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D.12.7.7 allrealst

Procedure from library rootsur.lib (see rootsur_lib).

Usage:
allrealst(p); poly p

Return:
int: 1 if and only if all the roots of p are real, 0 otherwise. Checks by using Sturm's Theorem whether all the roots of p are real

Assume:
p is a univariate polynomial with rational coefficients

Example:
 
LIB "rootsur.lib";
ring r = 0,x,dp;
poly p = (x+2)*(x-1)*(x-5);
allrealst(p);
==> 1
p = p*(x2+1);
allrealst(p);
==> 0
See also: allreal; sturm; sturmha.