D.7.3.3 triangM

Procedure from library triang.lib (see triang_lib).

Usage:

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

Assume:

G is the reduced lexicographical Groebner bases 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);