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cellularBinomialIsPrimary -- test for primaryness of a binomial ideal



A binomial ideal is primary only if it is cellular. If the cellular variables are known they can be given via the CellVariables option. If the ideal is not primary, either 'false' or two distinct associated primes can be returned. The behaviour can be changed using the options ReturnPrimes and ReturnPChars.
i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
i2 : I = ideal(x^2-1)

o2 = ideal(x  - 1)

o2 : Ideal of R
i3 : cellularBinomialIsPrimary (I,ReturnPrimes=>true)
The radical is not prime, as the character is not saturated

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

o3 : List

See also

Ways to use cellularBinomialIsPrimary :

For the programmer

The object cellularBinomialIsPrimary is a method function with options.