Say I have
a > c && c > b
What function can eliminate c to yield:
a > b
A lot like:
Eliminate[a == c && c == b, c]
but for inequalities
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1 Answer
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This is fairly close:
Reduce[a > c && c > b, {a, b}, {c}]
(* a ∈ Reals && b < a *)
Reference for this (now undocumented) form of the third argument of Solve/Reduce:
Behavior of Reduce with variables as domain
answered Sep 20, 2016 at 23:45
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$\begingroup$ I didn't know you can pass that as domain... $\endgroup$– koznerSep 20, 2016 at 23:56
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$\begingroup$ @kozner If you read Mr.Wizard's answer to the linked question, you'll see that this form for the "domain" is interpreted as a list of variables to be eliminated. It used to be documented, but the form was dropped from the documentation a few versions ago. $\endgroup$ Sep 21, 2016 at 0:03
Resolveis the function of choice for this.In[92]:= Resolve[Exists[c, a > c && c > b], {a, b}, Reals] Out[92]= b < a$\endgroup$