Project is now named Celeste

celeste/math/groups.py

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+'''
+This library exists to isolate all math functions
+related to groups and their representations. 
+'''
+
+from math import gcd
+
+'''
+Returns the multiplicative cyclic subgroup 
+generated by an element g modulo m.
+Returns the cyclic subgroup as a list[int],
+    the order of that subgroup, and a boolean
+    indicating whether g is infinitely repeating
+    with period == ord<g> (or otherwise if it
+    terminates with g**ord<g> == 0).
+'''
+def cyclic_subgrp(g: int, 
+                  m: int, 
+                  ignore_zero: bool = True) -> tuple[list[int], int, bool]:
+    G = []
+    order = 0
+    periodic = True
+    a = 1 # start at identity
+    for _ in range(m):
+        a = (a * g) % m
+        if a == 0:
+            if not ignore_zero:
+                G.append(a)
+                order += 1
+            periodic = False
+            break
+        # check if we've reached something periodic
+        elif a in G[:1]:
+            break        
+        G.append(a)
+        order += 1
+    return G, order, periodic