V6.sage

load("__common__.sage")

def generator():
    #Pick n vectors in Rn
    n=choice([3,4,5])
    vec=[]
    for i in range(0,n):
        v=[]
        for _ in range(0,n):
            v.append(randrange(-5,5))
        vec.append(vector(v))

    #Pick if yes a basis combination or not
    basis = choice([false,true])

    #If dependent, Generate the 3, 4, 5th vector sometimes 
    if basis==0:
        if choice([false,true]):
            vec[2] = randrange(-3,3)*vec[0]+randrange(-3,3)*vec[1]
        if n>3 and choice([false,true]):
            vec[3] = randrange(-3,3)*vec[0]+randrange(-3,3)*vec[1]+randrange(-3,3)*vec[2]
        if n>4 and choice([false,true]):
            vec[4] = randrange(-3,3)*vec[0]+randrange(-3,3)*vec[1]+randrange(-3,3)*vec[3]

    A=matrix(vec).transpose()
    if rank(A)<n:
        basis=false
    else:
        basis=true


    return {
      "basis": basis,
      "vecset": vectorSet(vec),
      "dim": str(n),
      "prompt": choice([true,false]),
      "matrix": A,
      "rref": A.rref(),
    }