A2.sage

load("__common__.sage")

def generator():
    # create a mxn standard matrix
    Scolumns = randrange(2,5)
    Srows = min(randrange(5,8)-Scolumns,4)
    A = random_matrix(QQ,Srows,Scolumns,algorithm='echelonizable',rank=min(Srows,Scolumns),upper_bound=9)

    Tcolumns = randrange(2,5)
    Trows = min(randrange(5,8)-Tcolumns,4)
    B = random_matrix(QQ,Trows,Tcolumns,algorithm='echelonizable',rank=min(Trows,Tcolumns),upper_bound=9)

    # construct variables
    xs=choice([
      column_matrix(vector([var("x_"+str(i+1)) for i in range(0,Scolumns)])),
      column_matrix(vector([var("x"),var("y"),var("z"),var("zw",latex_name="w")][0:Scolumns])),
    ])

    # give vector to transform
    v = column_matrix([randrange(-8,9) for _ in range(0,Tcolumns)])


    return {
      "Srows": Srows,
      "Scols": Scolumns,
      "varmap": A*xs,
      "varvector": xs,
      "Sstandardmatrix": A,
      "Trows": Trows,
      "Tcols": Tcolumns,
      "Tstandardmatrix": B,
      "vector": v,
      "Tvector": B*v
    }