
import unicodedata
return unicodedata.normalize('NFKD', to_clean).encode('ASCII', 'ignore').lower().strip().replace(' ', ).translate(None, string.punctuation)
|
def clean_word(to_clean):
'Normalizes and cleans a non-ascii string.\n\n Args:\n to_clean (string): the string to clean and normalize.\n\n Returns:\n A cleaned and normalized string\n '
import string
import unicodedata
return unicodedata.normalize('NFKD', to_clean).encode('ASCII', 'ignore').lower().strip().replace(' ', ).translate(None, string.punctuation)<|docstring|>Normalizes and cleans a non-ascii string.
Args:
to_clean (string): the string to clean and normalize.
Returns:
A cleaned and normalized string<|endoftext|>
|
f25f8caf5c61968c6d1b95286aae3f3253e61911e8aa531487f21923ad91f072
|
def is_anagram(first_word, second_word):
'Determining if two strings are anagrams of each other.\n\n Args:\n first_word (string): a string to test for anagram property\n second_word (string): a string to test for anagram property against\n the first.\n\n Returns:\n True or False, based on whether the strings are anagram of each other\n '
clean_first_word = clean_word(first_word)
clean_second_word = clean_word(second_word)
if (len(clean_first_word) != len(clean_second_word)):
return False
clean_second_iter = iter(clean_second_word)
while True:
try:
if (next(clean_second_iter) not in clean_first_word):
return False
except StopIteration:
return True
|
Determining if two strings are anagrams of each other.
Args:
first_word (string): a string to test for anagram property
second_word (string): a string to test for anagram property against
the first.
Returns:
True or False, based on whether the strings are anagram of each other
|
9. is_anagram/anagram.py
|
is_anagram
|
jeury301/python-morsels
| 2 |
python
|
def is_anagram(first_word, second_word):
'Determining if two strings are anagrams of each other.\n\n Args:\n first_word (string): a string to test for anagram property\n second_word (string): a string to test for anagram property against\n the first.\n\n Returns:\n True or False, based on whether the strings are anagram of each other\n '
clean_first_word = clean_word(first_word)
clean_second_word = clean_word(second_word)
if (len(clean_first_word) != len(clean_second_word)):
return False
clean_second_iter = iter(clean_second_word)
while True:
try:
if (next(clean_second_iter) not in clean_first_word):
return False
except StopIteration:
return True
|
def is_anagram(first_word, second_word):
'Determining if two strings are anagrams of each other.\n\n Args:\n first_word (string): a string to test for anagram property\n second_word (string): a string to test for anagram property against\n the first.\n\n Returns:\n True or False, based on whether the strings are anagram of each other\n '
clean_first_word = clean_word(first_word)
clean_second_word = clean_word(second_word)
if (len(clean_first_word) != len(clean_second_word)):
return False
clean_second_iter = iter(clean_second_word)
while True:
try:
if (next(clean_second_iter) not in clean_first_word):
return False
except StopIteration:
return True<|docstring|>Determining if two strings are anagrams of each other.
Args:
first_word (string): a string to test for anagram property
second_word (string): a string to test for anagram property against
the first.
Returns:
True or False, based on whether the strings are anagram of each other<|endoftext|>
|
c95875569dcc5ffc8950d2c4ece5616d06ab78164eb865331804a7f284b936a2
|
def conv3x3(in_planes, out_planes, stride=1, groups=1, dilation=1):
'3x3 convolution with padding'
return nn.Conv2d(in_planes, out_planes, kernel_size=3, stride=stride, padding=dilation, groups=groups, bias=False, dilation=dilation)
|
3x3 convolution with padding
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
conv3x3
|
minhtannguyen/RAdam
| 0 |
python
|
def conv3x3(in_planes, out_planes, stride=1, groups=1, dilation=1):
return nn.Conv2d(in_planes, out_planes, kernel_size=3, stride=stride, padding=dilation, groups=groups, bias=False, dilation=dilation)
|
def conv3x3(in_planes, out_planes, stride=1, groups=1, dilation=1):
return nn.Conv2d(in_planes, out_planes, kernel_size=3, stride=stride, padding=dilation, groups=groups, bias=False, dilation=dilation)<|docstring|>3x3 convolution with padding<|endoftext|>
|
7447c07b06cc8d16674f31fc29f40a376c8d7a0321f9f661635b233109ed88c5
|
def conv1x1(in_planes, out_planes, stride=1):
'1x1 convolution'
return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False)
|
1x1 convolution
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
conv1x1
|
minhtannguyen/RAdam
| 0 |
python
|
def conv1x1(in_planes, out_planes, stride=1):
return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False)
|
def conv1x1(in_planes, out_planes, stride=1):
return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False)<|docstring|>1x1 convolution<|endoftext|>
|
3eeb63ed21a1e3cf7377ab8616b9ff240781f8ec3174bfb7797ac0ce9208c849
|
def horesnet18(pretrained=False, progress=True, **kwargs):
'ResNet-18 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet18', BasicBlock, [2, 2, 2, 2], pretrained, progress, **kwargs)
|
ResNet-18 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnet18
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnet18(pretrained=False, progress=True, **kwargs):
'ResNet-18 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet18', BasicBlock, [2, 2, 2, 2], pretrained, progress, **kwargs)
|
def horesnet18(pretrained=False, progress=True, **kwargs):
'ResNet-18 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet18', BasicBlock, [2, 2, 2, 2], pretrained, progress, **kwargs)<|docstring|>ResNet-18 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
15a5918ee3b9ea6522f5f002cd07e67fe91fbcbe671f3387f3836393cae10b98
|
def horesnet34(pretrained=False, progress=True, **kwargs):
'ResNet-34 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet34', BasicBlock, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
ResNet-34 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnet34
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnet34(pretrained=False, progress=True, **kwargs):
'ResNet-34 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet34', BasicBlock, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
def horesnet34(pretrained=False, progress=True, **kwargs):
'ResNet-34 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet34', BasicBlock, [3, 4, 6, 3], pretrained, progress, **kwargs)<|docstring|>ResNet-34 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
1bb41955bd64d089670e97b0b04e84c8494ef7235a88681b139fc7b5fc06c45b
|
def horesnet50(pretrained=False, progress=True, **kwargs):
'ResNet-50 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet50', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
ResNet-50 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnet50
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnet50(pretrained=False, progress=True, **kwargs):
'ResNet-50 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet50', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
def horesnet50(pretrained=False, progress=True, **kwargs):
'ResNet-50 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet50', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)<|docstring|>ResNet-50 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
ed267532dfb5b423112510b0fb48676ddc27deef00a596b7839442116f4a1dca
|
def horesnet101(pretrained=False, progress=True, **kwargs):
'ResNet-101 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet101', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)
|
ResNet-101 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnet101
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnet101(pretrained=False, progress=True, **kwargs):
'ResNet-101 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet101', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)
|
def horesnet101(pretrained=False, progress=True, **kwargs):
'ResNet-101 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet101', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)<|docstring|>ResNet-101 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
fb241393713e6a2c2f9c19a9cbaaaa705fdc4b3dc2ff4463217443040901b475
|
def horesnet152(pretrained=False, progress=True, **kwargs):
'ResNet-152 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet152', Bottleneck, [3, 8, 36, 3], pretrained, progress, **kwargs)
|
ResNet-152 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnet152
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnet152(pretrained=False, progress=True, **kwargs):
'ResNet-152 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet152', Bottleneck, [3, 8, 36, 3], pretrained, progress, **kwargs)
|
def horesnet152(pretrained=False, progress=True, **kwargs):
'ResNet-152 model from\n `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
return _horesnet('horesnet152', Bottleneck, [3, 8, 36, 3], pretrained, progress, **kwargs)<|docstring|>ResNet-152 model from
`"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
4ccad11c6f0202b5fd3aa5c3b51cc5d2cfe575553769c0538346564294b73722
|
def horesnext50_32x4d(pretrained=False, progress=True, **kwargs):
'ResNeXt-50 32x4d model from\n `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['groups'] = 32
kwargs['width_per_group'] = 4
return _horesnet('horesnext50_32x4d', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
ResNeXt-50 32x4d model from
`"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnext50_32x4d
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnext50_32x4d(pretrained=False, progress=True, **kwargs):
'ResNeXt-50 32x4d model from\n `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['groups'] = 32
kwargs['width_per_group'] = 4
return _horesnet('horesnext50_32x4d', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
def horesnext50_32x4d(pretrained=False, progress=True, **kwargs):
'ResNeXt-50 32x4d model from\n `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['groups'] = 32
kwargs['width_per_group'] = 4
return _horesnet('horesnext50_32x4d', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)<|docstring|>ResNeXt-50 32x4d model from
`"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
e51abf6290772a99fc1e341737ff2130651e016217c43bd66fd5a676a45ab7a4
|
def horesnext101_32x8d(pretrained=False, progress=True, **kwargs):
'ResNeXt-101 32x8d model from\n `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['groups'] = 32
kwargs['width_per_group'] = 8
return _horesnet('horesnext101_32x8d', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)
|
ResNeXt-101 32x8d model from
`"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
horesnext101_32x8d
|
minhtannguyen/RAdam
| 0 |
python
|
def horesnext101_32x8d(pretrained=False, progress=True, **kwargs):
'ResNeXt-101 32x8d model from\n `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['groups'] = 32
kwargs['width_per_group'] = 8
return _horesnet('horesnext101_32x8d', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)
|
def horesnext101_32x8d(pretrained=False, progress=True, **kwargs):
'ResNeXt-101 32x8d model from\n `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['groups'] = 32
kwargs['width_per_group'] = 8
return _horesnet('horesnext101_32x8d', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)<|docstring|>ResNeXt-101 32x8d model from
`"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
9b7fca18291a72e1966033572a28a509223a003f4fed9ba98babb7b6aee3c86e
|
def howide_resnet50_2(pretrained=False, progress=True, **kwargs):
'Wide ResNet-50-2 model from\n `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_\n The model is the same as ResNet except for the bottleneck number of channels\n which is twice larger in every block. The number of channels in outer 1x1\n convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048\n channels, and in Wide ResNet-50-2 has 2048-1024-2048.\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['width_per_group'] = (64 * 2)
return _horesnet('howide_resnet50_2', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
Wide ResNet-50-2 model from
`"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_
The model is the same as ResNet except for the bottleneck number of channels
which is twice larger in every block. The number of channels in outer 1x1
convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048
channels, and in Wide ResNet-50-2 has 2048-1024-2048.
