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 .