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# binomialAssociatedPrimes -- Associated primes of a binomial ideal

- Usage:
    `binomialAssociatedPrimes I`
- Inputs:
  - I, a binomial ideal
- Outputs:
  - the list of associated primes of I

## Description

First a cellular decomposition is run, then the associated primes of each cellular component are determined.

    i1 : R = QQ[x,y]

    o1 = R

    o1 : PolynomialRing

    i2 : I = ideal(x^2-y,y^2-x)

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

    o2 : Ideal of R

    i3 : binomialAssociatedPrimes I
    Not yet implemented
    I will compute a primary decomposition and take radicals!
    Primary Decomposition found, taking radicals now:

    o3 = {ideal (y - 1, x - 1), ideal (y - ww , x + ww  + 1), ideal (y + ww  + 1,
                                             3        3                    3
         ------------------------------------------------------------------------
         x - ww ), ideal (y, x, x, y)}
               3

    o3 : List

## See also

- binomialMinimalPrimes -- minimal primes of a binomial Ideal
- cellularBinomialAssociatedPrimes -- Associated primes of a cellular binomial ideal

## For the programmer

The object binomialAssociatedPrimes is a function closure.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Binomials.m2:1560:0.