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Binomials :: binomialPrimaryDecomposition

binomialPrimaryDecomposition -- Binomial Primary Decomposition

Synopsis

Description

This routine returns a minimal primary decomposition of a binomial ideal 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
Running cellular decomposition:
cellular components found: 1
cellular components found: 2
Decomposing cellular components:
Decomposing cellular component: 1 of 2
1 monomial to consider for this cellular component 
done
Decomposing cellular component: 2 of 2
1 monomial to consider for this cellular component 
done
Removing redundant components...
2 Ideals to check
1 Ideals to check
0 redundant ideals removed. Computing mingens of result.
              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

Note that if the coefficient field needs to be extended, strange things can happen

See also

Ways to use binomialPrimaryDecomposition :