next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Binomials :: binomialAssociatedPrimes

binomialAssociatedPrimes -- Associated primes of a binomial ideal

Synopsis

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

See also