next | previous | forward | backward | up | top | index | toc | Macaulay2 website
RealRoots :: SturmSequence(RingElement)

SturmSequence(RingElement)

Synopsis

Description

This computes the Sturm Sequence 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