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Binomials :: binomialUnmixedDecomposition

binomialUnmixedDecomposition -- Binomial Unmixed Decomposition

Synopsis

Description

This routine returns an unmixed decomposition of a binomial ideal into binomial ideals. The implemented algorithm is a variant of Algorithm 4 in [OS00].
i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : I = ideal (x^2, x*y, y^2, x*(z^3-1), y*(z^2-1))

             2        2     3         2
o2 = ideal (x , x*y, y , x*z  - x, y*z  - y)

o2 : Ideal of R
i3 : bud = binomialUnmixedDecomposition I

              2        2     2         3
o3 = {ideal (y , x*y, x , y*z  - y, x*z  - x)}

o3 : List
i4 : intersect bud == I

o4 = true
A synonym for this function is BUD.

Caveat

Apart from unmixedness, properties of the output decomposition are defined only by the course of the algorithm, in particular it is not mesoprimary decomposition of [KM11].

See also

Ways to use binomialUnmixedDecomposition :

For the programmer

The object binomialUnmixedDecomposition is a method function with options.