# realRootIsolation(RingElement,RR)

## Synopsis

• Function: realRootIsolation
• Usage:
realRootIsolation(f,eps)
• Inputs:
• f,
• eps,
• Outputs:
• a list, the number of real roots of a univariate polynomialf not counting multiplicity

## Description

This method uses a Sturm sequence and a bisection method to isolate real solutions of a polynomialf to a real univariate polynomial and it lists an interval for which each real solution is located

 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,0.5) 69 23 23 69 23 207 299 161 o3 = {{- --, - --}, {--, --}, {--, ---}, {---, ---}} 64 32 32 64 8 64 64 32 o3 : List