Subresultants

Subresultants[poly1, poly2, var]
generates a list of the principal subresultant coefficients of the polynomials and with respect to the variable var.

Subresultants[poly1, poly2, var, Modulus->p]
computes the principal subresultant coefficients modulo the prime p.

Details and OptionsDetails and Options

  • The first k subresultants of two polynomials a and b, both with leading coefficient one, are zero when a and b have k common roots.
  • Subresultants returns a list whose length is Min[Exponent[poly1, var], Exponent[poly2, var]]+1. »

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

The first three principal subresultant coefficients (PSCs) are zero when there are three common roots, multiplicities counted:

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PSCs of two cubic polynomials:

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When the polynomials have a pair of equal roots, the first PSC disappears:

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When two pairs of roots are equal, the first two PSCs disappear:

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