BUILT-IN MATHEMATICA SYMBOL

# 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:

 Out[1]=

Subresultant polynomial remainder sequence of polynomials with symbolic coefficients:

 Out[1]=

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

 Out[2]=