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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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