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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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