D.4.15.1 modQuotient

Usage:

modQuotient(I, J, #); I, J ideals, # an optional list which is either empty (not entered) or consists of precisely one integer which is 0 or 1.

Assume:

The common basering of I and J is defined over the rationals.

Return:

The ideal quotient I:J.

Note:

- The resulting ideal is given by a standard basis in the basering.
- The final result will be checked for correctness if # is either empty (not entered) or if #[1] = 1. Without the check, the functions returns a result which is correct with high probability.

LIB "modquotient.lib";
ring R = 0, (x,y,z), dp;
ideal I = x2+xyz, y2-z3y, z3+y5xz;
ideal J = maxideal(3);
ideal K = modQuotient(I, J);
K;
==> K[1]=yz2+xz
==> K[2]=xz2+y2
==> K[3]=y2z+xy
==> K[4]=xyz+x2
==> K[5]=y3-x2z
==> K[6]=z4-yz
==> K[7]=x4y-z2
==> K[8]=x5+z3