 ring r=0,(e,f,h,a),Dp;
matrix d[4][4];
d[1,2]=h; d[1,3]=2*e; d[2,3]=2*f;
def R=nc_algebra(1,d); setring R;
// this algebra is U(sl_2), tensored with K[a] over K
option(redSB);
option(redTail);
poly p = 4*e*f+h^22*h  a;
// p is a central element with parameter
ideal I = e^3, f^3, h^34*h, p; // take this ideal
// and intersect I with the ring K[a]
ideal J = eliminate(I,e*f*h);
// if we want substitute 'a' with a value,
// it has to be a root of this polynomial
J;
==> J[1]=a332a2+192a
// now we try to eliminate h,
// that is we intersect I with the subalgebra S,
// generated by e and f.
// But S is not closed in itself, since f*ee*f=h !
// the next command will definitely produce an error
eliminate(I,h);
==> ? no elimination is possible: subalgebra is not admissible
==> ? error occurred in or before ./examples/eliminate_(plural).sing l\
ine 21: `eliminate(I,h);`
// since a commutes with e,f,h, we can eliminate it:
eliminate(I,a);
==> _[1]=h34h
==> _[2]=fh22fh
==> _[3]=f3
==> _[4]=eh2+2eh
==> _[5]=2efhh22h
==> _[6]=e3
