## Posts tagged ‘Gröbner basis’

### Operads in Haskell

Mikael Vejdemo Johansson, who was at the Operads conference in Luminy (which I also attended), wrote in only one week a Haskell module computing Gröbner bases for operads. Nice work !

### Computing Gröbner bases in Haskell

I wrote a small package to compute Gröbner bases in Haskell with the Buchberger algorithm (with applications to variable elimination). Performance is quite bad compared to specialised software like Macaulay, but it seems to work ! I put a Cabal package here. Maybe I’ll add several functions afterwards.

A testcase :

`import Data.Polynomial`

import Data.Ring

import Algebra.GroebnerBasis

import Algebra.Elimination

type R = Polynom QQ VarXYZ

[x,y,z,t,u,v] = map returnp [X,Y,Z,T,U,V] :: [R]

-- projection from a point on the intersection of quadrics

main = do

print $ step_eliminate [T] $ MakeIdeal

[x^2 - 3*y*z + z*t + 2*x*t,

z^2 + 5*y^2 + z*x - 2*t*z]

The output should be :

`[x*y^2+2/5*x^2*z+1/2*y^2*z+3/10*x*z^2+-3/5*y*z^2+1/10*z^3]`

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