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
|