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
howide_resnet50_2
|
minhtannguyen/RAdam
| 0 |
python
|
def howide_resnet50_2(pretrained=False, progress=True, **kwargs):
'Wide ResNet-50-2 model from\n `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_\n The model is the same as ResNet except for the bottleneck number of channels\n which is twice larger in every block. The number of channels in outer 1x1\n convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048\n channels, and in Wide ResNet-50-2 has 2048-1024-2048.\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['width_per_group'] = (64 * 2)
return _horesnet('howide_resnet50_2', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)
|
def howide_resnet50_2(pretrained=False, progress=True, **kwargs):
'Wide ResNet-50-2 model from\n `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_\n The model is the same as ResNet except for the bottleneck number of channels\n which is twice larger in every block. The number of channels in outer 1x1\n convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048\n channels, and in Wide ResNet-50-2 has 2048-1024-2048.\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['width_per_group'] = (64 * 2)
return _horesnet('howide_resnet50_2', Bottleneck, [3, 4, 6, 3], pretrained, progress, **kwargs)<|docstring|>Wide ResNet-50-2 model from
`"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_
The model is the same as ResNet except for the bottleneck number of channels
which is twice larger in every block. The number of channels in outer 1x1
convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048
channels, and in Wide ResNet-50-2 has 2048-1024-2048.
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
a354af382f4d7dd3321d8ef0cf283c0a86116b9837d8ef81f9c403917389ec4d
|
def howide_resnet101_2(pretrained=False, progress=True, **kwargs):
'Wide ResNet-101-2 model from\n `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_\n The model is the same as ResNet except for the bottleneck number of channels\n which is twice larger in every block. The number of channels in outer 1x1\n convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048\n channels, and in Wide ResNet-50-2 has 2048-1024-2048.\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['width_per_group'] = (64 * 2)
return _horesnet('howide_resnet101_2', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)
|
Wide ResNet-101-2 model from
`"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_
The model is the same as ResNet except for the bottleneck number of channels
which is twice larger in every block. The number of channels in outer 1x1
convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048
channels, and in Wide ResNet-50-2 has 2048-1024-2048.
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr
|
cifar_imagenet/models_backup/imagenet_v4_1/horesnet.py
|
howide_resnet101_2
|
minhtannguyen/RAdam
| 0 |
python
|
def howide_resnet101_2(pretrained=False, progress=True, **kwargs):
'Wide ResNet-101-2 model from\n `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_\n The model is the same as ResNet except for the bottleneck number of channels\n which is twice larger in every block. The number of channels in outer 1x1\n convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048\n channels, and in Wide ResNet-50-2 has 2048-1024-2048.\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['width_per_group'] = (64 * 2)
return _horesnet('howide_resnet101_2', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)
|
def howide_resnet101_2(pretrained=False, progress=True, **kwargs):
'Wide ResNet-101-2 model from\n `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_\n The model is the same as ResNet except for the bottleneck number of channels\n which is twice larger in every block. The number of channels in outer 1x1\n convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048\n channels, and in Wide ResNet-50-2 has 2048-1024-2048.\n Args:\n pretrained (bool): If True, returns a model pre-trained on ImageNet\n progress (bool): If True, displays a progress bar of the download to stderr\n '
kwargs['width_per_group'] = (64 * 2)
return _horesnet('howide_resnet101_2', Bottleneck, [3, 4, 23, 3], pretrained, progress, **kwargs)<|docstring|>Wide ResNet-101-2 model from
`"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_
The model is the same as ResNet except for the bottleneck number of channels
which is twice larger in every block. The number of channels in outer 1x1
convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048
channels, and in Wide ResNet-50-2 has 2048-1024-2048.
Args:
pretrained (bool): If True, returns a model pre-trained on ImageNet
progress (bool): If True, displays a progress bar of the download to stderr<|endoftext|>
|
67798ab9748c2afc5f5298c4ee684a16eb1239bb597019a8dff498b16c1b7991
|
def validateParams(sOn, sOff, herd, nAgents, echo=False):
'\n Function checks whether parameter set is valid. This is done by checking\n the maximum probability, defiend as max(s) + h*N. If maximum probability\n is equal to or greater than 1, then Error is raised. If maximum probability\n is equal to or greater than 0.5, then Warning is raised.\n \n Parameters\n ----------\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n nAgents : int or float\n number of agents within the model\n \n Returns\n -------\n int\n 1 - everything is fine,\n 0 - warning\n -1 - error\n '
maxSigma = np.max(np.array([sOn, sOff]))
maxProb = switchProb(maxSigma, herd, nAgents, nAgents)
if (maxProb >= 1):
if echo:
print(sOn, sOff, herd, nAgents, sep=',')
print('ERROR! Maximum probability larger than 1: {:.2f}'.format(maxProb))
return (- 1)
if (maxProb >= 0.5):
if echo:
print(sOn, sOff, herd, nAgents, sep=',')
print('WARNING! Maximum probability larger than 0.5: {:.2f}'.format(maxProb))
return 0
if echo:
minSigma = np.min(np.array([sOn, sOff]))
minProb = switchProb(minSigma, herd, 0, nAgents)
print(sOn, sOff, herd, nAgents, sep=',')
print('GOOD! Probability is within [{:.2f}; {:.2f}]'.format(minProb, maxProb))
return 1
|
Function checks whether parameter set is valid. This is done by checking
the maximum probability, defiend as max(s) + h*N. If maximum probability
is equal to or greater than 1, then Error is raised. If maximum probability
is equal to or greater than 0.5, then Warning is raised.
Parameters
----------
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
nAgents : int or float
number of agents within the model
Returns
-------
int
1 - everything is fine,
0 - warning
-1 - error
|
modelNumba.py
|
validateParams
|
akononovicius/noisy-voter-model-for-parliamentary-presence
| 0 |
python
|
def validateParams(sOn, sOff, herd, nAgents, echo=False):
'\n Function checks whether parameter set is valid. This is done by checking\n the maximum probability, defiend as max(s) + h*N. If maximum probability\n is equal to or greater than 1, then Error is raised. If maximum probability\n is equal to or greater than 0.5, then Warning is raised.\n \n Parameters\n ----------\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n nAgents : int or float\n number of agents within the model\n \n Returns\n -------\n int\n 1 - everything is fine,\n 0 - warning\n -1 - error\n '
maxSigma = np.max(np.array([sOn, sOff]))
maxProb = switchProb(maxSigma, herd, nAgents, nAgents)
if (maxProb >= 1):
if echo:
print(sOn, sOff, herd, nAgents, sep=',')
print('ERROR! Maximum probability larger than 1: {:.2f}'.format(maxProb))
return (- 1)
if (maxProb >= 0.5):
if echo:
print(sOn, sOff, herd, nAgents, sep=',')
print('WARNING! Maximum probability larger than 0.5: {:.2f}'.format(maxProb))
return 0
if echo:
minSigma = np.min(np.array([sOn, sOff]))
minProb = switchProb(minSigma, herd, 0, nAgents)
print(sOn, sOff, herd, nAgents, sep=',')
print('GOOD! Probability is within [{:.2f}; {:.2f}]'.format(minProb, maxProb))
return 1
|
def validateParams(sOn, sOff, herd, nAgents, echo=False):
'\n Function checks whether parameter set is valid. This is done by checking\n the maximum probability, defiend as max(s) + h*N. If maximum probability\n is equal to or greater than 1, then Error is raised. If maximum probability\n is equal to or greater than 0.5, then Warning is raised.\n \n Parameters\n ----------\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n nAgents : int or float\n number of agents within the model\n \n Returns\n -------\n int\n 1 - everything is fine,\n 0 - warning\n -1 - error\n '
maxSigma = np.max(np.array([sOn, sOff]))
maxProb = switchProb(maxSigma, herd, nAgents, nAgents)
if (maxProb >= 1):
if echo:
print(sOn, sOff, herd, nAgents, sep=',')
print('ERROR! Maximum probability larger than 1: {:.2f}'.format(maxProb))
return (- 1)
if (maxProb >= 0.5):
if echo:
print(sOn, sOff, herd, nAgents, sep=',')
print('WARNING! Maximum probability larger than 0.5: {:.2f}'.format(maxProb))
return 0
if echo:
minSigma = np.min(np.array([sOn, sOff]))
minProb = switchProb(minSigma, herd, 0, nAgents)
print(sOn, sOff, herd, nAgents, sep=',')
print('GOOD! Probability is within [{:.2f}; {:.2f}]'.format(minProb, maxProb))
return 1<|docstring|>Function checks whether parameter set is valid. This is done by checking
the maximum probability, defiend as max(s) + h*N. If maximum probability
is equal to or greater than 1, then Error is raised. If maximum probability
is equal to or greater than 0.5, then Warning is raised.
Parameters
----------
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
nAgents : int or float
number of agents within the model
Returns
-------
int
1 - everything is fine,
0 - warning
-1 - error<|endoftext|>
|
e55807c2448eac346fa4411c8a7aed37fbf167f94aeecc47833c88354c0ca288
|
@jit(nopython=True)
def step(sOn, sOff, herd, state):
'\n Function performs a single step according to herding model rules. Namely\n switching probability to state ``i`` is assumed to be given by:\n prob[i] = sigma[i] + h*N[i] ,\n wher N[i] is the number of agents in ``i`` state.\n \n Parameters\n ----------\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n \n Returns\n -------\n array_like\n updated state array\n '
_istate = state.copy()
nTotal = len(_istate)
nOn = np.sum((_istate == 1))
prob = np.zeros(nTotal)
prob[(_istate == 1)] = switchProb(sOff, herd, (nTotal - nOn), nTotal)
prob[(_istate == (- 1))] = switchProb(sOn, herd, nOn, nTotal)
r = np.random.rand(nTotal)
_istate[(r < prob)] = (- _istate[(r < prob)])
return _istate
|
Function performs a single step according to herding model rules. Namely
switching probability to state ``i`` is assumed to be given by:
prob[i] = sigma[i] + h*N[i] ,
wher N[i] is the number of agents in ``i`` state.
