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D.12.7.11 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 beginning with p, p' and goes on with the negative part 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
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See also:
sturm;
sturmhaseq.
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