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RealRoots :: SturmSequence

SturmSequence -- the Sturm sequence of a rational univariate polynomial

Synopsis

Description

This computes the Sturm sequence of the square-free part of a univariate polynomial f.

i1 : R = QQ[t]

o1 = R

o1 : PolynomialRing
i2 : f = 45 - 39*t - 34*t^2 + 38*t^3 - 11*t^4 + t^5

      5      4      3      2
o2 = t  - 11t  + 38t  - 34t  - 39t + 45

o2 : R
i3 : roots f

o3 = {-1, 1, 3, 3, 5}

o3 : List
i4 : SturmSequence(f)

       4     3      2              3      2             104 2   432    232 
o4 = {t  - 8t  + 14t  + 8t - 15, 5t  - 29t  + 27t + 13, ---t  - ---t + ---,
                                                         25      25     25 
     ------------------------------------------------------------------------
     3100    5300  194688
     ----t - ----, ------, 0}
      169     169   24025

o4 : List

See also

Ways to use SturmSequence :

For the programmer

The object SturmSequence is a method function.