Parameters
----------
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
state : array_like
array containing states of all agents ("on" state is assumed to be
encoded by 1, while "off" state is assumed to be encoded by -1)
Returns
-------
array_like
updated state array
|
modelNumba.py
|
step
|
akononovicius/noisy-voter-model-for-parliamentary-presence
| 0 |
python
|
@jit(nopython=True)
def step(sOn, sOff, herd, state):
'\n Function performs a single step according to herding model rules. Namely\n switching probability to state ``i`` is assumed to be given by:\n prob[i] = sigma[i] + h*N[i] ,\n wher N[i] is the number of agents in ``i`` state.\n \n Parameters\n ----------\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n \n Returns\n -------\n array_like\n updated state array\n '
_istate = state.copy()
nTotal = len(_istate)
nOn = np.sum((_istate == 1))
prob = np.zeros(nTotal)
prob[(_istate == 1)] = switchProb(sOff, herd, (nTotal - nOn), nTotal)
prob[(_istate == (- 1))] = switchProb(sOn, herd, nOn, nTotal)
r = np.random.rand(nTotal)
_istate[(r < prob)] = (- _istate[(r < prob)])
return _istate
|
@jit(nopython=True)
def step(sOn, sOff, herd, state):
'\n Function performs a single step according to herding model rules. Namely\n switching probability to state ``i`` is assumed to be given by:\n prob[i] = sigma[i] + h*N[i] ,\n wher N[i] is the number of agents in ``i`` state.\n \n Parameters\n ----------\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n \n Returns\n -------\n array_like\n updated state array\n '
_istate = state.copy()
nTotal = len(_istate)
nOn = np.sum((_istate == 1))
prob = np.zeros(nTotal)
prob[(_istate == 1)] = switchProb(sOff, herd, (nTotal - nOn), nTotal)
prob[(_istate == (- 1))] = switchProb(sOn, herd, nOn, nTotal)
r = np.random.rand(nTotal)
_istate[(r < prob)] = (- _istate[(r < prob)])
return _istate<|docstring|>Function performs a single step according to herding model rules. Namely
switching probability to state ``i`` is assumed to be given by:
prob[i] = sigma[i] + h*N[i] ,
wher N[i] is the number of agents in ``i`` state.
Parameters
----------
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
state : array_like
array containing states of all agents ("on" state is assumed to be
encoded by 1, while "off" state is assumed to be encoded by -1)
Returns
-------
array_like
updated state array<|endoftext|>
|
8f0776e8ad9ee7eb6bb0ff13da0a0497791d70964a0777e73980176f6c398e69
|
@jit(nopython=True)
def rawSeries(nPoints, sOn, sOff, herd, state, warmup=0):
'\n Function performs multiple steps according to herding model rules (see\n the documentation of step function).\n \n Parameters\n ----------\n nPoints : int\n number of points to perform\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n warmup : int, optional\n number of warmup steps to perform (so that the model could have a\n chance to "forget" the initial state). Zero by default.\n \n Returns\n -------\n array_like\n array of state observations\n \n See also\n --------\n step\n '
_istate = state.copy()
output = np.zeros((nPoints, len(state)))
if (warmup > 0):
for i in np.arange(0, warmup):
_istate = step(sOn, sOff, herd, _istate)
for i in np.arange(0, nPoints):
_istate = step(sOn, sOff, herd, _istate)
output[i] = _istate.copy()
return output
|
Function performs multiple steps according to herding model rules (see
the documentation of step function).
Parameters
----------
nPoints : int
number of points to perform
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
state : array_like
array containing states of all agents ("on" state is assumed to be
encoded by 1, while "off" state is assumed to be encoded by -1)
warmup : int, optional
number of warmup steps to perform (so that the model could have a
chance to "forget" the initial state). Zero by default.
Returns
-------
array_like
array of state observations
See also
--------
step
|
modelNumba.py
|
rawSeries
|
akononovicius/noisy-voter-model-for-parliamentary-presence
| 0 |
python
|
@jit(nopython=True)
def rawSeries(nPoints, sOn, sOff, herd, state, warmup=0):
'\n Function performs multiple steps according to herding model rules (see\n the documentation of step function).\n \n Parameters\n ----------\n nPoints : int\n number of points to perform\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n warmup : int, optional\n number of warmup steps to perform (so that the model could have a\n chance to "forget" the initial state). Zero by default.\n \n Returns\n -------\n array_like\n array of state observations\n \n See also\n --------\n step\n '
_istate = state.copy()
output = np.zeros((nPoints, len(state)))
if (warmup > 0):
for i in np.arange(0, warmup):
_istate = step(sOn, sOff, herd, _istate)
for i in np.arange(0, nPoints):
_istate = step(sOn, sOff, herd, _istate)
output[i] = _istate.copy()
return output
|
@jit(nopython=True)
def rawSeries(nPoints, sOn, sOff, herd, state, warmup=0):
'\n Function performs multiple steps according to herding model rules (see\n the documentation of step function).\n \n Parameters\n ----------\n nPoints : int\n number of points to perform\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n warmup : int, optional\n number of warmup steps to perform (so that the model could have a\n chance to "forget" the initial state). Zero by default.\n \n Returns\n -------\n array_like\n array of state observations\n \n See also\n --------\n step\n '
_istate = state.copy()
output = np.zeros((nPoints, len(state)))
if (warmup > 0):
for i in np.arange(0, warmup):
_istate = step(sOn, sOff, herd, _istate)
for i in np.arange(0, nPoints):
_istate = step(sOn, sOff, herd, _istate)
output[i] = _istate.copy()
return output<|docstring|>Function performs multiple steps according to herding model rules (see
the documentation of step function).
Parameters
----------
nPoints : int
number of points to perform
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
state : array_like
array containing states of all agents ("on" state is assumed to be
encoded by 1, while "off" state is assumed to be encoded by -1)
warmup : int, optional
number of warmup steps to perform (so that the model could have a
chance to "forget" the initial state). Zero by default.
Returns
-------
array_like
array of state observations
See also
--------
step<|endoftext|>
|
b553de037e8ed9687b08779d6d0885828d70a8afa9bc30b6b7eaa68542791f31
|
def noisySeries(nPoints, pOn, pOff, sOn, sOff, herd, state, warmup=0):
'\n Function performs multiple steps according to herding model rules (see\n the documentation of step function) and adds external noise. Namely, "on"\n and "off" states now would mean that the states are noisy. Agent in "on"\n state is on with probability given by pOn and agent in "off" state is on\n with probability given by pOff.\n \n Parameters\n ----------\n nPoints : int\n number of points to perform\n pOn : float\n probability that agent in the "on" state will be "on"\n pOff : float\n probability that agent in the "off" state will be "on"\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n warmup : int, optional\n number of warmup steps to perform (so that the model could have a\n chance to "forget" the initial state). Zero by default.\n \n Returns\n -------\n array_like\n array of state observations (if parameters are valid) or array of None\n (if parameters are not valid)\n \n See also\n --------\n step, rawSeries\n '
series = rawSeries(nPoints, sOn, sOff, herd, state, warmup=warmup)
nseries = np.zeros(series.shape)
nseries[(series < 0)] = (np.random.rand(np.sum((series < 0))) < pOff)
nseries[(series > 0)] = (np.random.rand(np.sum((series > 0))) < pOn)
return nseries
|
Function performs multiple steps according to herding model rules (see
the documentation of step function) and adds external noise. Namely, "on"
and "off" states now would mean that the states are noisy. Agent in "on"
state is on with probability given by pOn and agent in "off" state is on
with probability given by pOff.
Parameters
----------
nPoints : int
number of points to perform
pOn : float
probability that agent in the "on" state will be "on"
pOff : float
probability that agent in the "off" state will be "on"
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
state : array_like
array containing states of all agents ("on" state is assumed to be
encoded by 1, while "off" state is assumed to be encoded by -1)
warmup : int, optional
number of warmup steps to perform (so that the model could have a
chance to "forget" the initial state). Zero by default.
Returns
-------
array_like
array of state observations (if parameters are valid) or array of None
(if parameters are not valid)
See also
--------
step, rawSeries
|
modelNumba.py
|
noisySeries
|
akononovicius/noisy-voter-model-for-parliamentary-presence
| 0 |
python
|
def noisySeries(nPoints, pOn, pOff, sOn, sOff, herd, state, warmup=0):
'\n Function performs multiple steps according to herding model rules (see\n the documentation of step function) and adds external noise. Namely, "on"\n and "off" states now would mean that the states are noisy. Agent in "on"\n state is on with probability given by pOn and agent in "off" state is on\n with probability given by pOff.\n \n Parameters\n ----------\n nPoints : int\n number of points to perform\n pOn : float\n probability that agent in the "on" state will be "on"\n pOff : float\n probability that agent in the "off" state will be "on"\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n warmup : int, optional\n number of warmup steps to perform (so that the model could have a\n chance to "forget" the initial state). Zero by default.\n \n Returns\n -------\n array_like\n array of state observations (if parameters are valid) or array of None\n (if parameters are not valid)\n \n See also\n --------\n step, rawSeries\n '
series = rawSeries(nPoints, sOn, sOff, herd, state, warmup=warmup)
nseries = np.zeros(series.shape)
nseries[(series < 0)] = (np.random.rand(np.sum((series < 0))) < pOff)
nseries[(series > 0)] = (np.random.rand(np.sum((series > 0))) < pOn)
return nseries
|
def noisySeries(nPoints, pOn, pOff, sOn, sOff, herd, state, warmup=0):
'\n Function performs multiple steps according to herding model rules (see\n the documentation of step function) and adds external noise. Namely, "on"\n and "off" states now would mean that the states are noisy. Agent in "on"\n state is on with probability given by pOn and agent in "off" state is on\n with probability given by pOff.\n \n Parameters\n ----------\n nPoints : int\n number of points to perform\n pOn : float\n probability that agent in the "on" state will be "on"\n pOff : float\n probability that agent in the "off" state will be "on"\n sOn : float\n sigma parameter for agents switching from "off" state to "on" state\n sOff : float\n sigma parameter for agents switching from "on" state to "off" state\n herd : float\n h parameter for interaction between agents\n state : array_like\n array containing states of all agents ("on" state is assumed to be\n encoded by 1, while "off" state is assumed to be encoded by -1)\n warmup : int, optional\n number of warmup steps to perform (so that the model could have a\n chance to "forget" the initial state). Zero by default.\n \n Returns\n -------\n array_like\n array of state observations (if parameters are valid) or array of None\n (if parameters are not valid)\n \n See also\n --------\n step, rawSeries\n '
series = rawSeries(nPoints, sOn, sOff, herd, state, warmup=warmup)
nseries = np.zeros(series.shape)
nseries[(series < 0)] = (np.random.rand(np.sum((series < 0))) < pOff)
nseries[(series > 0)] = (np.random.rand(np.sum((series > 0))) < pOn)
return nseries<|docstring|>Function performs multiple steps according to herding model rules (see
the documentation of step function) and adds external noise. Namely, "on"
and "off" states now would mean that the states are noisy. Agent in "on"
state is on with probability given by pOn and agent in "off" state is on
with probability given by pOff.
