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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     2 2       2 2     2 
o2 = ideal (c*r  - u x, b*k  - e*v , l r  - j w , d*e x  - i, i o p - r ,
     ------------------------------------------------------------------------
          2 2         2   2
     i*o*r w  - 1, a*g h*v  - 1)

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

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

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.