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D.4.16.6 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:
| | LIB "mregular.lib";
ring r=0,(x,y,z,t,u),dp;
ideal i1=y,z,t,u; ideal i2=x,z,t,u; ideal i3=x,y,t,u; ideal i4=x,y,z,u;
ideal i5=x,y,z,t; ideal i=intersect(i1,i2,i3,i4,i5);
is_NP(i);
==> 0
ideal ch=x,y,z,t,x+y+z+t+u;
map phi=ch;
is_NP(phi(i));
==> 1
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