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RealRoots :: realRootIsolation

realRootIsolation -- a list that isolates the real roots of a rational univariate polynomial

Synopsis

Description

This method uses a Sturm sequence and a bisection method to isolate real solutions of f in intervals of length at most r.

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 : realRootIsolation(f,1/2)

         69    23    23  69    23  207    299  161
o3 = {{- --, - --}, {--, --}, {--, ---}, {---, ---}}
         64    32    32  64     8   64     64   32

o3 : List
i4 : realRootIsolation(f,.2)

         69    115    115  69    23  391    621  161
o4 = {{- --, - ---}, {---, --}, {--, ---}, {---, ---}}
         64    128    128  64     8  128    128   32

o4 : List

See also

Ways to use realRootIsolation :

For the programmer

The object realRootIsolation is a method function.