# binomialAssociatedPrimes -- Associated primes of a binomial ideal

## Synopsis

• Usage:
binomialAssociatedPrimes I
• Inputs:
• I, a binomial ideal
• Outputs:
• l, 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! 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 BinomialSolve created a cyclotomic field of order 3 done Decomposing cellular component: 2 of 2 1 monomial to consider for this cellular component done Removing redundant components... 4 Ideals to check 3 Ideals to check 2 Ideals to check 1 Ideals to check 0 redundant ideals removed. Computing mingens of result.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 (x, y)} 3 o3 : List```