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EquivariantGB :: reduce

reduce -- computes an equivariant normal form



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})

o2 = x

o2 : R


The output does not necessarily belong to the same ring as the input.

Ways to use reduce :

For the programmer

The object reduce is a method function with options.