# Subresultants

Subresultants[poly1,poly2,var]

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

Subresultants[poly1,poly2,var,Modulusp]

computes the principal subresultant coefficients modulo the prime p.

# Details 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. »

# Examples

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## 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:

 In[2]:=
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When two pairs of roots are equal, the first two PSCs disappear:

 In[3]:=
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# Tutorials

Introduced in 1999
(4.0)
| Updated in 2012
(9.0)