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authordhuth <derickhuth@gmail.com>2014-11-21 13:35:20 -0700
committerdhuth <derickhuth@gmail.com>2014-11-21 13:35:20 -0700
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Merge branch 'master' into doe
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+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R3 := {[x] -> [y] : (y = x) | (y = 3x)};
+#
+#
+# Rf := {[x] -> [y] : x <= y <= 3x};
+#
+#
+# R3;
+
+{[x] -> [x] } union
+ {[x] -> [3x] }
+
+#
+#
+# Rf;
+
+{[x] -> [y] : x <= y <= 3x}
+
+#
+#
+# s12 := {[x] : 1 <= x <= 2};
+#
+# s12;
+
+{[x]: 1 <= x <= 2}
+
+#
+#
+# sd3 := R3(s12);
+#
+# sd3;
+
+{[y]: 1 <= y <= 2} union
+ {[y]: Exists ( alpha : y = 3alpha && 3 <= y <= 6)}
+
+#
+#
+# sc3 := Rf(s12);
+#
+# sc3;
+
+{[y]: 1 <= y <= 6}
+
+#
+#
+# sc3 intersection sd3;
+
+{[y]: 1 <= y <= 2} union
+ {[y]: Exists ( alpha : y = 3alpha && 3 <= y <= 6)}
+
+#
+#
+# # I think this is faulty
+# sc3 - sd3;
+
+{[y]: 4 <= y <= 5}
+
+#
+#
+# # This is OK
+# sd3 - sc3;
+
+{[y] : FALSE }
+
+#
+#
+# complement sc3;
+
+{[y]: y <= 0} union
+ {[y]: 7 <= y}
+
+#
+# complement sd3;
+
+{[y]: y <= 0} union
+ {[y]: 7 <= y} union
+ {[y]: 4 <= y <= 5}
+
+#
+#
+# sc3;
+
+{[y]: 1 <= y <= 6}
+
+#
+#
+# sc3 intersection (complement sd3);
+
+{[y]: 4 <= y <= 5}
+
+#
+#
+# # alternative description of sd3;
+# sd3' := {[y] : 1 <= y <= 3 | y = 6};
+#
+# sd3';
+
+{[y]: 1 <= y <= 3} union
+ {[6]}
+
+#
+# sc3 - sd3';
+
+{[y]: 4 <= y <= 5}
+
+#
+#
+# # sd3 wrt sd3';
+#
+# sd3 - sd3';
+
+{[y] : FALSE }
+
+#
+#
+# sd3' - sd3;
+
+{[y] : FALSE }
+
+#