Template:Algebraic normal form/python

Walsh permutations and Sierpiński triangles

This code uses the Python library discrete helpers. from discretehelpers.walsh_perm import WalshPerm from discretehelpers.binv import Binv def anf_int_to_boolf(input_integer): from discretehelpers.boolf import Boolf input_indices = Binv(intval=input_integer).indices if input_indices == set(): return Boolf(False) result_boolf = Boolf(False) for i in input_indices: loop_indices = Binv(intval=i).indices loop_boolf = Boolf(multi_and=loop_indices) result_boolf = result_boolf ^ loop_boolf return result_boolf def create_sequence(arity): sequence = [] for i in range(2 ** 2 ** arity): boolf = anf_int_to_boolf(i) binv = Binv(boolf.truth_table(arity)) sequence.append(binv.intval) return sequence sequence_0 = create_sequence(0) # [0, 1] sequence_1 = create_sequence(1) # [0, 3, 2, 1] sequence_2 = create_sequence(2) # [0, 15, 10, 5, 12, 3, 6, 9, 8, 7, 2, 13, 4, 11, 14, 1] sequence_3 = create_sequence(3) # [0, 255, 170, 85 ... 84, 171, 254, 1] sequence_4 = create_sequence(4) # [0, 65535, 43690, 21845 ... 21844, 43691, 65534, 1] wp_0 = WalshPerm(perm=sequence_0) wp_1 = WalshPerm(perm=sequence_1) wp_2 = WalshPerm(perm=sequence_2) wp_3 = WalshPerm(perm=sequence_3) wp_4 = WalshPerm(perm=sequence_4) wp_0.matrix() # array([[1]]) wp_1.matrix() # array([[1, 0], # [1, 1]]) wp_2.matrix() # array([[1, 0, 0, 0], # [1, 1, 0, 0], # [1, 0, 1, 0], # [1, 1, 1, 1]]) wp_3.matrix() # array([[1, 0, 0, 0, 0, 0, 0, 0], # [1, 1, 0, 0, 0, 0, 0, 0], # [1, 0, 1, 0, 0, 0, 0, 0], # [1, 1, 1, 1, 0, 0, 0, 0], # [1, 0, 0, 0, 1, 0, 0, 0], # [1, 1, 0, 0, 1, 1, 0, 0], # [1, 0, 1, 0, 1, 0, 1, 0], # [1, 1, 1, 1, 1, 1, 1, 1]]) wp_4.matrix() # array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], # [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], # [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], # [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], # [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], # [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0], # [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0], # [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], # [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]])