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
o2 = ideal (m*o - e*v, n*u  - l w, h*n*r - m, h u  - g q, n p  - s*t, c*k r 
     ------------------------------------------------------------------------
        2     2 2
     - v , a*b n  - q)

o2 : Ideal of R

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

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

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.