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# cellularBinomialPrimaryDecomposition -- Primary decomposition of a cellular binomial ideal

- Usage:
    `cellularBinomialPrimaryDecomposition I`
- Inputs:
  - I, a cellular binomial ideal
- Optional inputs:
  - CellVariables => ..., default value null, cellular variables
  - Verbose => ..., default value false, generate informative output
- Outputs:
  - a binomial primary decomposition of I

## Description

If the cell variables are known, they can be given via the option CellVariables otherwise they are computed.

    i1 : R = QQ[x,y]

    o1 = R

    o1 : PolynomialRing

    i2 : I = ideal(x^3-1,y-x)

                 3
    o2 = ideal (x  - 1, - x + y)

    o2 : Ideal of R

    i3 : cv = isCellular (I,ReturnCellVars=>true)

    o3 = {x, y}

    o3 : List

    i4 : pd = cellularBinomialPrimaryDecomposition (I,CellVariables=>cv)

    o4 = {ideal (y - 1, x - 1), ideal (y - ww , x - ww ), ideal (y + ww  + 1, x +
                                             3        3                3
         ------------------------------------------------------------------------
         ww  + 1)}
           3

    o4 : List

    i5 : mingens \ pd

    o5 = {| y-1 x-1 |, | y-ww_3 x-ww_3 |, | y+ww_3+1 x+ww_3+1 |}

    o5 : List

## Caveat

This function will not return minimal generators for performance reasons.

## See also

- binomialAssociatedPrimes -- Associated primes of a binomial ideal

## Ways to use cellularBinomialPrimaryDecomposition:

- `cellularBinomialPrimaryDecomposition(Ideal)`

## For the programmer

The object cellularBinomialPrimaryDecomposition is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Binomials.m2:1746:0.