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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)
- @property
- 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])
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