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Binomials :: cellularBinomialIsPrimary

cellularBinomialIsPrimary -- test for primaryness of a binomial ideal

Synopsis

Description

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)

            2
o2 = ideal(x  - 1)

o2 : Ideal of R
i3 : cellularBinomialIsPrimary (I,ReturnPrimes=>true)
-------------------------------------------------
4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
4ti2 comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome
to redistribute it under certain conditions.
For details, see the file COPYING.
-------------------------------------------------
Using 64 bit integers.
4ti2 Total Time:  0.00 secs.
-------------------------------------------------
4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
4ti2 comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome
to redistribute it under certain conditions.
For details, see the file COPYING.
-------------------------------------------------
Using 64 bit integers.
4ti2 Total Time:  0.00 secs.
The radical is not prime, as the character is not saturated
using temporary file name /tmp/M2-18774-0/0
using temporary file name /tmp/M2-18774-0/1

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

o3 : List

See also

Ways to use cellularBinomialIsPrimary :