def classical_groups(m): """Returns list of classical groups, such that \pi(G) is contained in the set of first m primes. """ ret = [] primes = first_primes(m) set_primes = set(primes) for p in primes: for n in range(1, m + 2): t = _min_power(p, n, primes) for alpha in range(1, t + 1): field = Field(p, alpha) to_check = [] if n >= 2 and (n, field.order) not in [(2, 2), (2, 3)]: to_check.append(ClassicalGroup("PSL", n, field)) if (n, field.order) != (1, 2): if n > 1: to_check.append(ClassicalGroup("PSU", 2 * n, field)) to_check.append(ClassicalGroup("PSU", 2 * n + 1, field)) if n >= 2 and field.char % 2 == 1: to_check.append(ClassicalGroup("Omega", 2 * n + 1, field)) if n >= 3: to_check.append( ClassicalGroup("POmega+", 2 * (n + 1), field)) to_check.append( ClassicalGroup("POmega-", 2 * (n + 1), field)) if n >= 2: to_check.append(ClassicalGroup("PSp", 2 * n, field)) valid = lambda group: _prime_factors(group.order() ) <= set_primes ret.extend(filter(valid, to_check)) ret.sort( key=lambda group: (max(group.order().factors.keys()), group.order())) return ret
def print_max_elems(): for dimension in xrange(4, 36): group = ClassicalGroup("Omega+", 2 * dimension, 4) dim_expansion = " + ".join( [str(x) for x in numeric.binary_expansion(dimension)]) print "{}:".format(group).ljust(12), print "n = {} = {}".format(dimension, dim_expansion).ljust(30) print for elem in max_orders_wrapped(group, StringViewFormatter.VERBOSE): print str(elem).ljust(len(str(elem)) + 5).rjust(60), sorted( elem.object.partition, reverse=True) print
def selected_group(self): """Returns currently selected group """ if self._group_type.get() == "Alternating": self._alt_degree.refresh_input() return AlternatingGroup(self._alt_degree.get_number()) if self._group_type.get() == "Classical": self._clas_dim.refresh_input() self._clas_field.refresh_input() return ClassicalGroup(self._clas_type.variable.get(), self._clas_dim.get_number(), self._clas_field.get_number()) if self._group_type.get() == "Sporadic": return SporadicGroup(self._sporadic_group.variable.get()) if self._group_type.get() == "Exceptional": self._ex_field.refresh_input() return ExceptionalGroup(self._ex_type.variable.get(), self._ex_field.get_number())
def test_symplectic(self, n): group = ClassicalGroup("Sp", 2 * n, 2) max_elems = max_orders.maximal_orders(group) max_elems_2 = maximal_orders(group, 2) self.assertEqual(max_elems[0], max_elems_2[0]) self.assertEqual(max_elems[1], max_elems_2[1])
def test_classical_orders(self, params): g = ClassicalGroup(*params) order = orders_data.classical_orders_data[params] self.assertEqual(order, g.order())
def test_classical_field(self): for g in (ClassicalGroup("PSp", 4, Field(2, 3)), ClassicalGroup("PSp", 4, 2, 3), ClassicalGroup("PSp", 4, 8)): self.assertEqual(2, g.field.char) self.assertEqual(3, g.field.pow)
def test_classical_str(self): g = ClassicalGroup("PSp", 4, Field(2, 3)) self.assertEqual("PSp(4, 8)", str(g))
def test_classical_spectra(self, params): g = ClassicalGroup(*params) apex = spectra_data.classical[params] self.assertSetEqual(set(apex), set(g.apex()))
def test_apex_nums_are_integers(self, params): g = ClassicalGroup(*params) self.assertTrue(all(isinstance(i, int) for i in g.apex()), g.apex())