D.4.1.3 inSubring
.................
Procedure from library algebra.lib (see algebra_lib).

Usage:
inSubring(p,i); p poly, i ideal

Return:
         a list l of size 2, l[1] integer, l[2] string
         l[1]=1 iff p is in the subring generated by i=i[1],...,i[k],
                and then l[2] = y(0)-h(y(1),...,y(k)) if p = h(i[1],...,i[k])
         l[1]=0 iff p is in not the subring generated by i,
                and then l[2] = h(y(0),y(1),...,y(k) where p satisfies the
                nonlinear relation h(p,i[1],...,i[k])=0.

Note:
the proc algebra_containment tests the same with a different
algorithm, which is often faster

Example:
LIB "algebra.lib";
ring q=0,(x,y,z,u,v,w),dp;
poly p=xyzu2w-1yzu2w2+u4w2-1xu2vw+u2vw2+xyz-1yzw+2u2w-1xv+vw+2;
ideal I =x-w,u2w+1,yz-v;
inSubring(p,I);
==> [1]:
==>    1
==> [2]:
==>    y(1)*y(2)*y(3)+y(2)^2-y(0)+1

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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