Add test of injectivity lemma in the paper.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>

injectivitylemma.py

@@ -0,0 +1,22 @@
+#!/usr/bin/python
+
+from itertools import product
+
+def gamma_delta():
+    yield (-1,  0)
+    yield ( 1,  0)
+    yield ( 0, -1)
+    yield ( 0,  1)
+
+def sums_mod4(gd):
+    return (sum([gd[j][0] * (2**j) for j in range(k)]) % 4, sum([gd[j][1] * (2**j) for j in range(k)]) % 4)
+
+for k in (1, 2):
+    M_k = [list(s) for s in product(gamma_delta(), repeat=k)]
+    assert(len(M_k) == 4**k)
+
+    for (gd, gd_dash) in product(M_k, repeat=2):
+        if gd[0] != gd_dash[0]:
+            assert(sums_mod4(gd) != sums_mod4(gd_dash))
+
+print("QED")