Group properties checker

group.py

#!/usr/bin/env python3

from abc import ABCMeta, abstractmethod


class Biop(metaclass=ABCMeta):
  _set = None

  @property
  def set(self):
    return self._set

  @property
  def set_len(self):
    return len(self._set)

  @abstractmethod
  def __call__(self, a, b): pass


class TableBiop(Biop):
  @property
  def group_cord(self):
    return self._group_cord

  def __init__(self, table):
    self._set = range(len(table))
    assert(all(len(row) == self.set_len for row in table))
    assert(all(v >= 0 and v < self.set_len for row in table for v in row))
    self._table = table

  def __call__(self, a, b):
    return self._table[a][b]


def is_assoc(op):
  for i in op.set:
    for j in op.set:
      for k in op.set:
        if op(op(i,j),k) != op(i,op(j,k)):
          return False
  return True

def has_neutral(op):
  return all(op(i, 0) == op(0, i) == i for i in op.set)

def has_inverse(op):
  def inv_exists(i):
    for j in op.set:
      if op(i,j) == op(j,i) == 0:
        return True
    return False
  return all(inv_exists(i) for i in op.set)

def is_group_op(op):
  return is_assoc(op) and has_neutral(op) and has_inverse(op)


op = TableBiop([
    [0, 1, 2],
    [1, 2, 0],
    [2, 0, 1]
    ])

print(is_group_op(op))