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D.11.8.11 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 univariate polynomial with rational coefficients
- Theory:
- The Sturm sequence of p (also called remainder sequence) is the
sequence begininng with p, p' and goes on with the negative of 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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