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RealRoots :: SylvesterCount

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

Synopsis

Description

This computes the difference in variations of the Sylvester sequence of f and f'g on the interval $(a,b]$.

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 : SylvesterCount(f,g,a,b)

o6 = 1

See also

Ways to use SylvesterCount :

For the programmer

The object SylvesterCount is a method function with options.