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