16 lines
782 B
Python
16 lines
782 B
Python
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def linear_representation_polynomials(polynomial, list_of_polynomials):
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'''Given >list_of_polynomials< and >polynomial<, which is a linear combination of polynomials in the list (over the base ring),
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find coefficients of this combination.'''
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F = polynomial.parent().base_ring()
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monomials = polynomial.monomials()
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for pol in list_of_polynomials:
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monomials += pol.monomials()
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monomials = Set(monomials)
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monomials = list(monomials)
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d = len(monomials)
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M = matrix(F, d, len(list_of_polynomials))
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for i, pol in enumerate(list_of_polynomials):
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for j, m in enumerate(monomials):
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M[j, i] = pol.monomial_coefficient(m)
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v = vector([polynomial.monomial_coefficient(m) for m in monomials])
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return list(M.solve_right(v))
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