initial

FiniteGroup.py

@@ -0,0 +1,64 @@
+from group import Group
+
+"""
+from group import Set
+from group import Function
+"""
+
+class FiniteGroup(Group):
+	def __init__(self, group, function):
+		self.set = group
+		self.function = function
+		_check_if_group(group, function)
+		self.identity = self._find_identity()
+
+	def cayley_table(self):
+		cayley = [self.function(a, b) for a in self.set for b in self.set]
+		return cayley
+
+	def print_cayley_table(self):
+		"""
+		Need a better way to print this shit !!
+		"""
+		print self.cayley_table()
+
+	@property
+	def isFinite(self):
+		return True
+
+	@property
+	def identity(self):
+		return self.identity
+
+	@property
+	def isAbelian(self):
+		if all(self.function(a, b) == self.function(b, a) for a in self.set for b in self.set):
+			return True
+		return False
+
+	def _find_identity(self):
+		for element in self.set:
+			if all(element*x == x for x in self.set):
+				return element
+		raise TypeError('The given set has no identity element on the function')
+
+	@property
+	def order(self):
+		return len(self.set)
+
+
+def _check_if_group(group, function):
+	if not _check_closure(group, function):
+		raise TypeError('The set is not closed under the given function')
+	if not  _check_associativity(group, function):
+		raise TypeError('The function is not associative on the group')
+
+def _check_closure(group, function):
+	if not all(function(a, b)%len(group) in group for a in group for b in group):
+		return False
+	return True
+
+def _check_associativity(group, function):
+	if not all(function(a, function(b, c)) == function(function(a, b), c) for a in group for b in group for c in group):
+		return False
+	return True

FiniteGroup.py~

@@ -0,0 +1,64 @@
+from group import Group
+
+"""
+from group import Set
+from group import Function
+"""
+
+class FiniteGroup(Group):
+	def __init__(self, group, function):
+		self.set = group
+		self.function = function
+		_check_if_group(group, function)
+		self.identity = self._find_identity()
+
+	def cayley_table(self):
+		cayley = [self.function(a, b) for a in self.set for b in self.set]
+		return cayley
+
+	def print_cayley_table(self):
+		"""
+		Need a better way to print this shit !!
+		"""
+		print self.cayley_table()
+
+	@property
+	def isFinite(self):
+		return True
+
+	@property
+	def identity(self):
+		return self.identity
+
+	@property
+	def isAbelian(self):
+		if all(self.function(a, b) == self.function(b, a) for a in self.set for b in self.set):
+			return True
+		return False
+
+	def _find_identity(self):
+		for element in self.set:
+			if all(element*x == x for x in self.set):
+				return element
+		raise TypeError('The given set has no identity element on the function')
+
+	@property
+	def order(self):
+		return len(self.set)
+
+
+def _check_if_group(group, function):
+	if not _check_closure(group, function):
+		raise TypeError('The set is not closed under the given function')
+	if not  _check_associativity(group, function):
+		raise TypeError('The function is not associative on the group')
+
+def _check_closure(group, function):
+	if not all(function(a, b)%len(group) in group for a in group for b in group):
+		return False
+	return True
+
+def _check_associativity(group, function):
+	if not all(function(a, function(b, c)) == function(function(a, b), c) for a in group for b in group for c in group):
+		return False
+	return True

group.py

@@ -0,0 +1,39 @@
+import types
+
+def check_if_group(group, function):
+	if not len(group):
+		return False, "the set is empty"
+	if not _check_associvity(group, function):
+		return False, "the function is not associative on the group elements"
+	if not _check_closure(group, function):
+		return False, "the function is not closed"
+
+class Group():
+	def __init__(self, group, function=None):
+		self.is_multiplicative = False
+		if function is None:
+			self.is_multiplicative = True
+			pass
+		elif not isinstance(function, types.FunctionType):
+			raise TypeError('should supply a function')
+		self.group = group
+		self.function = function
+
+	def cayley_table(self):
+		raise NotImplementedError
+
+	@property
+	def isFinite(self):
+		return True
+
+	@property
+	def isAbelian(self):
+		raise NotImplementedError
+
+	@property
+	def order(self):
+		raise NotImplementedError
+
+	@property
+	def is_Multiplicative(self):
+		return self.is_multiplicative

group.py~

@@ -0,0 +1,39 @@
+import types
+
+def check_if_group(group, function):
+	if not len(group):
+		return False, "the set is empty"
+	if not _check_associvity(group, function):
+		return False, "the function is not associative on the group elements"
+	if not _check_closure(group, function):
+		return False, "the function is not closed"
+
+class Group():
+	def __init__(self, group, function=None):
+		self.is_multiplicative = False
+		if function is None:
+			self.is_multiplicative = True
+			pass
+		elif not isinstance(function, types.FunctionType):
+			raise TypeError('should supply a function')
+		self.group = group
+		self.function = function
+
+	def cayley_table(self):
+		raise NotImplementedError
+
+	@property
+	def isFinite(self):
+		return True
+
+	@property
+	def isAbelian(self):
+		raise NotImplementedError
+
+	@property
+	def order(self):
+		raise NotImplementedError
+
+	@property
+	def is_Multiplicative(self):
+		return self.is_multiplicative

setup.py

@@ -0,0 +1 @@
+from distutils.core import setup

setup.py~

@@ -0,0 +1 @@
+from distutils.core import setup

test.py

@@ -0,0 +1,4 @@
+import types
+func = lambda x, y : x*y
+print func(3, 4)
+print isinstance(func, types.FunctionType)

test.py~

@@ -0,0 +1,4 @@
+import types
+func = lambda x, y : x*y
+print func(3, 4)
+print isinstance(func, types.FunctionType)

test_groups.py

@@ -0,0 +1,5 @@
+from group import Group as G
+from FiniteGroup import FiniteGroup as FG
+
+x =  FG([0, 1, 2, 3], lambda x, y: x-y)
+print x.isAbelian

test_groups.py~

@@ -0,0 +1,5 @@
+from group import Group as G
+from FiniteGroup import FiniteGroup as FG
+
+x =  FG([0, 1, 2, 3], lambda x, y: x-y)
+print x.isAbelian