r = reduce(f,F)
Reduces f by the Incorbits of the set F until f is in a normal form. That is the lead monomial of f is a standard monomial, not divisible by any monomial in the orbit of any lead monomial of an element of F. If F is an equivariant Gröbner basis then r is 0 if and only if f is in the ideal generated by the orbits of F.
If the optional argument Completely is set to true then normal form r will contain only standard monomials. If F is an equivariant Gröbner basis, then the completely reduced normal form r is uniquely determined, otherwise there is no such guarantee.


The output does not necessarily belong to the same ring as the input.
The object reduce is a method function with options.