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D.8.3.3 triangM
Procedure from library triang.lib (see triang_lib).
- Usage:
- triangM(G[,i]); G=ideal, i=integer,
- Assume:
- G is the reduced lexicographical Groebner basis of the
zero-dimensional ideal (G), sorted by increasing leading terms.
- Return:
- a list of finitely many triangular systems, such that
the union of their varieties equals the variety of (G).
If i = 2, then each polynomial of the triangular systems
is factorized.
- Note:
- Algorithm of Moeller (see: Moeller, H.M.: On decomposing systems of
polynomial equations with finitely many solutions, Appl. Algebra Eng.
Commun. Comput. 4, 217 - 230, 1993).
Example:
| LIB "triang.lib";
ring rC5 = 0,(e,d,c,b,a),lp;
triangM(stdfglm(cyclic(5))); //oder: triangM(stdfglm(cyclic(5)),2);
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