{{ message }}

Instantly share code, notes, and snippets.

# Brandon-Rozek/symmetricgroups.py

Created Apr 21, 2019
Symmetric Elements (Group Theory)
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode characters
 import numpy as np class SymmetricElement: def __init__(self, *args): self.data = np.array(list(args), dtype=np.int64) # Confirm that there is at least one mapping assert len(self.data) > 0 # Check bijective assert len(np.unique(self.data)) == len(self) # Check that range is between 1-length assert self.data.min() == 1 assert self.data.max() == len(self) def inverse(self): inverse = np.empty(len(self), dtype=np.int64) for x, fx in zip(range(len(self)), self.data): inverse[fx.item() - 1] = x + 1 return SymmetricElement(*list(inverse)) def __len__(self): return len(self.data) def __mul__(self, g): assert len(self) == len(g) codomain = np.empty(len(self), dtype=np.int64) for x in range(len(self)): codomain[x] = self.data[g.data[x] - 1] return SymmetricElement(*list(codomain)) def __eq__(self, g): return (self.data == g.data).all() # Print the element in two row notation def __repr__(self): two_row = np.empty((2, len(self))) two_row[0] = range(1, len(self) + 1) two_row[1] = self.data return two_row.__repr__() class Cycle(SymmetricElement): def __init__(self, group_order, *args): self.cycle = np.array(list(args), dtype=np.int64) # Check to make sure the cycle is well formed (no repeats) assert len(self.cycle) <= group_order assert len(np.unique(self.cycle)) == len(self.cycle) codomain = np.array(list(range(1, group_order + 1))) for index, element in enumerate(self.cycle): next_element = self.cycle[index + 1] if index < len(self.cycle) - 1 else self.cycle[0] codomain[element - 1] = next_element super(Cycle, self).__init__(*list(codomain)) def inverse(self): return Cycle(len(self.cycle), *list(np.flip(self.cycle))) def __repr__(self): return "(" + ",".join([str(x) for x in self.cycle]) + ")"