Parameters
----------
nPoints : int
number of points to perform
pOn : float
probability that agent in the "on" state will be "on"
pOff : float
probability that agent in the "off" state will be "on"
sOn : float
sigma parameter for agents switching from "off" state to "on" state
sOff : float
sigma parameter for agents switching from "on" state to "off" state
herd : float
h parameter for interaction between agents
state : array_like
array containing states of all agents ("on" state is assumed to be
encoded by 1, while "off" state is assumed to be encoded by -1)
warmup : int, optional
number of warmup steps to perform (so that the model could have a
chance to "forget" the initial state). Zero by default.
Returns
-------
array_like
array of state observations (if parameters are valid) or array of None
(if parameters are not valid)
See also
--------
step, rawSeries<|endoftext|>
|
abe0512f4ee28e3c3fd12d1c52b8c48a85a031399b854d09776cb48b26c144c7
|
def iter_variables(self):
'\n Iterates over all variables in the expression.\n\n Returns:\n iterator: An iterator over all variables present in the operand.\n '
for (v, k) in self.iter_terms():
(yield v)
|
Iterates over all variables in the expression.
Returns:
iterator: An iterator over all variables present in the operand.
|
.environment/lib/python3.8/site-packages/docplex/mp/operand.py
|
iter_variables
|
LuisMi1245/QPath-and-Snakes
| 0 |
python
|
def iter_variables(self):
'\n Iterates over all variables in the expression.\n\n Returns:\n iterator: An iterator over all variables present in the operand.\n '
for (v, k) in self.iter_terms():
(yield v)
|
def iter_variables(self):
'\n Iterates over all variables in the expression.\n\n Returns:\n iterator: An iterator over all variables present in the operand.\n '
for (v, k) in self.iter_terms():
(yield v)<|docstring|>Iterates over all variables in the expression.
Returns:
iterator: An iterator over all variables present in the operand.<|endoftext|>
|
451322e9607a11b9c59e2e46ee87cf9cd4ba671e9fdb474454c69389e83a964b
|
def get_linear_part(self):
' Returns the linear part of the expression: for a linear expression,\n returns the expression itself.\n\n Defined for compatibility with quadratic expressions.\n\n :return: a linear expression\n '
return self
|
Returns the linear part of the expression: for a linear expression,
returns the expression itself.
Defined for compatibility with quadratic expressions.
:return: a linear expression
|
.environment/lib/python3.8/site-packages/docplex/mp/operand.py
|
get_linear_part
|
LuisMi1245/QPath-and-Snakes
| 0 |
python
|
def get_linear_part(self):
' Returns the linear part of the expression: for a linear expression,\n returns the expression itself.\n\n Defined for compatibility with quadratic expressions.\n\n :return: a linear expression\n '
return self
|
def get_linear_part(self):
' Returns the linear part of the expression: for a linear expression,\n returns the expression itself.\n\n Defined for compatibility with quadratic expressions.\n\n :return: a linear expression\n '
return self<|docstring|>Returns the linear part of the expression: for a linear expression,
returns the expression itself.
Defined for compatibility with quadratic expressions.
:return: a linear expression<|endoftext|>
|
b5863ac5ca1e8de547491276f7172c05d78c48ca3aed81e533650e9a9f7b50b1
|
@property
def linear_part(self):
' Returns the linear part of the expression: for a linear expression,\n returns the expression itself.\n\n Defined for compatibility with quadratic expressions.\n\n :return: a linear expression (returns itself for any linear operand).\n '
return self
|
Returns the linear part of the expression: for a linear expression,
returns the expression itself.
Defined for compatibility with quadratic expressions.
:return: a linear expression (returns itself for any linear operand).
|
.environment/lib/python3.8/site-packages/docplex/mp/operand.py
|
linear_part
|
LuisMi1245/QPath-and-Snakes
| 0 |
python
|
@property
def linear_part(self):
' Returns the linear part of the expression: for a linear expression,\n returns the expression itself.\n\n Defined for compatibility with quadratic expressions.\n\n :return: a linear expression (returns itself for any linear operand).\n '
return self
|
@property
def linear_part(self):
' Returns the linear part of the expression: for a linear expression,\n returns the expression itself.\n\n Defined for compatibility with quadratic expressions.\n\n :return: a linear expression (returns itself for any linear operand).\n '
return self<|docstring|>Returns the linear part of the expression: for a linear expression,
returns the expression itself.
Defined for compatibility with quadratic expressions.
:return: a linear expression (returns itself for any linear operand).<|endoftext|>
|
e81092b49f8ac87c9bd3a8872bc0a4693903027e248c0dda28af0d804ad012fc
|
def __contains__(self, dvar):
'Overloads operator `in` for an expression and a variable.\n\n :param: dvar (:class:`docplex.mp.dvar.Var`): A decision variable.\n\n Returns:\n Boolean: True if the variable is present in the expression, else False.\n '
return self.contains_var(dvar)
|
Overloads operator `in` for an expression and a variable.
:param: dvar (:class:`docplex.mp.dvar.Var`): A decision variable.
Returns:
Boolean: True if the variable is present in the expression, else False.
|
.environment/lib/python3.8/site-packages/docplex/mp/operand.py
|
__contains__
|
LuisMi1245/QPath-and-Snakes
| 0 |
python
|
def __contains__(self, dvar):
'Overloads operator `in` for an expression and a variable.\n\n :param: dvar (:class:`docplex.mp.dvar.Var`): A decision variable.\n\n Returns:\n Boolean: True if the variable is present in the expression, else False.\n '
return self.contains_var(dvar)
|
def __contains__(self, dvar):
'Overloads operator `in` for an expression and a variable.\n\n :param: dvar (:class:`docplex.mp.dvar.Var`): A decision variable.\n\n Returns:\n Boolean: True if the variable is present in the expression, else False.\n '
return self.contains_var(dvar)<|docstring|>Overloads operator `in` for an expression and a variable.
:param: dvar (:class:`docplex.mp.dvar.Var`): A decision variable.
Returns:
Boolean: True if the variable is present in the expression, else False.<|endoftext|>
|
eb6454c467f73c625dac9f5f91b73c0a0194b3539a21ef63568539dcdd9a8242
|
def solve(grid):
'\n\n . . .\n .1.1.\n . .3.\n\n '
s = z3.Solver()
Dot = z3.Datatype('Dot')
for d in grid.dots():
Dot.declare('dot_{}'.format(d))
Dot = Dot.create()
dot_atom = {d: getattr(Dot, 'dot_{}'.format(d)) for d in grid.dots()}
dot = {d: z3.Bool('dot-{}'.format(d)) for d in grid.dots()}
line = {l: z3.Bool('line-{}'.format(l)) for l in grid.lines()}
bool_to_int = z3.Function('bool_to_int', z3.BoolSort(), z3.IntSort())
s.add((bool_to_int(True) == 1))
s.add((bool_to_int(True) != 0))
s.add((bool_to_int(False) == 0))
s.add((bool_to_int(False) != 1))
for d in grid.dots():
ls = [line[l] for l in d.lines()]
sm = z3.Sum(*(bool_to_int(l) for l in ls))
s.add(z3.Implies(dot[d], (sm == 2)))
s.add(z3.Implies(z3.Not(dot[d]), (sm == 0)))
for l in line:
(d1, d2) = l.ends()
s.add(z3.Implies(line[l], z3.And(dot[d1], dot[d2])))
connected = z3.Function('connected', Dot, Dot, z3.BoolSort())
for d1 in grid.dots():
for d2 in grid.dots():
a = dot_atom[d1]
b = dot_atom[d2]
if ((l := grid.line(d1, d2)) is None):
s.add((connected(a, b) != True))
else:
s.add(z3.Implies(line[l], connected(a, b)))
s.add(z3.Implies(z3.Not(line[l]), z3.Not(connected(a, b))))
path_connected = z3.TransitiveClosure(connected)
xy3 = [xy for (xy, c) in grid.cells() if (c == '3')][0]
dot3 = grid.cell_dots(*xy3)[0]
atom3 = dot_atom[dot3]
for d in grid.dots():
s.add(z3.Implies(dot[d], path_connected(dot_atom[d], atom3)))
s.add(z3.Implies(z3.Not(dot[d]), z3.Not(path_connected(dot_atom[d], atom3))))
def line_count_of_cell(xy):
'xy is the dot at the top-left\n Return an invocation of line_count for the lines around it.\n '
return z3.Sum(*(bool_to_int(line[l]) for l in grid.cell_lines(*xy)))
for (xy, c) in grid.cells():
if (c != ' '):
print('adding constraint for ', xy, c, [str(l) for l in grid.cell_lines(*xy)])
s.add((line_count_of_cell(xy) == int(c)))
print('check: ', s.check())
m = s.model()
print()
grid.print(dot_on=(lambda d: m.eval(dot[d])), line_on=(lambda l: m.eval(line[l])))
|
. . .
.1.1.
