Reduces f by the Inc-orbits 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.
i1 : R = buildERing({symbol x}, {1}, QQ, 3); |
i2 : reduce(x_0^2 + x_0*x_2, {x_1}) 2 o2 = x 0 o2 : R |
The output does not necessarily belong to the same ring as the input.
The object reduce is a method function with options.