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=(1-x)*(x2-y3);
poly h=y2-x2;
ideal i=g,h;
poly f=x2-x2y; 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=(1-x)*(x2-y3);
poly h=y2-x2;
ideal i=g,h;
poly f=x2-x2y; NF(f,std(i));
=> 0

Valladolid (Spain) 5-00

http://www.singular.uni-kl.de