D.7.3.2 triangLfak

Procedure from library triang.lib (see triang_lib).

Usage:

triangLfak(G); G=ideal

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).

Note:

Algorithm of Lazard with factorization (see: Lazard, D.: Solving zero-dimensional algebraic systems, J. Symb. Comp. 13, 117 - 132, 1992).

Remark:

each polynomial of the triangular systems is factorized.

Example:

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