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D.4.2.3 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 if and only if 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 if and only if 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 using a different algorithm, which is often faster
if l[1] == 0 then l[2] may contain more than one relation h(y(0),y(1),...,y(k)), separated by comma

Example:
 


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