V9.sage

load("__common__.sage")

def generator():
    # create a 3x5,4x4,5x3 matrix
    rows = randrange(3,6)
    columns = 8-rows

    #start with nice RREF
    max_number_of_pivots = min(rows,columns-1)
    number_of_pivots = randrange(2,max_number_of_pivots+1)
    A=simple_random_matrix_of_rank(number_of_pivots,rows=rows,columns=columns)

    basis=A.right_kernel(basis='pivot').basis()
    A=A.augment(zero_vector(QQ, len(A.rows())),subdivide=true)

    return {
      "system": latex_system_from_matrix(A),
      "basis": vectorSet(basis),
      'solutions': latex_solution_set_from_matrix(A),
      "matrix": A,
      "rref": A.rref(),
    }