D.7.3.4 triangMH

Procedure from library triang.lib (see triang_lib).

Usage:

triangMH(G[,i]); G=ideal, i=integer

Assume:

G is the reduced lexicographical Groebner bases of the zero-dimensional ideal (G), sorted by increasing leading terms.

Return:

a list of finitely many triangular systems, such that the disjoint 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 and Hillebrand (see: Moeller, H.M.: On decomposing systems of polynomial equations with finitely many solutions, Appl. Algebra Eng. Commun. Comput. 4, 217 - 230, 1993 and Hillebrand, D.: Triangulierung nulldimensionaler Ideale - Implementierung und Vergleich zweier Algorithmen, master thesis, Universitaet Dortmund, Fachbereich Mathematik, Prof. Dr. H.M. Moeller, 1999).

Example:

LIB "triang.lib";
ring rC5 = 0,(e,d,c,b,a),lp;
triangMH(stdfglm(cyclic(5)));