M1.sage

load("__common__.sage")

def generator():
    # shuffle 2,3,4,5 to get dimensions
    dims = [2,3,4]
    shuffle(dims)

    # create matrices. only first two are multiply-able
    m = list(zip([
      random_matrix(QQ,dims[0],dims[1],algorithm='echelonizable',rank=min(dims[0],dims[1]),upper_bound=7),
      random_matrix(QQ,dims[1],dims[2],algorithm='echelonizable',rank=min(dims[1],dims[2]),upper_bound=7),
      random_matrix(QQ,dims[0],dims[2],algorithm='echelonizable',rank=min(dims[0],dims[2]),upper_bound=7),
    ],["L","R","N"]))
    shuffle(m)

    matrices, indices = zip(*m)

    letters = ["A","B","C"]

    productName = letters[indices.index("L")] + letters[indices.index("R")]
    product = matrices[indices.index("L")] * matrices[indices.index("R")]


    return {
      "A": matrices[0],
      "B": matrices[1],
      "C": matrices[2],
      "productName": productName,
      "product": product
    }