numSylvester(RingElement,RingElement,Number,Number)

Synopsis

• Function: numSylvester

• Usage:

  numSylvester(f,g,a,b)

• Inputs:
  • f, a ring element
  • g, a ring element
  • a, a number
  • b, a number
• Outputs:
  • an integer, the difference between number of roots of f when gis positive and when g is negative

Description

This computes the difference in variations of the Sylvester sequence of f and f'g at the valuesa and b

i1 : R = QQ[t]

o1 = R

o1 : PolynomialRing

i2 : f = (t-2)*(t-1)*(t+3)

      3
o2 = t  - 7t + 6

o2 : R

i3 : g = t+1

o3 = t + 1

o3 : R

i4 : a = -5

o4 = -5

i5 : b = 4

o5 = 4

i6 : numSylvester(f,g,a,b)

o6 = 1

See also

• SylvesterSequence