. .3.
|
slither/solve.py
|
solve
|
jan-g/slitherlink
| 1 |
python
|
def solve(grid):
'\n\n . . .\n .1.1.\n . .3.\n\n '
s = z3.Solver()
Dot = z3.Datatype('Dot')
for d in grid.dots():
Dot.declare('dot_{}'.format(d))
Dot = Dot.create()
dot_atom = {d: getattr(Dot, 'dot_{}'.format(d)) for d in grid.dots()}
dot = {d: z3.Bool('dot-{}'.format(d)) for d in grid.dots()}
line = {l: z3.Bool('line-{}'.format(l)) for l in grid.lines()}
bool_to_int = z3.Function('bool_to_int', z3.BoolSort(), z3.IntSort())
s.add((bool_to_int(True) == 1))
s.add((bool_to_int(True) != 0))
s.add((bool_to_int(False) == 0))
s.add((bool_to_int(False) != 1))
for d in grid.dots():
ls = [line[l] for l in d.lines()]
sm = z3.Sum(*(bool_to_int(l) for l in ls))
s.add(z3.Implies(dot[d], (sm == 2)))
s.add(z3.Implies(z3.Not(dot[d]), (sm == 0)))
for l in line:
(d1, d2) = l.ends()
s.add(z3.Implies(line[l], z3.And(dot[d1], dot[d2])))
connected = z3.Function('connected', Dot, Dot, z3.BoolSort())
for d1 in grid.dots():
for d2 in grid.dots():
a = dot_atom[d1]
b = dot_atom[d2]
if ((l := grid.line(d1, d2)) is None):
s.add((connected(a, b) != True))
else:
s.add(z3.Implies(line[l], connected(a, b)))
s.add(z3.Implies(z3.Not(line[l]), z3.Not(connected(a, b))))
path_connected = z3.TransitiveClosure(connected)
xy3 = [xy for (xy, c) in grid.cells() if (c == '3')][0]
dot3 = grid.cell_dots(*xy3)[0]
atom3 = dot_atom[dot3]
for d in grid.dots():
s.add(z3.Implies(dot[d], path_connected(dot_atom[d], atom3)))
s.add(z3.Implies(z3.Not(dot[d]), z3.Not(path_connected(dot_atom[d], atom3))))
def line_count_of_cell(xy):
'xy is the dot at the top-left\n Return an invocation of line_count for the lines around it.\n '
return z3.Sum(*(bool_to_int(line[l]) for l in grid.cell_lines(*xy)))
for (xy, c) in grid.cells():
if (c != ' '):
print('adding constraint for ', xy, c, [str(l) for l in grid.cell_lines(*xy)])
s.add((line_count_of_cell(xy) == int(c)))
print('check: ', s.check())
m = s.model()
print()
grid.print(dot_on=(lambda d: m.eval(dot[d])), line_on=(lambda l: m.eval(line[l])))
|
def solve(grid):
'\n\n . . .\n .1.1.\n . .3.\n\n '
s = z3.Solver()
Dot = z3.Datatype('Dot')
for d in grid.dots():
Dot.declare('dot_{}'.format(d))
Dot = Dot.create()
dot_atom = {d: getattr(Dot, 'dot_{}'.format(d)) for d in grid.dots()}
dot = {d: z3.Bool('dot-{}'.format(d)) for d in grid.dots()}
line = {l: z3.Bool('line-{}'.format(l)) for l in grid.lines()}
bool_to_int = z3.Function('bool_to_int', z3.BoolSort(), z3.IntSort())
s.add((bool_to_int(True) == 1))
s.add((bool_to_int(True) != 0))
s.add((bool_to_int(False) == 0))
s.add((bool_to_int(False) != 1))
for d in grid.dots():
ls = [line[l] for l in d.lines()]
sm = z3.Sum(*(bool_to_int(l) for l in ls))
s.add(z3.Implies(dot[d], (sm == 2)))
s.add(z3.Implies(z3.Not(dot[d]), (sm == 0)))
for l in line:
(d1, d2) = l.ends()
s.add(z3.Implies(line[l], z3.And(dot[d1], dot[d2])))
connected = z3.Function('connected', Dot, Dot, z3.BoolSort())
for d1 in grid.dots():
for d2 in grid.dots():
a = dot_atom[d1]
b = dot_atom[d2]
if ((l := grid.line(d1, d2)) is None):
s.add((connected(a, b) != True))
else:
s.add(z3.Implies(line[l], connected(a, b)))
s.add(z3.Implies(z3.Not(line[l]), z3.Not(connected(a, b))))
path_connected = z3.TransitiveClosure(connected)
xy3 = [xy for (xy, c) in grid.cells() if (c == '3')][0]
dot3 = grid.cell_dots(*xy3)[0]
atom3 = dot_atom[dot3]
for d in grid.dots():
s.add(z3.Implies(dot[d], path_connected(dot_atom[d], atom3)))
s.add(z3.Implies(z3.Not(dot[d]), z3.Not(path_connected(dot_atom[d], atom3))))
def line_count_of_cell(xy):
'xy is the dot at the top-left\n Return an invocation of line_count for the lines around it.\n '
return z3.Sum(*(bool_to_int(line[l]) for l in grid.cell_lines(*xy)))
for (xy, c) in grid.cells():
if (c != ' '):
print('adding constraint for ', xy, c, [str(l) for l in grid.cell_lines(*xy)])
s.add((line_count_of_cell(xy) == int(c)))
print('check: ', s.check())
m = s.model()
print()
grid.print(dot_on=(lambda d: m.eval(dot[d])), line_on=(lambda l: m.eval(line[l])))<|docstring|>. . .
.1.1.
. .3.<|endoftext|>
|
6991267dbe28995dae21bb24c17599f3ecd727207ed221cf562511b51ed7c291
|
def line_count_of_cell(xy):
'xy is the dot at the top-left\n Return an invocation of line_count for the lines around it.\n '
return z3.Sum(*(bool_to_int(line[l]) for l in grid.cell_lines(*xy)))
|
xy is the dot at the top-left
Return an invocation of line_count for the lines around it.
|
slither/solve.py
|
line_count_of_cell
|
jan-g/slitherlink
| 1 |
python
|
def line_count_of_cell(xy):
'xy is the dot at the top-left\n Return an invocation of line_count for the lines around it.\n '
return z3.Sum(*(bool_to_int(line[l]) for l in grid.cell_lines(*xy)))
|
def line_count_of_cell(xy):
'xy is the dot at the top-left\n Return an invocation of line_count for the lines around it.\n '
return z3.Sum(*(bool_to_int(line[l]) for l in grid.cell_lines(*xy)))<|docstring|>xy is the dot at the top-left
Return an invocation of line_count for the lines around it.<|endoftext|>
|
c2095744fd8ec17a3f78fab821f3d84daf0cd8d343b9d8ae56c9bec1a2bf4baf
|
def create(self, validated_data):
'create and return a new user'
user = models.UserProfile.objects.create_user(email=validated_data['email'], name=validated_data['name'], password=validated_data['password'])
return user
|
create and return a new user
|
app/core/serializers.py
|
create
|
loop-assembly/backend-api
| 3 |
python
|
def create(self, validated_data):
user = models.UserProfile.objects.create_user(email=validated_data['email'], name=validated_data['name'], password=validated_data['password'])
return user
|
def create(self, validated_data):
user = models.UserProfile.objects.create_user(email=validated_data['email'], name=validated_data['name'], password=validated_data['password'])
return user<|docstring|>create and return a new user<|endoftext|>
|
a19d1cc68966ee7626bc94cc695faed4b6f313c19f15de78e99842f119441177
|
def _activeJobs(self):
' Return a list with all active Jobs (not DONE) '
return (self.todo + [n for n in self.inprogress.values()])
|
Return a list with all active Jobs (not DONE)
|
bots/curfew/abn/jobs.py
|
_activeJobs
|
alv67/Lux-AI-challenge
| 0 |
python
|
def _activeJobs(self):
' '
return (self.todo + [n for n in self.inprogress.values()])
|
def _activeJobs(self):
' '
return (self.todo + [n for n in self.inprogress.values()])<|docstring|>Return a list with all active Jobs (not DONE)<|endoftext|>
|
3c10ece68c5d3ffe27ffe7e298d53ac804d9bc7c231b3baee4587e30d3b922f1
|
def jobReject(self, unit_id: str):
'\n The rejected job is returned from inProgress to ToDo list, \n mantains the unit_id so this job will not be assigned to the unit\n that rejected it.\n '
if (unit_id in self.inprogress):
j = self.inprogress[unit_id]
j.subtask = 0
if (j.task in [Task.EXPLORE, Task.BUILD]):
self.todo.append(j)
del self.inprogress[unit_id]
|
The rejected job is returned from inProgress to ToDo list,
mantains the unit_id so this job will not be assigned to the unit
that rejected it.
