PolynomialTools[GcdFreeBasis] - compute a gcd free basis of a set or list of polynomials
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Calling Sequence
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GcdFreeBasis(S)
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Parameters
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S
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set or list of polynomials
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Description
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The GcdFreeBasis command uses repeated gcd computations to compute a gcd free basis B of the polynomials in S. B satisfies the following properties.
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Each polynomial in S can be written as a constant times a product of polynomials from B.
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The polynomials in B are pairwise coprime, that is, their gcd is constant.
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With respect to cardinality, B is minimal with these properties. (This is equivalent to saying that B can be computed using gcds and divisions only, but not factorization.)
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The gcd free basis is unique up to ordering and multiplication of the basis elements by constants.
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GcdFreeBasis can handle the same types of coefficients as the Maple function gcd.
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If S is a set, then the output is a set as well. If S is a list, then the output is also a list. The ordering of the elements in the result is not determined in either case.
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Zero polynomials and constants are ignored. In particular, for a constant const, GcdFreeBasis([const]) returns [ ]. The empty set or list is a valid input and is returned unchanged.
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References
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Bach, Eric.; Driscoll, James.; and Shallit, Jeffrey. "Factor Refinement." Journal of Algorithms Vol. 15(2), (1993): 199-222.
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Download Help Document
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