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  • $\begingroup$ In my cases, there will be no Or, so don't worry about that. $\endgroup$ Commented Dec 9, 2013 at 5:04
  • $\begingroup$ So in your solution, we still have to call Reduce 3 times, right? Since my system of expressions may include up to 100 variables, it will definitely cost the efficiency if we call Reduce 100 times... $\endgroup$ Commented Dec 9, 2013 at 5:09
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    $\begingroup$ I tried your solution with a == b + c && a >= 12 && b <= 10 && c <= 10 && b >= 1 && c >= 1, the result is not clean. I expect something like 20 >= a >= 12, 10 >= b >= 2, 10 >= c >= 2. $\endgroup$ Commented Dec 9, 2013 at 9:01
  • $\begingroup$ @Loi.Luu That's because the expressions returned by Reduce contain Or. $\endgroup$ Commented Dec 9, 2013 at 11:12
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    $\begingroup$ @Loi.Luu According to the documentation, you can specify the domain to be Integers for MinValue and MaxValue. You could also use Ceiling and Floor on them. Finally one can add && Element[a, Integers] to the inequalities. $\endgroup$ Commented Dec 10, 2013 at 2:29