reduce -- computes an equivariant normal form

Synopsis

Usage:

r = reduce(f,F)
Inputs:
- f, a ring element, an element of a ring created by buildERing.
- F, a list, a list of polynomials from the same ring as f.
Optional inputs:
- Completely => ..., default value false
Outputs:
- r, a ring element, an equivariant normal form of f with respect to F.

Description

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

Caveat

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

Ways to use reduce:

reduce(RingElement,List)

For the programmer

The object reduce is a method function with options.