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| from sympy.core.singleton import S | |
| from sympy.core.sympify import _sympify | |
| from sympy.polys.polytools import Poly | |
| from .matexpr import MatrixExpr | |
| class CompanionMatrix(MatrixExpr): | |
| """A symbolic companion matrix of a polynomial. | |
| Examples | |
| ======== | |
| >>> from sympy import Poly, Symbol, symbols | |
| >>> from sympy.matrices.expressions import CompanionMatrix | |
| >>> x = Symbol('x') | |
| >>> c0, c1, c2, c3, c4 = symbols('c0:5') | |
| >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x) | |
| >>> CompanionMatrix(p) | |
| CompanionMatrix(Poly(x**5 + c4*x**4 + c3*x**3 + c2*x**2 + c1*x + c0, | |
| x, domain='ZZ[c0,c1,c2,c3,c4]')) | |
| """ | |
| def __new__(cls, poly): | |
| poly = _sympify(poly) | |
| if not isinstance(poly, Poly): | |
| raise ValueError("{} must be a Poly instance.".format(poly)) | |
| if not poly.is_monic: | |
| raise ValueError("{} must be a monic polynomial.".format(poly)) | |
| if not poly.is_univariate: | |
| raise ValueError( | |
| "{} must be a univariate polynomial.".format(poly)) | |
| if not poly.degree() >= 1: | |
| raise ValueError( | |
| "{} must have degree not less than 1.".format(poly)) | |
| return super().__new__(cls, poly) | |
| def shape(self): | |
| poly = self.args[0] | |
| size = poly.degree() | |
| return size, size | |
| def _entry(self, i, j): | |
| if j == self.cols - 1: | |
| return -self.args[0].all_coeffs()[-1 - i] | |
| elif i == j + 1: | |
| return S.One | |
| return S.Zero | |
| def as_explicit(self): | |
| from sympy.matrices.immutable import ImmutableDenseMatrix | |
| return ImmutableDenseMatrix.companion(self.args[0]) | |