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authorTuowen Zhao <ztuowen@gmail.com>2016-09-17 03:22:53 +0000
committerTuowen Zhao <ztuowen@gmail.com>2016-09-17 03:22:53 +0000
commit75ff98e4d65862ff5b36b533b4f6e3ea71ede1d5 (patch)
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+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Symbolic n, f(1), f_last, f_first;
+#
+#
+# True := { [] : 1 = 1 };
+#
+#
+# old_R1 := { [x] -> [] : (1 <= x <= n and f(x) > 0)};
+#
+# old_R2 := { [x] -> [] : (1 <= x <= n and f(x) <=0)};
+#
+# True - range old_R1 - range old_R2;
+
+{ 1 <= n && UNKNOWN} union
+ { n <= 0}
+
+#
+#
+# R1 := { [x] -> [] : (3 <= x <= n-1 and f(x) > 0)
+# or (1 <= n and f_last > 0)
+# or (1 <= n and f_first > 0) };
+#
+# R2 := { [x] -> [] : (3 <= x <= n-1 and f(x) <=0)
+# or (1 <= n and f_last <=0)
+# or (1 <= n and f_first <=0) };
+#
+# True - range R1 - range R2;
+
+{ n <= 0}
+
+#
+#
+# R1a := { [x] -> [] : (1 <= x <= n and (f(x) > 0 or f_first > 0 or f_last > 0)) };
+#
+# R2a := { [x] -> [] : (1 <= x <= n and (f(x) <=0 or f_first <=0 or f_last <=0)) };
+#
+# True - range R1a - range R2a;
+
+{ f_last <= 0 && n <= 0} union
+ { n <= 0 && 1 <= f_last}
+
+#