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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 (d*g - f*k, f*m  - l*o , b*k  - i*s, a d - e*w , a*l*v  - w, g j x
     ------------------------------------------------------------------------
        2         2
     - c , d*e*r*t  - 1)

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

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

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.