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Binomials :: randomBinomialIdeal

randomBinomialIdeal -- Random Binomial Ideals

Synopsis

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
o2 = ideal (e*h*v - r, e*g*n - j, f t  - j*s, n r  - h*l , a*j q - m, k p*x 
     ------------------------------------------------------------------------
             2 2
     - n, e*i w  - a)

o2 : Ideal of R
i3 : randomBinomialIdeal (R,3,4,10,false)

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