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D.4.22.1 NPos_test
Procedure from library noether.lib (see noether_lib).
- 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.
Example:
| | 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
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