Fano(ZZ,Ideal,Ring)  Fano scheme
Synopsis

 Usage:
 Fano(k,I,GR)

Function: Fano

Inputs:

k, an integer, a positive integer less than r

I, an ideal, an ideal representing a variety in in projective rspace

GR, a ring,

Outputs:

an ideal, the ideal of a Fano scheme in the Grassmannian
Description
Given an ideal I representing a projective variety X in P^r, a positive integer k<r, and optionally a ring GR with (exactly) r+1 choose k+1 variables, representing the ambient space of the Grassmannian of kplanes in P^r, this routine returns the ideal in GR of the Fano scheme that parametrizes the kplanes lying on X. If the optional third argument is not present, the routine fabricates its own ring, and returns an ideal in it.