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authorTuowen Zhao <ztuowen@gmail.com>2016-09-19 11:52:51 -0600
committerTuowen Zhao <ztuowen@gmail.com>2016-09-19 11:52:51 -0600
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remove omegacalc as subproject
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-# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
-# #
-# # Extract from omega4
-# # removed "eqnarray" commands, associated &'s, and overbrace commands
-# # added declaration of n
-# # added semicolon
-# #
-# # It would be nice not to have to do the following:
-# # removed \ in front of variable names
-# #
-#
-# $$
-# symbolic n;
-#
-# R := \{\ [ii] \rightarrow [ki] \mid
-# 1 \leq ii \leq 2n
-# \ \land \ 1 \leq ki \leq 2n
-# \land ii = ki
-# \land ii = ki\\
-# \t \land
-# \ \neg (\ \exists [ji, jj] \st
-# (1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
-# \land (ii \leq ji \land ji \leq ki) \land (2jj = ki)\ )\\
-# \t
-# \land \
-# \neg (\ \exists [ji, jj] \st
-# (1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
-# \land (ii \leq ji \land ji \leq ki) \land (2jj\!+\!1 = ki)\ )
-# \ \}
-# ;
-#
-#
-# R;
-
-{[ii] -> [ii] : n = 1 && 1 <= ii <= 2} union
- {[2n] -> [2n] : 2 <= n} union
- {[1] -> [1] : 2 <= n}
-
-#
-# $$
-# # S := \{\ [\ii] \rightarrow [\ki] \mid
-# # 1 \leq \ii \leq 2\n
-# # \ \land \ 1 \leq \ki \leq 2\n
-# # \land \ii = \ki
-# # \land \ii = \ki\\
-# # \t \land
-# # \ \neg (\ \exists [\ji, \jj] \st
-# # (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
-# # \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj = \ki)\ )\\
-# # \t
-# # \land \
-# # \neg (\ \exists [\ji, \jj] \st
-# # (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
-# # \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj\!+\!1 = \ki)\ )
-# # \ \}
-# # ;
-# #
-# # S;