randomDeterminantalIdeal -- produces a random determinantal ideal

Synopsis

Usage:

I = randomDeterminantalIdeal(R,M)
Inputs:
- R, a ring
- M, a matrix, of integers
Outputs:
- I, an ideal, in the ring R

Description

Given a ring and a degree matrix, we produce a random determinantal ideal with forms in prescribed degree. Forms of non-positive degrees are taken as 0 to ensure minimality of presentation.

i1 : randomDeterminantalIdeal(ZZ/101[x,y,z],matrix{{1,1},{1,1},{1,1}})

                 2              2                      2    2              2
o1 = ideal (- 10x  - 50x*y - 21y  + 42x*z + 13y*z - 37z , 8x  + 15x*y - 11y 
     ------------------------------------------------------------------------
                         2       2              2                     2
     - 38x*z - 20y*z + 2z , - 36x  + 21x*y - 36y  - 8x*z + 25y*z - 24z )

               ZZ
o1 : Ideal of ---[x..z]
              101

Ways to use randomDeterminantalIdeal :

randomDeterminantalIdeal(Ring,Matrix)

For the programmer

The object randomDeterminantalIdeal is a method function.