|
bots/curfew/abn/jobs.py
|
jobReject
|
alv67/Lux-AI-challenge
| 0 |
python
|
def jobReject(self, unit_id: str):
'\n The rejected job is returned from inProgress to ToDo list, \n mantains the unit_id so this job will not be assigned to the unit\n that rejected it.\n '
if (unit_id in self.inprogress):
j = self.inprogress[unit_id]
j.subtask = 0
if (j.task in [Task.EXPLORE, Task.BUILD]):
self.todo.append(j)
del self.inprogress[unit_id]
|
def jobReject(self, unit_id: str):
'\n The rejected job is returned from inProgress to ToDo list, \n mantains the unit_id so this job will not be assigned to the unit\n that rejected it.\n '
if (unit_id in self.inprogress):
j = self.inprogress[unit_id]
j.subtask = 0
if (j.task in [Task.EXPLORE, Task.BUILD]):
self.todo.append(j)
del self.inprogress[unit_id]<|docstring|>The rejected job is returned from inProgress to ToDo list,
mantains the unit_id so this job will not be assigned to the unit
that rejected it.<|endoftext|>
|
9bf89d80bda89dee554c263c94d55e8a4162de5ab0c6225c3ab66099b6d1a4c4
|
def count(self, task: str, pos: Position=None, city_id: str='') -> int:
'\n Return total number of active (not DONE) tasks with given parameters\n '
retvalue = 0
for job in self._activeJobs():
if (job.task == task):
if (pos and (pos != job.pos)):
continue
if (city_id and (city_id != job.city_id)):
continue
retvalue += 1
return retvalue
|
Return total number of active (not DONE) tasks with given parameters
|
bots/curfew/abn/jobs.py
|
count
|
alv67/Lux-AI-challenge
| 0 |
python
|
def count(self, task: str, pos: Position=None, city_id: str=) -> int:
'\n \n '
retvalue = 0
for job in self._activeJobs():
if (job.task == task):
if (pos and (pos != job.pos)):
continue
if (city_id and (city_id != job.city_id)):
continue
retvalue += 1
return retvalue
|
def count(self, task: str, pos: Position=None, city_id: str=) -> int:
'\n \n '
retvalue = 0
for job in self._activeJobs():
if (job.task == task):
if (pos and (pos != job.pos)):
continue
if (city_id and (city_id != job.city_id)):
continue
retvalue += 1
return retvalue<|docstring|>Return total number of active (not DONE) tasks with given parameters<|endoftext|>
|
5a580266c5508b6deabc760aaecc747947386e9eb9532c44b6546bbb0991fef3
|
def jobRequest(self, unit: Unit):
" \n Unit can ask for a job, the function returns:\n - an 'inprogress' job for that unit_id if it's present\n - a new job from the 'todo' list\n "
job = self.inprogress.get(unit.id)
if job:
return job
job = self._nextJob(unit)
if job:
job.unit_id = unit.id
job.subtask = 0
self.inprogress[unit.id] = job
return job
else:
job = Job(Task.EXPLORE, unit.pos)
job.unit_id = unit.id
self.inprogress[unit.id] = job
return job
|
Unit can ask for a job, the function returns:
- an 'inprogress' job for that unit_id if it's present
- a new job from the 'todo' list
|
bots/curfew/abn/jobs.py
|
jobRequest
|
alv67/Lux-AI-challenge
| 0 |
python
|
def jobRequest(self, unit: Unit):
" \n Unit can ask for a job, the function returns:\n - an 'inprogress' job for that unit_id if it's present\n - a new job from the 'todo' list\n "
job = self.inprogress.get(unit.id)
if job:
return job
job = self._nextJob(unit)
if job:
job.unit_id = unit.id
job.subtask = 0
self.inprogress[unit.id] = job
return job
else:
job = Job(Task.EXPLORE, unit.pos)
job.unit_id = unit.id
self.inprogress[unit.id] = job
return job
|
def jobRequest(self, unit: Unit):
" \n Unit can ask for a job, the function returns:\n - an 'inprogress' job for that unit_id if it's present\n - a new job from the 'todo' list\n "
job = self.inprogress.get(unit.id)
if job:
return job
job = self._nextJob(unit)
if job:
job.unit_id = unit.id
job.subtask = 0
self.inprogress[unit.id] = job
return job
else:
job = Job(Task.EXPLORE, unit.pos)
job.unit_id = unit.id
self.inprogress[unit.id] = job
return job<|docstring|>Unit can ask for a job, the function returns:
- an 'inprogress' job for that unit_id if it's present
- a new job from the 'todo' list<|endoftext|>
|
d0e946751d769245f51d9a6007b2b14b6e2c26a11b36f65eb460d67e75d2d95f
|
def checkActiveJobs(self, units: List):
' \n Using list of Units check if there are some InProgress Jobs assigned to \n Unit no more on the list (dead unit). If the case then:\n - return Job to ToDos\n - add dead unit.id to rip List\n '
morgue = []
for unit_id in self.inprogress:
if (unit_id not in [u.id for u in units]):
morgue.append(unit_id)
for unit_id in morgue:
self.jobReject(unit_id)
self.rip.append(unit_id)
|
Using list of Units check if there are some InProgress Jobs assigned to
Unit no more on the list (dead unit). If the case then:
- return Job to ToDos
- add dead unit.id to rip List
|
bots/curfew/abn/jobs.py
|
checkActiveJobs
|
alv67/Lux-AI-challenge
| 0 |
python
|
def checkActiveJobs(self, units: List):
' \n Using list of Units check if there are some InProgress Jobs assigned to \n Unit no more on the list (dead unit). If the case then:\n - return Job to ToDos\n - add dead unit.id to rip List\n '
morgue = []
for unit_id in self.inprogress:
if (unit_id not in [u.id for u in units]):
morgue.append(unit_id)
for unit_id in morgue:
self.jobReject(unit_id)
self.rip.append(unit_id)
|
def checkActiveJobs(self, units: List):
' \n Using list of Units check if there are some InProgress Jobs assigned to \n Unit no more on the list (dead unit). If the case then:\n - return Job to ToDos\n - add dead unit.id to rip List\n '
morgue = []
for unit_id in self.inprogress:
if (unit_id not in [u.id for u in units]):
morgue.append(unit_id)
for unit_id in morgue:
self.jobReject(unit_id)
self.rip.append(unit_id)<|docstring|>Using list of Units check if there are some InProgress Jobs assigned to
Unit no more on the list (dead unit). If the case then:
- return Job to ToDos
- add dead unit.id to rip List<|endoftext|>
|
bb9128b93c187ef7ec0986e94e58c8fb70fa75bb58a310ec7a2519a3abe9e29e
|
def train(model, dataset_dir, subset):
'Train the model.'
dataset_train = ChickenDataset()
dataset_train.load_chickens(dataset_dir, subset)
dataset_train.prepare()
dataset_val = ChickenDataset()
dataset_val.load_chickens(dataset_dir, 'val')
dataset_val.prepare()
augmentation = iaa.SomeOf((1, 3), [iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.OneOf([iaa.Affine(rotate=90), iaa.Affine(rotate=180), iaa.Affine(rotate=270)]), iaa.Multiply((0.8, 1.5)), iaa.GaussianBlur(sigma=(0.0, 5.0))])
print('Train network heads')
model.train(dataset_train, dataset_val, learning_rate=config.LEARNING_RATE, epochs=60, augmentation=augmentation, layers='heads')
print('Train all layers')
model.train(dataset_train, dataset_val, learning_rate=config.LEARNING_RATE, epochs=120, augmentation=augmentation, layers='all')
|
Train the model.
|
AP.py
|
train
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def train(model, dataset_dir, subset):
dataset_train = ChickenDataset()
dataset_train.load_chickens(dataset_dir, subset)
dataset_train.prepare()
dataset_val = ChickenDataset()
dataset_val.load_chickens(dataset_dir, 'val')
dataset_val.prepare()
augmentation = iaa.SomeOf((1, 3), [iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.OneOf([iaa.Affine(rotate=90), iaa.Affine(rotate=180), iaa.Affine(rotate=270)]), iaa.Multiply((0.8, 1.5)), iaa.GaussianBlur(sigma=(0.0, 5.0))])
print('Train network heads')
model.train(dataset_train, dataset_val, learning_rate=config.LEARNING_RATE, epochs=60, augmentation=augmentation, layers='heads')
print('Train all layers')
model.train(dataset_train, dataset_val, learning_rate=config.LEARNING_RATE, epochs=120, augmentation=augmentation, layers='all')
|
def train(model, dataset_dir, subset):
dataset_train = ChickenDataset()
dataset_train.load_chickens(dataset_dir, subset)
dataset_train.prepare()
dataset_val = ChickenDataset()
dataset_val.load_chickens(dataset_dir, 'val')
dataset_val.prepare()
augmentation = iaa.SomeOf((1, 3), [iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.OneOf([iaa.Affine(rotate=90), iaa.Affine(rotate=180), iaa.Affine(rotate=270)]), iaa.Multiply((0.8, 1.5)), iaa.GaussianBlur(sigma=(0.0, 5.0))])
print('Train network heads')
model.train(dataset_train, dataset_val, learning_rate=config.LEARNING_RATE, epochs=60, augmentation=augmentation, layers='heads')
print('Train all layers')
model.train(dataset_train, dataset_val, learning_rate=config.LEARNING_RATE, epochs=120, augmentation=augmentation, layers='all')<|docstring|>Train the model.<|endoftext|>
|
31495480f284420deacc67fe8ea1925e9da46e12b2db29a119427d3df3ebe045
|
def rle_encode(mask):
'Encodes a mask in Run Length Encoding (RLE).\n Returns a string of space-separated values.\n '
assert (mask.ndim == 2), 'Mask must be of shape [Height, Width]'
m = mask.T.flatten()
g = np.diff(np.concatenate([[0], m, [0]]), n=1)
rle = (np.where((g != 0))[0].reshape([(- 1), 2]) + 1)
rle[(:, 1)] = (rle[(:, 1)] - rle[(:, 0)])
return ' '.join(map(str, rle.flatten()))
|
Encodes a mask in Run Length Encoding (RLE).
Returns a string of space-separated values.
|
AP.py
|
rle_encode
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def rle_encode(mask):
'Encodes a mask in Run Length Encoding (RLE).\n Returns a string of space-separated values.\n '
assert (mask.ndim == 2), 'Mask must be of shape [Height, Width]'
m = mask.T.flatten()
g = np.diff(np.concatenate([[0], m, [0]]), n=1)
rle = (np.where((g != 0))[0].reshape([(- 1), 2]) + 1)
rle[(:, 1)] = (rle[(:, 1)] - rle[(:, 0)])
return ' '.join(map(str, rle.flatten()))
|
def rle_encode(mask):
'Encodes a mask in Run Length Encoding (RLE).\n Returns a string of space-separated values.\n '
assert (mask.ndim == 2), 'Mask must be of shape [Height, Width]'
m = mask.T.flatten()
g = np.diff(np.concatenate([[0], m, [0]]), n=1)
rle = (np.where((g != 0))[0].reshape([(- 1), 2]) + 1)
rle[(:, 1)] = (rle[(:, 1)] - rle[(:, 0)])
return ' '.join(map(str, rle.flatten()))<|docstring|>Encodes a mask in Run Length Encoding (RLE).
