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

o2 : Ideal of R

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

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

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.