Singular

D.4.18.1 NPos_test

Usage:

NPos_test (I); I monomial ideal

Return:

A list whose first element is 1, if i is in Noether position, 0 otherwise. The second element of this list is a list of variables ordered such that those variables are listed first, of which a power belongs to the initial ideal of i. If i is in Noether position, the method returns furthermore the dimension of i.

Assume:

i is a nonzero monomial ideal.

LIB "noether.lib";
ring r=0,(X,Y,a,b),dp;
poly f=X^8+a*Y^4-Y;
poly g=Y^8+b*X^4-X;
poly h=diff(f,X)*diff(g,Y)-diff(f,Y)*diff(g,X);
ideal i=f,g,h;
NPos_test(i);
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       b
==>    [2]:
==>       a
==>    [3]:
==>       Y
==>    [4]:
==>       X