Returns a string of space-separated values.<|endoftext|>
|
827dc1a8ba59bb67132631d8e92f7436fb4ad49c9c3cb5f618c2ef59a4ac8986
|
def rle_decode(rle, shape):
'Decodes an RLE encoded list of space separated\n numbers and returns a binary mask.'
rle = list(map(int, rle.split()))
rle = np.array(rle, dtype=np.int32).reshape([(- 1), 2])
rle[(:, 1)] += rle[(:, 0)]
rle -= 1
mask = np.zeros([(shape[0] * shape[1])], np.bool)
for (s, e) in rle:
assert (0 <= s < mask.shape[0])
assert (1 <= e <= mask.shape[0]), 'shape: {} s {} e {}'.format(shape, s, e)
mask[s:e] = 1
mask = mask.reshape([shape[1], shape[0]]).T
return mask
|
Decodes an RLE encoded list of space separated
numbers and returns a binary mask.
|
AP.py
|
rle_decode
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def rle_decode(rle, shape):
'Decodes an RLE encoded list of space separated\n numbers and returns a binary mask.'
rle = list(map(int, rle.split()))
rle = np.array(rle, dtype=np.int32).reshape([(- 1), 2])
rle[(:, 1)] += rle[(:, 0)]
rle -= 1
mask = np.zeros([(shape[0] * shape[1])], np.bool)
for (s, e) in rle:
assert (0 <= s < mask.shape[0])
assert (1 <= e <= mask.shape[0]), 'shape: {} s {} e {}'.format(shape, s, e)
mask[s:e] = 1
mask = mask.reshape([shape[1], shape[0]]).T
return mask
|
def rle_decode(rle, shape):
'Decodes an RLE encoded list of space separated\n numbers and returns a binary mask.'
rle = list(map(int, rle.split()))
rle = np.array(rle, dtype=np.int32).reshape([(- 1), 2])
rle[(:, 1)] += rle[(:, 0)]
rle -= 1
mask = np.zeros([(shape[0] * shape[1])], np.bool)
for (s, e) in rle:
assert (0 <= s < mask.shape[0])
assert (1 <= e <= mask.shape[0]), 'shape: {} s {} e {}'.format(shape, s, e)
mask[s:e] = 1
mask = mask.reshape([shape[1], shape[0]]).T
return mask<|docstring|>Decodes an RLE encoded list of space separated
numbers and returns a binary mask.<|endoftext|>
|
baa54fad288f9060022ae4f414b415bc65d087c484a7f5ea9e9c755405c123d6
|
def mask_to_rle(image_id, mask, scores):
'Encodes instance masks to submission format.'
assert (mask.ndim == 3), 'Mask must be [H, W, count]'
if (mask.shape[(- 1)] == 0):
return '{},'.format(image_id)
order = (np.argsort(scores)[::(- 1)] + 1)
mask = np.max((mask * np.reshape(order, [1, 1, (- 1)])), (- 1))
lines = []
for o in order:
m = np.where((mask == o), 1, 0)
if (m.sum() == 0.0):
continue
rle = rle_encode(m)
lines.append('{}, {}'.format(image_id, rle))
return '\n'.join(lines)
|
Encodes instance masks to submission format.
|
AP.py
|
mask_to_rle
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def mask_to_rle(image_id, mask, scores):
assert (mask.ndim == 3), 'Mask must be [H, W, count]'
if (mask.shape[(- 1)] == 0):
return '{},'.format(image_id)
order = (np.argsort(scores)[::(- 1)] + 1)
mask = np.max((mask * np.reshape(order, [1, 1, (- 1)])), (- 1))
lines = []
for o in order:
m = np.where((mask == o), 1, 0)
if (m.sum() == 0.0):
continue
rle = rle_encode(m)
lines.append('{}, {}'.format(image_id, rle))
return '\n'.join(lines)
|
def mask_to_rle(image_id, mask, scores):
assert (mask.ndim == 3), 'Mask must be [H, W, count]'
if (mask.shape[(- 1)] == 0):
return '{},'.format(image_id)
order = (np.argsort(scores)[::(- 1)] + 1)
mask = np.max((mask * np.reshape(order, [1, 1, (- 1)])), (- 1))
lines = []
for o in order:
m = np.where((mask == o), 1, 0)
if (m.sum() == 0.0):
continue
rle = rle_encode(m)
lines.append('{}, {}'.format(image_id, rle))
return '\n'.join(lines)<|docstring|>Encodes instance masks to submission format.<|endoftext|>
|
7917d783e198794f93abb88809951dc3749b093123f69e07a223502726860294
|
def detect(model, dataset_dir, subset):
'Run detection on images in the given directory.'
print('Running on {}'.format(dataset_dir))
if (not os.path.exists(RESULTS_DIR)):
os.makedirs(RESULTS_DIR)
submit_dir = 'submit_{:%Y%m%dT%H%M%S}'.format(datetime.datetime.now())
submit_dir = os.path.join(RESULTS_DIR, submit_dir)
os.makedirs(submit_dir)
dataset = ChickenDataset()
dataset.load_chickens(dataset_dir, subset)
dataset.prepare()
dataset_val = ChickenDataset()
dataset_val.load_chickens(dataset_dir, 'stage1_test')
dataset_val.load_chickens(dataset_dir, 'val')
dataset_val.prepare()
submission = []
image_id = random.choice(dataset_val.image_ids)
(original_image, image_meta, gt_class_id, gt_bbox, gt_mask) = modellib.load_image_gt(dataset_val, inference_config, image_id, use_mini_mask=False)
log('original_image', original_image)
log('image_meta', image_meta)
log('gt_class_id', gt_class_id)
log('gt_bbox', gt_bbox)
log('gt_mask', gt_mask)
image_ids = np.random.choice(dataset_val.image_ids, 10)
APs = []
num = 0
count = 0
for image_id in dataset.image_ids:
image = dataset.load_image(image_id)
count = (count + 1)
(image, image_meta, gt_class_id, gt_bbox, gt_mask) = modellib.load_image_gt(dataset_val, inference_config, image_id, use_mini_mask=False)
molded_images = np.expand_dims(modellib.mold_image(image, inference_config), 0)
r = model.detect([image], verbose=0)[0]
(APss, precisions, recalls, overlaps) = utils.compute_ap(gt_bbox, gt_class_id, gt_mask, r['rois'], r['class_ids'], r['scores'], r['masks'])
APs.append(APss)
num = (num + APss)
source_id = dataset.image_info[image_id]['id']
rle = mask_to_rle(source_id, r['masks'], r['scores'])
submission.append(rle)
visualize.display_instances(image, r['rois'], r['masks'], r['class_ids'], dataset.class_names, r['scores'], title='Predictions')
plt.savefig('{}/{}.jpg'.format(submit_dir, dataset.image_info[image_id]['id']))
print(APs)
print((num / count))
submission = ('ImageId,EncodedPixels\n' + '\n'.join(submission))
file_path = os.path.join(submit_dir, 'submit.csv')
with open(file_path, 'w') as f:
f.write(submission)
print('Saved to ', submit_dir)
|
Run detection on images in the given directory.
|
AP.py
|
detect
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def detect(model, dataset_dir, subset):
print('Running on {}'.format(dataset_dir))
if (not os.path.exists(RESULTS_DIR)):
os.makedirs(RESULTS_DIR)
submit_dir = 'submit_{:%Y%m%dT%H%M%S}'.format(datetime.datetime.now())
submit_dir = os.path.join(RESULTS_DIR, submit_dir)
os.makedirs(submit_dir)
dataset = ChickenDataset()
dataset.load_chickens(dataset_dir, subset)
dataset.prepare()
dataset_val = ChickenDataset()
dataset_val.load_chickens(dataset_dir, 'stage1_test')
dataset_val.load_chickens(dataset_dir, 'val')
dataset_val.prepare()
submission = []
image_id = random.choice(dataset_val.image_ids)
(original_image, image_meta, gt_class_id, gt_bbox, gt_mask) = modellib.load_image_gt(dataset_val, inference_config, image_id, use_mini_mask=False)
log('original_image', original_image)
log('image_meta', image_meta)
log('gt_class_id', gt_class_id)
log('gt_bbox', gt_bbox)
log('gt_mask', gt_mask)
image_ids = np.random.choice(dataset_val.image_ids, 10)
APs = []
num = 0
count = 0
for image_id in dataset.image_ids:
image = dataset.load_image(image_id)
count = (count + 1)
(image, image_meta, gt_class_id, gt_bbox, gt_mask) = modellib.load_image_gt(dataset_val, inference_config, image_id, use_mini_mask=False)
molded_images = np.expand_dims(modellib.mold_image(image, inference_config), 0)
r = model.detect([image], verbose=0)[0]
(APss, precisions, recalls, overlaps) = utils.compute_ap(gt_bbox, gt_class_id, gt_mask, r['rois'], r['class_ids'], r['scores'], r['masks'])
APs.append(APss)
num = (num + APss)
source_id = dataset.image_info[image_id]['id']
rle = mask_to_rle(source_id, r['masks'], r['scores'])
submission.append(rle)
visualize.display_instances(image, r['rois'], r['masks'], r['class_ids'], dataset.class_names, r['scores'], title='Predictions')
plt.savefig('{}/{}.jpg'.format(submit_dir, dataset.image_info[image_id]['id']))
print(APs)
print((num / count))
submission = ('ImageId,EncodedPixels\n' + '\n'.join(submission))
file_path = os.path.join(submit_dir, 'submit.csv')
with open(file_path, 'w') as f:
f.write(submission)
print('Saved to ', submit_dir)
|
def detect(model, dataset_dir, subset):
print('Running on {}'.format(dataset_dir))
if (not os.path.exists(RESULTS_DIR)):
os.makedirs(RESULTS_DIR)
submit_dir = 'submit_{:%Y%m%dT%H%M%S}'.format(datetime.datetime.now())
submit_dir = os.path.join(RESULTS_DIR, submit_dir)
os.makedirs(submit_dir)
dataset = ChickenDataset()
dataset.load_chickens(dataset_dir, subset)
dataset.prepare()
dataset_val = ChickenDataset()
dataset_val.load_chickens(dataset_dir, 'stage1_test')
dataset_val.load_chickens(dataset_dir, 'val')
dataset_val.prepare()
submission = []
image_id = random.choice(dataset_val.image_ids)
(original_image, image_meta, gt_class_id, gt_bbox, gt_mask) = modellib.load_image_gt(dataset_val, inference_config, image_id, use_mini_mask=False)
log('original_image', original_image)
log('image_meta', image_meta)
log('gt_class_id', gt_class_id)
log('gt_bbox', gt_bbox)
log('gt_mask', gt_mask)
image_ids = np.random.choice(dataset_val.image_ids, 10)
APs = []
num = 0
count = 0
for image_id in dataset.image_ids:
image = dataset.load_image(image_id)
count = (count + 1)
(image, image_meta, gt_class_id, gt_bbox, gt_mask) = modellib.load_image_gt(dataset_val, inference_config, image_id, use_mini_mask=False)
molded_images = np.expand_dims(modellib.mold_image(image, inference_config), 0)
r = model.detect([image], verbose=0)[0]
(APss, precisions, recalls, overlaps) = utils.compute_ap(gt_bbox, gt_class_id, gt_mask, r['rois'], r['class_ids'], r['scores'], r['masks'])
APs.append(APss)
num = (num + APss)
source_id = dataset.image_info[image_id]['id']
rle = mask_to_rle(source_id, r['masks'], r['scores'])
submission.append(rle)
visualize.display_instances(image, r['rois'], r['masks'], r['class_ids'], dataset.class_names, r['scores'], title='Predictions')
plt.savefig('{}/{}.jpg'.format(submit_dir, dataset.image_info[image_id]['id']))
print(APs)
print((num / count))
submission = ('ImageId,EncodedPixels\n' + '\n'.join(submission))
file_path = os.path.join(submit_dir, 'submit.csv')
with open(file_path, 'w') as f:
f.write(submission)
print('Saved to ', submit_dir)<|docstring|>Run detection on images in the given directory.<|endoftext|>
|
1880e09d18eab246942cc9846da1691c89b50ff7ee9f16e7539172dc030d0d1d
|
def load_chickens(self, dataset_dir, subset):
'Load a subset of the nuclei dataset.\n\n dataset_dir: Root directory of the dataset\n subset: Subset to load. Either the name of the sub-directory,\n such as stage1_train, stage1_test, ...etc. or, one of:\n * train: stage1_train excluding validation images\n * val: validation images from VAL_IMAGE_IDS\n '
self.add_class('chicken', 1, 'head')
assert (subset in ['train', 'val', 'stage1_train', 'stage1_test', 'stage2_test'])
subset_dir = ('stage1_train' if (subset in ['train', 'val']) else subset)
dataset_dir = os.path.join(dataset_dir, subset_dir)
if (subset == 'val'):
image_ids = VAL_IMAGE_IDS
else:
image_ids = next(os.walk(dataset_dir))[1]
if (subset == 'train'):
image_ids = list((set(image_ids) - set(VAL_IMAGE_IDS)))
for image_id in image_ids:
self.add_image('chicken', image_id=image_id, path=os.path.join(dataset_dir, image_id, 'images/{fname}.{ext}'.format(fname=image_id, ext=IMAGE_EXT)))
|
Load a subset of the nuclei dataset.
