V4.sage

load("__common__.sage")

def generator():
    dim = choice([2,3,4])
    v=vector([var("x"),var("y"),var("z"),var("w")][0:dim])

    if( dim == 2):
        subspacePredicate = choice([
            (randrange(1,8)*v[0]+randrange(1,8)*v[1] == 0),
            (randrange(2,8)*v[0]==randrange(1,7)*v[1])
        ])
        notsubspacePredicate = choice([
            (v[0]^randrange(2,4)+randrange(1,8)*v[1] == 0),
            (v[0]^randrange(2,4)==randrange(1,8)*v[1]),
            (randrange(2,8)*v[0]*v[1]^randrange(2,4) == 0),
            (randrange(2,8)*v[0]==v[1]^randrange(2,4)),
        ])
    if( dim==3):
        subspacePredicate = choice([
            (randrange(1,8)*v[0] +randrange(1,8)*v[1] + randrange(2,6)*v[2]==0),
            (randrange(1,8)*v[0] +randrange(1,8)*v[1] == randrange(2,6)*v[2]),
            (randrange(1,8)*v[0] ==randrange(1,8)*v[1] + randrange(2,6)*v[2]),
            (randrange(1,8)*v[1] ==randrange(1,8)*v[0] - randrange(2,6)*v[2]),
        ])
        notsubspacePredicate = choice([ 
            (v[0]^randrange(2,4) +randrange(1,8)*v[1] + randrange(2,6)*v[2]==0),
            (v[1]^randrange(2,4) +randrange(1,8)*v[0] == randrange(2,6)*v[2]),
            (randrange(1,8)*v[0] == randrange(2,6)*v[1]+v[2]^randrange(2,4) ),
            (v[0]^randrange(2,4)*randrange(1,8)*v[1] + randrange(2,6)*v[2]==0),
            (v[1]^2-randrange(2,8)*v[2]^2 == randrange(1,7)*v[0])
        ])
    if( dim==4):
        subspacePredicate = choice([
            (randrange(1,8)*v[0] +randrange(1,8)*v[1] + randrange(2,6)*v[2]==randrange(2,7)*v[3]),
            (randrange(1,8)*v[0] +randrange(1,8)*v[3] == randrange(2,6)*v[2]),
            (randrange(2,8)*v[0]+randrange(1,7)*v[3] ==randrange(1,8)*v[1] + randrange(2,6)*v[2]),
            (randrange(1,8)*v[1]-randrange(-6,7)*v[3] ==randrange(1,8)*v[0] - randrange(2,6)*v[2]),
        ])
        notsubspacePredicate = choice([ 
            (v[0]^randrange(2,4) +randrange(1,8)*v[1] + randrange(2,6)*v[2]==randrange(2,6)*v[3]),
            (v[1]^randrange(2,4) +randrange(1,8)*v[0] == randrange(2,6)*v[2]),
            (randrange(1,8)*v[0] == randrange(2,6)*v[1]+v[2]^randrange(2,4)-randrange(2,6)*v[3] ),
            (v[0]^randrange(2,4)*randrange(1,8)*v[1] + randrange(2,6)*v[2]*v[3]==0),
            (v[1]^2-randrange(2,8)*v[2]^2 == randrange(1,7)*v[0])
        ])



    #Write sets in order subspace, not subspace
    predicates=[subspacePredicate,notsubspacePredicate]
    #Randomly swap order so 2nd is subspace
    subspace = choice(["U","W"])
    if(subspace=="W"):
        predicates.reverse()

    return {
      "U": setBuilder(column_matrix(v),[predicates[0]]),
      "W": setBuilder(column_matrix(v),[predicates[1]]),
      "subspace": subspace,
      "dim": dim
    }