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D.4.13.6 is_NP

Procedure from library mregular.lib (see mregular_lib).

Usage:
is_NP (i); i ideal

Return:
1 if K[x(n-d+1),...,x(n)] is a Noether normalization of S/i where S=K[x(0),...x(n)] is the basering, and d=dim(S/i), 0 otherwise.
(returns -1 if i=(0) or i=(1)).

Assume:
i is a nonzero proper homogeneous ideal.

Note:
1. If i is not homogeneous and is_NP(i)=1 then K[x(n-d+1),...,x(n)] is a Noether normalization of S/i. The converse may be wrong if the ideal is not homogeneous.
2. is_NP is used in the procedures regIdeal, depthIdeal, satiety, and NoetherPosition.

Example:
 


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