# SylvesterSequence -- the Sylvester sequence of two rational univariate polynomials

## Synopsis

• Usage:
SylvesterSequence(f,g)
• Inputs:
• f, , a rational univariate polynomial
• g, , a rational univariate polynomial in the same variable as f
• Outputs:
• a list, the Sylvester sequence of f and g

## Description

This computes the Sylvester sequence of two rational univariate polynomials f and g in the same ring.

 i1 : R = QQ[t] o1 = R o1 : PolynomialRing i2 : f = (t + 1)*(t + 2) 2 o2 = t + 3t + 2 o2 : R i3 : g = t + 2 o3 = t + 2 o3 : R i4 : SylvesterSequence(f,g) o4 = {t + 1, 1, 0} o4 : List

• SylvesterCount -- the difference in variations of the Sylvester sequence of two rational univariate polynomials

## Ways to use SylvesterSequence :

• "SylvesterSequence(RingElement,RingElement)"

## For the programmer

The object SylvesterSequence is .