SylvesterSequence -- the Sylvester sequence of two rational univariate polynomials

Synopsis

• Usage:

  SylvesterSequence(f,g)

• Inputs:
  • f, a ring element, a rational univariate polynomial
  • g, a ring element, 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

See also

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