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,Modulusp]
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:

In[1]:=
Click for copyable input
Out[1]=

PSCs of two cubic polynomials:

In[1]:=
Click for copyable input
Out[1]=

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

In[2]:=
Click for copyable input
Out[2]=

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

In[3]:=
Click for copyable input
Out[3]=
Introduced in 1999
(4.0)
| Updated in 2012
(9.0)