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# binomialMinimalPrimes -- minimal primes of a binomial Ideal

- Usage:
    `binomialMinimalPrimes I`
- Inputs:
  - I, a binomial ideal
- Optional inputs:
  - Verbose => ..., default value false, generate informative output
- Outputs:
  - the list of minimal primes of I

## Description

The binomial minimal primes of a binomial ideal over QQ exist only in extension fields.

    i1 : R = QQ[x,y,z]

    o1 = R

    o1 : PolynomialRing

    i2 : I = ideal(y^3,y^2*z^2-x^3,x*y^2*z,x^3*z-x*y)

                 3   2 2    3     2    3
    o2 = ideal (y , y z  - x , x*y z, x z - x*y)

    o2 : Ideal of R

    i3 : binomialMinimalPrimes I

    o3 = {ideal (y, x)}

    o3 : List

If the option Verbose is set (default), then output about the number of components found so far will be generated.

## See also

- binomialRadical -- Radical of a binomial ideal

## Ways to use binomialMinimalPrimes:

- `binomialMinimalPrimes(Ideal)`

## For the programmer

The object binomialMinimalPrimes is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Binomials.m2:1544:0.