D.4.1.9 noetherNormal

Procedure from library algebra.lib (see algebra_lib).

Usage:

noetherNormal(id[,p]); id ideal, p integer

Return:

a list l two ideals, say I,J: - I is generated by a subset of the variables with size(I) = dim(id) - J defines a map (coordinate change in the basering), such that: if we define map phi=basering,J; then k[var(1),...,var(n)]/phi(id) is finite over k[I]. If p is given, 0<=p<=100, a sparse coordinate change with p percent of the matrix entries being 0 (default: p=0 i.e. dense)

Note:

Designed for characteristic 0.It works also in char k > 0 if it terminates,but may result in an infinite loop in small characteristic

Example:

LIB "algebra.lib";
ring r=0,(x,y,z),dp;
ideal i= xy,xz;
noetherNormal(i);
→ [1]:
→    _[1]=x
→    _[2]=2x+y
→    _[3]=3x+4y+z
→ [2]:
→    _[1]=y
→    _[2]=z