# Commutative groupoids up to size 3 CGroupoid_count = [1, 4, 129] # total = 134 CGroupoid_index = [0, 1, 5] CGroupoid_list = [ CGroupoid(num = 0, mult = [ [0]]), CGroupoid(num = 1, mult = [ [0,0], [0,0]]), CGroupoid(num = 2, mult = [ [0,0], [0,1]]), CGroupoid(num = 3, mult = [ [0,1], [1,0]]), CGroupoid(num = 4, mult = [ [1,0], [0,0]]), CGroupoid(num = 5, mult = [ [0,0,0], [0,0,0], [0,0,0]]), CGroupoid(num = 6, mult = [ [0,0,0], [0,0,0], [0,0,1]]), CGroupoid(num = 7, mult = [ [0,0,0], [0,0,0], [0,0,2]]), CGroupoid(num = 8, mult = [ [0,0,0], [0,0,1], [0,1,0]]), CGroupoid(num = 9, mult = [ [0,0,0], [0,0,1], [0,1,1]]), CGroupoid(num = 10, mult = [ [0,0,0], [0,0,1], [0,1,2]]), CGroupoid(num = 11, mult = [ [0,0,0], [0,0,2], [0,2,1]]), CGroupoid(num = 12, mult = [ [0,0,0], [0,0,2], [0,2,2]]), CGroupoid(num = 13, mult = [ [0,0,0], [0,1,0], [0,0,1]]), CGroupoid(num = 14, mult = [ [0,0,0], [0,1,0], [0,0,2]]), CGroupoid(num = 15, mult = [ [0,0,0], [0,1,1], [0,1,1]]), CGroupoid(num = 16, mult = [ [0,0,0], [0,1,1], [0,1,2]]), CGroupoid(num = 17, mult = [ [0,0,0], [0,1,2], [0,2,1]]), CGroupoid(num = 18, mult = [ [0,0,0], [0,2,0], [0,0,1]]), CGroupoid(num = 19, mult = [ [0,0,0], [0,2,1], [0,1,1]]), CGroupoid(num = 20, mult = [ [0,0,1], [0,0,0], [1,0,0]]), CGroupoid(num = 21, mult = [ [0,0,1], [0,0,0], [1,0,1]]), CGroupoid(num = 22, mult = [ [0,0,1], [0,0,0], [1,0,2]]), CGroupoid(num = 23, mult = [ [0,0,1], [0,0,1], [1,1,0]]), CGroupoid(num = 24, mult = [ [0,0,1], [0,0,1], [1,1,1]]), CGroupoid(num = 25, mult = [ [0,0,1], [0,0,1], [1,1,2]]), CGroupoid(num = 26, mult = [ [0,0,1], [0,0,2], [1,2,0]]), CGroupoid(num = 27, mult = [ [0,0,1], [0,0,2], [1,2,1]]), CGroupoid(num = 28, mult = [ [0,0,1], [0,0,2], [1,2,2]]), CGroupoid(num = 29, mult = [ [0,0,1], [0,1,0], [1,0,0]]), CGroupoid(num = 30, mult = [ [0,0,1], [0,1,0], [1,0,1]]), CGroupoid(num = 31, mult = [ [0,0,1], [0,1,0], [1,0,2]]), CGroupoid(num = 32, mult = [ [0,0,1], [0,1,1], [1,1,0]]), CGroupoid(num = 33, mult = [ [0,0,1], [0,1,1], [1,1,1]]), CGroupoid(num = 34, mult = [ [0,0,1], [0,1,1], [1,1,2]]), CGroupoid(num = 35, mult = [ [0,0,1], [0,1,2], [1,2,0]]), CGroupoid(num = 36, mult = [ [0,0,1], [0,1,2], [1,2,1]]), CGroupoid(num = 37, mult = [ [0,0,1], [0,1,2], [1,2,2]]), CGroupoid(num = 38, mult = [ [0,0,1], [0,2,0], [1,0,0]]), CGroupoid(num = 39, mult = [ [0,0,1], [0,2,0], [1,0,1]]), CGroupoid(num = 40, mult = [ [0,0,1], [0,2,0], [1,0,2]]), CGroupoid(num = 41, mult = [ [0,0,1], [0,2,1], [1,1,0]]), CGroupoid(num = 42, mult = [ [0,0,1], [0,2,1], [1,1,1]]), CGroupoid(num = 43, mult = [ [0,0,1], [0,2,1], [1,1,2]]), CGroupoid(num = 44, mult = [ [0,0,1], [0,2,2], [1,2,0]]), CGroupoid(num = 45, mult = [ [0,0,1], [0,2,2], [1,2,1]]), CGroupoid(num = 46, mult = [ [0,0,2], [0,0,0], [2,0,0]]), CGroupoid(num = 47, mult = [ [0,0,2], [0,0,0], [2,0,1]]), CGroupoid(num = 48, mult = [ [0,0,2], [0,0,1], [2,1,0]]), CGroupoid(num = 49, mult = [ [0,0,2], [0,0,1], [2,1,1]]), CGroupoid(num = 50, mult = [ [0,0,2], [0,0,1], [2,1,2]]), CGroupoid(num = 51, mult = [ [0,0,2], [0,0,2], [2,2,0]]), CGroupoid(num = 52, mult = [ [0,0,2], [0,0,2], [2,2,1]]), CGroupoid(num = 53, mult = [ [0,0,2], [0,1,0], [2,0,0]]), CGroupoid(num = 54, mult = [ [0,0,2], [0,1,0], [2,0,1]]), CGroupoid(num = 55, mult = [ [0,0,2], [0,1,1], [2,1,0]]), CGroupoid(num = 56, mult = [ [0,0,2], [0,1,1], [2,1,2]]), CGroupoid(num = 57, mult = [ [0,0,2], [0,1,2], [2,2,0]]), CGroupoid(num = 58, mult = [ [0,0,2], [0,1,2], [2,2,1]]), CGroupoid(num = 59, mult = [ [0,0,2], [0,2,0], [2,0,0]]), CGroupoid(num = 60, mult = [ [0,0,2], [0,2,0], [2,0,1]]), CGroupoid(num = 61, mult = [ [0,0,2], [0,2,1], [2,1,0]]), CGroupoid(num = 62, mult = [ [0,0,2], [0,2,1], [2,1,1]]), CGroupoid(num = 63, mult = [ [0,0,2], [0,2,2], [2,2,0]]), CGroupoid(num = 64, mult = [ [0,0,2], [0,2,2], [2,2,1]]), CGroupoid(num = 65, mult = [ [0,1,1], [1,0,0], [1,0,0]]), CGroupoid(num = 66, mult = [ [0,1,1], [1,0,0], [1,0,1]]), CGroupoid(num = 67, mult = [ [0,1,1], [1,0,0], [1,0,2]]), CGroupoid(num = 68, mult = [ [0,1,1], [1,0,1], [1,1,0]]), CGroupoid(num = 69, mult = [ [0,1,1], [1,0,1], [1,1,1]]), CGroupoid(num = 70, mult = [ [0,1,1], [1,0,1], [1,1,2]]), CGroupoid(num = 71, mult = [ [0,1,1], [1,0,2], [1,2,0]]), CGroupoid(num = 72, mult = [ [0,1,1], [1,0,2], [1,2,1]]), CGroupoid(num = 73, mult = [ [0,1,1], [1,2,0], [1,0,0]]), CGroupoid(num = 74, mult = [ [0,1,1], [1,2,0], [1,0,1]]), CGroupoid(num = 75, mult = [ [0,1,1], [1,2,0], [1,0,2]]), CGroupoid(num = 76, mult = [ [0,1,1], [1,2,1], [1,1,0]]), CGroupoid(num = 77, mult = [ [0,1,1], [1,2,1], [1,1,1]]), CGroupoid(num = 78, mult = [ [0,1,1], [1,2,2], [1,2,0]]), CGroupoid(num = 79, mult = [ [0,1,1], [1,2,2], [1,2,1]]), CGroupoid(num = 80, mult = [ [0,1,2], [1,0,0], [2,0,0]]), CGroupoid(num = 81, mult = [ [0,1,2], [1,0,0], [2,0,1]]), CGroupoid(num = 82, mult = [ [0,1,2], [1,0,1], [2,1,0]]), CGroupoid(num = 83, mult = [ [0,1,2], [1,0,1], [2,1,1]]), CGroupoid(num = 84, mult = [ [0,1,2], [1,0,2], [2,2,1]]), CGroupoid(num = 85, mult = [ [0,1,2], [1,2,0], [2,0,1]]), CGroupoid(num = 86, mult = [ [0,1,2], [1,2,1], [2,1,1]]), CGroupoid(num = 87, mult = [ [0,2,1], [2,0,0], [1,0,0]]), CGroupoid(num = 88, mult = [ [0,2,1], [2,0,0], [1,0,1]]), CGroupoid(num = 89, mult = [ [0,2,1], [2,0,0], [1,0,2]]), CGroupoid(num = 90, mult = [ [0,2,1], [2,0,1], [1,1,0]]), CGroupoid(num = 91, mult = [ [0,2,1], [2,0,1], [1,1,1]]), CGroupoid(num = 92, mult = [ [0,2,1], [2,0,2], [1,2,1]]), CGroupoid(num = 93, mult = [ [0,2,1], [2,1,0], [1,0,2]]), CGroupoid(num = 94, mult = [ [0,2,1], [2,2,0], [1,0,1]]), CGroupoid(num = 95, mult = [ [0,2,1], [2,2,1], [1,1,1]]), CGroupoid(num = 96, mult = [ [1,0,0], [0,0,0], [0,0,0]]), CGroupoid(num = 97, mult = [ [1,0,0], [0,0,0], [0,0,1]]), CGroupoid(num = 98, mult = [ [1,0,0], [0,0,1], [0,1,0]]), CGroupoid(num = 99, mult = [ [1,0,0], [0,0,1], [0,1,1]]), CGroupoid(num = 100, mult = [ [1,0,0], [0,0,2], [0,2,0]]), CGroupoid(num = 101, mult = [ [1,0,0], [0,0,2], [0,2,1]]), CGroupoid(num = 102, mult = [ [1,0,0], [0,2,0], [0,0,0]]), CGroupoid(num = 103, mult = [ [1,0,0], [0,2,0], [0,0,1]]), CGroupoid(num = 104, mult = [ [1,0,0], [0,2,1], [0,1,0]]), CGroupoid(num = 105, mult = [ [1,0,0], [0,2,1], [0,1,1]]), CGroupoid(num = 106, mult = [ [1,0,0], [0,2,2], [0,2,0]]), CGroupoid(num = 107, mult = [ [1,0,0], [0,2,2], [0,2,1]]), CGroupoid(num = 108, mult = [ [1,0,1], [0,0,0], [1,0,0]]), CGroupoid(num = 109, mult = [ [1,0,1], [0,0,0], [1,0,1]]), CGroupoid(num = 110, mult = [ [1,0,1], [0,0,1], [1,1,0]]), CGroupoid(num = 111, mult = [ [1,0,1], [0,0,1], [1,1,1]]), CGroupoid(num = 112, mult = [ [1,0,1], [0,0,2], [1,2,0]]), CGroupoid(num = 113, mult = [ [1,0,1], [0,0,2], [1,2,1]]), CGroupoid(num = 114, mult = [ [1,0,1], [0,2,0], [1,0,0]]), CGroupoid(num = 115, mult = [ [1,0,1], [0,2,0], [1,0,1]]), CGroupoid(num = 116, mult = [ [1,0,1], [0,2,1], [1,1,0]]), CGroupoid(num = 117, mult = [ [1,0,1], [0,2,1], [1,1,1]]), CGroupoid(num = 118, mult = [ [1,0,1], [0,2,2], [1,2,0]]), CGroupoid(num = 119, mult = [ [1,0,2], [0,0,0], [2,0,1]]), CGroupoid(num = 120, mult = [ [1,0,2], [0,0,1], [2,1,0]]), CGroupoid(num = 121, mult = [ [1,0,2], [0,0,1], [2,1,1]]), CGroupoid(num = 122, mult = [ [1,0,2], [0,2,0], [2,0,1]]), CGroupoid(num = 123, mult = [ [1,0,2], [0,2,1], [2,1,0]]), CGroupoid(num = 124, mult = [ [1,1,0], [1,2,0], [0,0,0]]), CGroupoid(num = 125, mult = [ [1,1,0], [1,2,0], [0,0,1]]), CGroupoid(num = 126, mult = [ [1,1,0], [1,2,2], [0,2,0]]), CGroupoid(num = 127, mult = [ [1,1,1], [1,2,0], [1,0,0]]), CGroupoid(num = 128, mult = [ [1,1,1], [1,2,0], [1,0,1]]), CGroupoid(num = 129, mult = [ [1,1,2], [1,2,0], [2,0,1]]), CGroupoid(num = 130, mult = [ [1,2,0], [2,0,0], [0,0,1]]), CGroupoid(num = 131, mult = [ [1,2,0], [2,2,0], [0,0,1]]), CGroupoid(num = 132, mult = [ [1,2,1], [2,0,0], [1,0,0]]), CGroupoid(num = 133, mult = [ [1,2,1], [2,2,0], [1,0,0]])] # Computed with SAGE Version 2.1.4 on 2007-04-15 # This file can be used in SAGE or Python with execfile("filename")