Finish examples to 1.2.6, page 26

Author: rocky

test/test_combinatorica.py

@@ -13,14 +13,12 @@
      """
 )
 
-# A number of examples from Implementing Discrete Mathematics by
-# Steven Skiena and
-# A number of examples from Computation Discrete Mathematics by
-# Sriram Pemmaraju and Steven Skiena.
+# A number of examples from:
+#  * Implementing Discrete Mathematics by Steven Skiena and
+#  * Computation Discrete Mathematics by Sriram Pemmaraju and Steven Skiena.
 
 # Page numbers below come from the first book
 
-
 def test_combinatorica_permutations_1_1():
 
     for str_expr, str_expected, message in (
@@ -241,6 +239,38 @@ def test_combinatorica_permutations_1_2():
             "{90, 90}",
             "StirlingSecond 1.2.4, Page 24",
         ),
+        (
+            "SignaturePermutation[{1,3,2,4,5,6,7,8}]",
+            "-1",
+            "SignaturePermutation 1.2.5, Page 25",
+        ),
+        (
+            "SignaturePermutation[p] == SignaturePermutation[InversePermutation[p]]",
+            "True",
+            "A particular permutation has the same sign as its inverse 1.2.5, Page 25",
+        ),
+        (
+            "PermutationGroupQ[ Select [ Permutations[Range[4]], (SignaturePermutation[#]==1)&] ]",
+            "True",
+            "All permutations have the same sign as their inverse 1.2.5, Page 25",
+        ),
+        (
+            "Polya[Table[RotateRight[Range[8],i], {i, 8}], m]",
+            "(4 m + 2 m ^ 2 + m ^ 4 + m ^ 8) / 8",
+            "Polya counting resulting in polynomial 1.2.6, Page 25",
+        ),
+        # MapAt not finished which is probably causing Poly to fail here...
+        # (
+        #     "Polya[Automorphisms[Cycle[8]], m]",
+        #     "(4 m + 2 m ^ 2 + m ^ 4 + m ^ 8) / 8",
+        #     "Polya counting resulting in polynomial 1.2.6, Page 26",
+        # ),
+        (
+            "Factor[(4 m + 2 m^2 + 5m^4 + 4m^5 + m^8)/16]",
+            "m (1 + m) (4 - 2 m + 2 m ^ 2 + 3 m ^ 3 + m ^ 4 - m ^ 5 + m ^ 6) / 16",
+            "Factor example in Polya polynomial 1.2.6, Page 26",
+        ),
+
     ):
         check_evaluation(str_expr, str_expected, message)