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 (g*n - c*p, g*t  - r u, b c - h p, f*u x - a , a k  - b*o ,
     ------------------------------------------------------------------------
        2          2 2 2
     h*j m*w - 1, p r u v - 1)

o2 : Ideal of R

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

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

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.

For the programmer

The object randomBinomialIdeal is a function closure.