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D.12.8.13 sturmhaseq

Procedure from library rootsur.lib (see rootsur_lib).

Usage:
sturmhaseq(P); P poly.

Return:
list: the non-zero polynomials of the Sturm-Habicht sequence of P

Assume:
P is a univariate polynomial.

Theory:
The Sturm-Habicht sequence (also subresultant sequence) is closely related to the Sturm sequence, but behaves better with respect to the size of the coefficients. It is defined via subresultants. See: Basu, Pollack, Roy, Algorithms in Real Algebraic Geometry, Springer, 2003.

Example:
 
LIB "rootsur.lib";
ring r = 0,x,dp;
poly p = x5-x4+x-3/2;
list l = sturmhaseq(p);
l;
==> [1]:
==>    132949/16
==> [2]:
==>    -25x-332
==> [3]:
==>    -16x2+42x-24
==> [4]:
==>    4x3-20x+73/2
==> [5]:
==>    5x4-4x3+1
==> [6]:
==>    x5-x4+x-3/2
See also: sturm; sturmha; sturmseq.