randomBinomialIdeal -- Random Binomial Ideals

Synopsis

Usage:
randomBinomialIdeal (R,n,d,w,h)
Inputs:
- I, a ring for the output
- n, number of generators of the output
- d, maximum degree of each variable
- w, number of variables in each generator
- h, should the generators be 'as homogeneous as possible'
Outputs:
- a random ideal

Description

The exponents are drawn at random from {-d,...,d}. All coefficients are set to 1.

i1 : R = QQ[a..x]

o1 = R

o1 : PolynomialRing

i2 : randomBinomialIdeal (R,6,2,4,true)

                        2 2    2      2            2        2   2       2 2 2
o2 = ideal (m*n*v - k, c p  - d v, e*f p - d, a*c*e s - 1, a h*n  - k, n o r 
     ------------------------------------------------------------------------
        2   2 2 2 2
     - e , h o r w  - 1)

o2 : Ideal of R

i3 : randomBinomialIdeal (R,3,4,10,false)

             3 3 3 3 2      4 4 4    2 3 3 3 3    4 2 2   3   3 3 2 3 3 2  
o3 = ideal (a d p r v  - c*i j k x, a e k s t  - f j r w*x , i k o q t w  -
     ------------------------------------------------------------------------
      2   2 3   4 4 3 2 3 3    3 2 2 3
     a d*p x , a c d e s w  - g h n u )

o3 : Ideal of R

This function is mostly for internal testing purposes. Don't expect anything from it.

Caveat

Minimal generators are produced. These can be less than n and of higher degree. They also need not be homogeneous.