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# cellularBinomialUnmixedDecomposition -- Unmixed decomposition of a cellular binomial ideal

- Usage:
    `cellularBinomialUnmixedDecomposition I`
- Inputs:
  - I, a cellular binomial ideal
- Optional inputs:
  - CellVariables => ..., default value null, cellular variables
  - Verbose => ..., default value false, generate informative output
- Outputs:
  - an unmixed 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*(y^3-1),x^2)

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

    o2 : Ideal of R

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

    o3 = {y}

    o3 : List

    i4 : ud = cellularBinomialUnmixedDecomposition (I,CellVariables=>cv)

                    3       2
    o4 = {ideal (x*y  - x, x )}

    o4 : List

## See also

- binomialUnmixedDecomposition -- Binomial Unmixed Decomposition

## Ways to use cellularBinomialUnmixedDecomposition:

- `cellularBinomialUnmixedDecomposition(Ideal)`

## For the programmer

The object cellularBinomialUnmixedDecomposition 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.m2:1765:0.