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 basis:
        A=simple_random_matrix_of_rank(n,columns=n,rows=n)
    else:
        A=simple_random_matrix_of_rank(choice(range(2,n)),columns=n,rows=n)
        
    #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),
      "vecset": vectorSet(A.columns()),
      "dim": str(n),
      "prompt": choice([true,false]),
      "matrix": A,
      "rref": A.rref(),
    }