add group setup utilities

groups.py

@@ -0,0 +1,45 @@
+def cons(it, elem):
+    yield from it
+    yield elem
+
+
+def ezmults(ngens, rels):
+    mults = [[2] * ngens for _ in range(ngens)]
+
+    for (f, t), m in rels:
+        mults[f][t] = m
+        mults[t][f] = m
+
+    for i in range(ngens - 1):
+        for j in range(i + 1, ngens):
+            yield ((i, j), mults[i][j])
+
+
+def schlafli(*mults):
+    ngens = len(mults) + 1
+    return ngens, ezmults(ngens, (((i, i + 1), mult) for i, mult in enumerate(mults)))
+
+
+def torus(n):
+    return schlafli(n, 2, n)
+
+
+def cube(dim):
+    return schlafli(4, *[3] * (dim - 2))
+
+
+def icos(dim):
+    assert 2 <= dim <= 4
+
+    return schlafli(5, *[3] * (dim - 2))
+
+
+def E(n):
+    ngens, mults = schlafli(*[3] * (n - 2), 2)
+    mults = cons(mults, ((2, n - 1), 3))
+    return ngens, ezmults(ngens, mults)
+
+
+if __name__ == '__main__':
+    a, b = E(8)
+    print(list(b))