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D.4.13.5 NoetherPosition

Procedure from library mregular.lib (see mregular_lib).

Usage:
NoetherPosition (i); i ideal

Return:
ideal such that, for the homogeneous linear transformation map phi=S,NoetherPosition(i);
one has that K[x(n-d+1),...,x(n)] is a Noether normalization of S/phi(i) where S=K[x(0),...x(n)] is the basering and d=dim(S/i). (returns -1 if i = (0) or (1)).

Assume:
The field K is infinite and i is a nonzero proper ideal.

Note:
1. It works also if K is a finite field if it terminates, but may result in an infinite loop. If the procedure enters more than 30 loops, -1 is returned and a warning message is displayed.
2. If printlevel > 0 (default = 0), additional info is displayed: dim(S/i) and K[x(n-d+1),...,x(n)] are given.

Example:
 


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