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D.7.8.11 sturmseq

Procedure from library rootsur.lib (see rootsur_lib).

Usage:
sturmseq(p); p poly

Return:
list: a Sturm sequence of p

Assume:
p is a univarite polynomials with rational coefficients

Theory:
The Sturm sequence of p (also called remainder sequence) is the sequence begininng with p, p' and goes on with minus the remainder of the two previous polynomials, until the remainder is zero. See: Basu, Pollack, Roy, Algorithms in Real Algebraic Geometry, Springer, 2003.

Example:
 
LIB "rootsur.lib";
ring r = 0,(z,x),dp;
poly p = x5-3x4+12x3+7x-153;
sturmseq(p);
==> [1]:
==>    x5-3x4+12x3+7x-153
==> [2]:
==>    x4-12/5x3+36/5x2+7/5
==> [3]:
==>    -x3-9/7x2-5/3x+317/7
==> [4]:
==>    -x2-756/151x+2433/151
==> [5]:
==>    x-514191/177889
==> [6]:
==>    1
sturm, sturmhaseq


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            User manual for Singular version 3-0-1, October 2005, generated by texi2html.