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D.4.2.9 noetherNormal
Procedure from library algebra.lib (see algebra_lib).
- Usage:
- noetherNormal(id[,p]); id ideal, p integer
- Return:
| | a list l of two ideals, say I,J:
- I defines a map (coordinate change in the basering), such that:
- J is generated by a subset of the variables with size(J) = dim(id)
if we define map phi=basering,I;
then k[var(1),...,var(n)]/phi(id) is finite over k[J].
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)
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- 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
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