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Ideal membership
Check if a polynomial f is contained in a given
ideal I , based on the fact:
( f in
I )
if and only if
( NF( f, std( I )) = 0 ) .
Here, NF( f, std(I)) denotes a normal form of
f with respect to a standard basis of I.
ring r=0,(x,y),dp;
poly g=(1x)*(x2y3);
poly h=y2x2;
ideal i=g,h;
poly f=x2x2y;
NF(f,std(i));
=> y3+y2
It follows that f is not
contained in the ideal <g,h> of
Q[x,y].
This changes if we consider the localization at
<x,y> :
ring r1=0,(x,y),ds;
poly g=(1x)*(x2y3);
poly h=y2x2;
ideal i=g,h;
poly f=x2x2y;
NF(f,std(i));
=> 0

