SubresultantPolynomialRemainders

SubresultantPolynomialRemainders[poly1, poly2, var]
gives the subresultant polynomial remainder sequence of the polynomials and with respect to the variable var.

SubresultantPolynomialRemainders[poly1, poly2, var, Modulus->p]
computes the subresultant polynomial remainder sequence modulo the prime p.

Details and OptionsDetails and Options

  • SubresultantPolynomialRemainders is also known as subresultant polynomial remainder sequence or prs.
  • SubresultantPolynomialRemainders gives a list of polynomials of decreasing degrees in var.
  • Each polynomial in the list is a constant multiple of the PolynomialRemainder of the previous two polynomials, with and being the first two elements.
  • The last polynomial in the resulting list is a constant multiple of the polynomial GCD of univariate polynomials and in the variable var.

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

This gives the subresultant polynomial remainder sequence of two polynomials:

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Subresultant polynomial remainder sequence of polynomials with symbolic coefficients:

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The last element differs from the GCD of the polynomials by a factor independent of :

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