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from sympy.core.assumptions import check_assumptions
from sympy.core.logic import fuzzy_and
from sympy.core.sympify import _sympify
from sympy.matrices.kind import MatrixKind
from sympy.sets.sets import Set, SetKind
from sympy.core.kind import NumberKind
from .matexpr import MatrixExpr
class MatrixSet(Set):
"""
MatrixSet represents the set of matrices with ``shape = (n, m)`` over the
given set.
Examples
========
>>> from sympy.matrices import MatrixSet
>>> from sympy import S, I, Matrix
>>> M = MatrixSet(2, 2, set=S.Reals)
>>> X = Matrix([[1, 2], [3, 4]])
>>> X in M
True
>>> X = Matrix([[1, 2], [I, 4]])
>>> X in M
False
"""
is_empty = False
def __new__(cls, n, m, set):
n, m, set = _sympify(n), _sympify(m), _sympify(set)
cls._check_dim(n)
cls._check_dim(m)
if not isinstance(set, Set):
raise TypeError("{} should be an instance of Set.".format(set))
return Set.__new__(cls, n, m, set)
@property
def shape(self):
return self.args[:2]
@property
def set(self):
return self.args[2]
def _contains(self, other):
if not isinstance(other, MatrixExpr):
raise TypeError("{} should be an instance of MatrixExpr.".format(other))
if other.shape != self.shape:
are_symbolic = any(_sympify(x).is_Symbol for x in other.shape + self.shape)
if are_symbolic:
return None
return False
return fuzzy_and(self.set.contains(x) for x in other)
@classmethod
def _check_dim(cls, dim):
"""Helper function to check invalid matrix dimensions"""
ok = not dim.is_Float and check_assumptions(
dim, integer=True, nonnegative=True)
if ok is False:
raise ValueError(
"The dimension specification {} should be "
"a nonnegative integer.".format(dim))
def _kind(self):
return SetKind(MatrixKind(NumberKind))
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