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Binomials :: binomialSolve

binomialSolve -- solving zero-dimensional binomial Ideals

Synopsis

Description

The solutions of a set of unital binomial equations exist in a cyclotomic field. This function will compute the variety of a unital binomial ideal and construct an appropriate cyclotomic field containing the entire variety (as a subset of the algebraic closure of QQ).
i1 : R = QQ[x,y,z,w]

o1 = R

o1 : PolynomialRing
i2 : I = ideal (x-y,y-z,z*w-1*w,w^2-x)

                                    2
o2 = ideal (x - y, y - z, z*w - w, w  - x)

o2 : Ideal of R
i3 : dim I

o3 = 0
i4 : binomialSolve I

o4 = {{1, 1, 1, 1}, {1, 1, 1, -1}, {0, 0, 0, 0}}

o4 : List
i5 : J = ideal (x^3-1,y-x,z-1,w-1)

             3
o5 = ideal (x  - 1, - x + y, z - 1, w - 1)

o5 : Ideal of R
i6 : binomialSolve J

o6 = {{1, 1, 1, 1}, {ww , ww , 1, 1}, {- ww  - 1, - ww  - 1, 1, 1}}
                       3    3              3          3

o6 : List

Caveat

The current implementation can only handle unital binomial ideals.

See also

For the programmer

The object binomialSolve is a function closure.