# Revision history [back]

For multivariate division with remainder that takes the monomial ordering into account, you want to do

sage: f.reduce([g])
-y^2 + z


and you can obtain the quotient by

sage: (f - f.reduce([g])) // g
y


See the documentation of reduce().

For multivariate division with remainder that takes the monomial ordering into account, you want to do

sage: f.reduce([g])
-y^2 + z


and you can obtain the quotient by

sage: (f - f.reduce([g])) // g
y


See the documentation of reduce().

Edit: Actually this is inefficient because both can be computed simultaneously. The algorithm is simple. I don't know if it is included in Sage.

Also, the documentation of quo_rem() should refer to reduce().