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Binomials :: binomialPrimaryDecomposition

binomialPrimaryDecomposition -- Binomial Primary Decomposition

Synopsis

Description

This routine returns a primary decomposition of I into binomial ideals.
i1 : R = QQ[x,y,z]

o1 = R

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

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

o2 : Ideal of R
i3 : bpd = binomialPrimaryDecomposition I

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

o3 : List
i4 : intersect bpd == I

o4 = true
A synonym for this function is BPD.

Caveat

Currently it can not be guaranteed that the decomposition is irredundant, although serious attempts are made to reduce redundancy.

See also

Ways to use binomialPrimaryDecomposition :

For the programmer

The object binomialPrimaryDecomposition is a method function with options.