PolynomialTools[ShiftlessDecomposition] - compute a shiftless decomposition of a univariate polynomial
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Calling Sequence
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ShiftlessDecomposition(f,x)
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Parameters
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f
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polynomial in x
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x
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-
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indeterminate
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Description
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The ShiftlessDecomposition command computes a shiftless decomposition of f w.r.t. x.
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It satisfies the following properties.
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is constant w.r.t. x, and are nonconstant primitive polynomials w.r.t. x.
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The shiftless decomposition is unique up to reordering and multiplication by units. The are ordered by ascending degree in x, but the ordering within the same degree is not determined.
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If f is constant w.r.t. x, then the return value is .
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Partial factorizations of the input are not taken into account.
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References
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Gerhard, J.; Giesbrecht, M.; Storjohann, A.; and Zima, E.V. "Shiftless decomposition and polynomial-time rational summation." Proceedings International Symposium on Symbolic and Algebraic Computation, pp. 119-126. ed. J.R. Sendra. 2003.
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