Grassmannian -- find the ideal of a Grassmannian

Grassmannian -- find the ideal of a Grassmannian

Grassmannian(k,r) -- Grassmannian of k-planes in P^r
Grassmanian(k,r,R)

Given natural numbers k <= r, and optionally a ring R with at least binomial(r+1,k+1) variables, the routine finds the ideal of the Grassmannian of projective k-planes in P^r, using the first binomial(r+1,k+1) variables of R. If R is not given, the routine makes and uses ZZ/31991[vars(0..binomial(r+1,k+1)-1].

For example, the Grassmannian of projective lines in P^3:

i1 : J = Grassmannian(1,3)



o1 = ideal(c*d - b*e + a*f)



                ZZ

o1 : Ideal of ----- [a, b, c, d, e, f]

              31991

i2 : R = QQ[a..f];

i3 : J = Grassmannian(1,3,R)



o3 = ideal(c*d - b*e + a*f)



o3 : Ideal of R

Caveat:

Currently, this ideal is constructed using relations on minors of a generic matrix. It should really use the Pluecker equations.

Ways to use Grassmannian :

Grassmannian(ZZ,ZZ)

Grassmannian(ZZ,ZZ,Ring)