dataset_dir: Root directory of the dataset
subset: Subset to load. Either the name of the sub-directory,
such as stage1_train, stage1_test, ...etc. or, one of:
* train: stage1_train excluding validation images
* val: validation images from VAL_IMAGE_IDS
|
AP.py
|
load_chickens
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def load_chickens(self, dataset_dir, subset):
'Load a subset of the nuclei dataset.\n\n dataset_dir: Root directory of the dataset\n subset: Subset to load. Either the name of the sub-directory,\n such as stage1_train, stage1_test, ...etc. or, one of:\n * train: stage1_train excluding validation images\n * val: validation images from VAL_IMAGE_IDS\n '
self.add_class('chicken', 1, 'head')
assert (subset in ['train', 'val', 'stage1_train', 'stage1_test', 'stage2_test'])
subset_dir = ('stage1_train' if (subset in ['train', 'val']) else subset)
dataset_dir = os.path.join(dataset_dir, subset_dir)
if (subset == 'val'):
image_ids = VAL_IMAGE_IDS
else:
image_ids = next(os.walk(dataset_dir))[1]
if (subset == 'train'):
image_ids = list((set(image_ids) - set(VAL_IMAGE_IDS)))
for image_id in image_ids:
self.add_image('chicken', image_id=image_id, path=os.path.join(dataset_dir, image_id, 'images/{fname}.{ext}'.format(fname=image_id, ext=IMAGE_EXT)))
|
def load_chickens(self, dataset_dir, subset):
'Load a subset of the nuclei dataset.\n\n dataset_dir: Root directory of the dataset\n subset: Subset to load. Either the name of the sub-directory,\n such as stage1_train, stage1_test, ...etc. or, one of:\n * train: stage1_train excluding validation images\n * val: validation images from VAL_IMAGE_IDS\n '
self.add_class('chicken', 1, 'head')
assert (subset in ['train', 'val', 'stage1_train', 'stage1_test', 'stage2_test'])
subset_dir = ('stage1_train' if (subset in ['train', 'val']) else subset)
dataset_dir = os.path.join(dataset_dir, subset_dir)
if (subset == 'val'):
image_ids = VAL_IMAGE_IDS
else:
image_ids = next(os.walk(dataset_dir))[1]
if (subset == 'train'):
image_ids = list((set(image_ids) - set(VAL_IMAGE_IDS)))
for image_id in image_ids:
self.add_image('chicken', image_id=image_id, path=os.path.join(dataset_dir, image_id, 'images/{fname}.{ext}'.format(fname=image_id, ext=IMAGE_EXT)))<|docstring|>Load a subset of the nuclei dataset.
dataset_dir: Root directory of the dataset
subset: Subset to load. Either the name of the sub-directory,
such as stage1_train, stage1_test, ...etc. or, one of:
* train: stage1_train excluding validation images
* val: validation images from VAL_IMAGE_IDS<|endoftext|>
|
55ca69be2096d8d8921b1274fa8db914ee63007a48bca1cfadb6cc1aa788f1d9
|
def load_mask(self, image_id):
'Generate instance masks for an image.\n Returns:\n masks: A bool array of shape [height, width, instance count] with\n one mask per instance.\n class_ids: a 1D array of class IDs of the instance masks.\n '
info = self.image_info[image_id]
mask_dir = os.path.join(os.path.dirname(os.path.dirname(info['path'])), 'masks')
mask = []
for f in next(os.walk(mask_dir))[2]:
m = skimage.io.imread(os.path.join(mask_dir, f), as_grey=True).astype(np.bool)
mask.append(m)
mask = np.stack(mask, axis=(- 1))
return (mask, np.ones([mask.shape[(- 1)]], dtype=np.int32))
|
Generate instance masks for an image.
Returns:
masks: A bool array of shape [height, width, instance count] with
one mask per instance.
class_ids: a 1D array of class IDs of the instance masks.
|
AP.py
|
load_mask
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def load_mask(self, image_id):
'Generate instance masks for an image.\n Returns:\n masks: A bool array of shape [height, width, instance count] with\n one mask per instance.\n class_ids: a 1D array of class IDs of the instance masks.\n '
info = self.image_info[image_id]
mask_dir = os.path.join(os.path.dirname(os.path.dirname(info['path'])), 'masks')
mask = []
for f in next(os.walk(mask_dir))[2]:
m = skimage.io.imread(os.path.join(mask_dir, f), as_grey=True).astype(np.bool)
mask.append(m)
mask = np.stack(mask, axis=(- 1))
return (mask, np.ones([mask.shape[(- 1)]], dtype=np.int32))
|
def load_mask(self, image_id):
'Generate instance masks for an image.\n Returns:\n masks: A bool array of shape [height, width, instance count] with\n one mask per instance.\n class_ids: a 1D array of class IDs of the instance masks.\n '
info = self.image_info[image_id]
mask_dir = os.path.join(os.path.dirname(os.path.dirname(info['path'])), 'masks')
mask = []
for f in next(os.walk(mask_dir))[2]:
m = skimage.io.imread(os.path.join(mask_dir, f), as_grey=True).astype(np.bool)
mask.append(m)
mask = np.stack(mask, axis=(- 1))
return (mask, np.ones([mask.shape[(- 1)]], dtype=np.int32))<|docstring|>Generate instance masks for an image.
Returns:
masks: A bool array of shape [height, width, instance count] with
one mask per instance.
class_ids: a 1D array of class IDs of the instance masks.<|endoftext|>
|
d01d4e82b14777fa825b0f76bbb999fe37de94014b0a134fed36613a3edcfde8
|
def image_reference(self, image_id):
'Return the path of the image.'
info = self.image_info[image_id]
if (info['source'] == 'chicken'):
return info['id']
else:
super(self.__class__, self).image_reference(image_id)
|
Return the path of the image.
|
AP.py
|
image_reference
|
AlexHsuYu/ClumsyChickens
| 6 |
python
|
def image_reference(self, image_id):
info = self.image_info[image_id]
if (info['source'] == 'chicken'):
return info['id']
else:
super(self.__class__, self).image_reference(image_id)
|
def image_reference(self, image_id):
info = self.image_info[image_id]
if (info['source'] == 'chicken'):
return info['id']
else:
super(self.__class__, self).image_reference(image_id)<|docstring|>Return the path of the image.<|endoftext|>
|
b266469f75c94524e8127dd1469fbedc9a35432db2a6a27a096d6af4e40f4726
|
def test_simple_reverse_relation_included_renderer():
'\n Test renderer when a single reverse fk relation is passed.\n '
serializer = DummyTestSerializer(instance=Entry())
renderer = JSONRenderer()
rendered = renderer.render(serializer.data, renderer_context={'view': DummyTestViewSet()})
assert rendered
|
Test renderer when a single reverse fk relation is passed.
|
example/tests/unit/test_renderers.py
|
test_simple_reverse_relation_included_renderer
|
morenoh149/django-rest-framework-json-api
| 0 |
python
|
def test_simple_reverse_relation_included_renderer():
'\n \n '
serializer = DummyTestSerializer(instance=Entry())
renderer = JSONRenderer()
rendered = renderer.render(serializer.data, renderer_context={'view': DummyTestViewSet()})
assert rendered
|
def test_simple_reverse_relation_included_renderer():
'\n \n '
serializer = DummyTestSerializer(instance=Entry())
renderer = JSONRenderer()
rendered = renderer.render(serializer.data, renderer_context={'view': DummyTestViewSet()})
assert rendered<|docstring|>Test renderer when a single reverse fk relation is passed.<|endoftext|>
|
479709bc04f408691d3166c9be1c03ade0a52b0cae83416a033ecef0c0e9959c
|
@cached_property
def additional_properties_type():
'\n This must be a method because a model may have properties that are\n of type self, this must run after the class is loaded\n '
return (bool, date, datetime, dict, float, int, list, str, none_type)
|
This must be a method because a model may have properties that are
of type self, this must run after the class is loaded
|
clients/client/python/ory_client/model/schema_patch.py
|
additional_properties_type
|
ory/sdk
| 77 |
python
|
@cached_property
def additional_properties_type():
'\n This must be a method because a model may have properties that are\n of type self, this must run after the class is loaded\n '
return (bool, date, datetime, dict, float, int, list, str, none_type)
|
@cached_property
def additional_properties_type():
'\n This must be a method because a model may have properties that are\n of type self, this must run after the class is loaded\n '
return (bool, date, datetime, dict, float, int, list, str, none_type)<|docstring|>This must be a method because a model may have properties that are
of type self, this must run after the class is loaded<|endoftext|>
|
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