Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?

Question

I am playing around with Simplify amd assumptions. I noticed that: Simplify[x > (a + b)/e, x < (a + b)/e] False But if I add more variables to the numerator, Simplify is not able to get False Simplify[x > (a + b + c)/e, x < (a + b + c)/e] x > (a + b + c)/e Why is there such a difference and how can I avoid the latter situation?

kglr · Answer

You can set a higher value for the system sub-option "AssumptionsMaxNonlinearVariables" than its default value 4:

"AssumptionsMaxNonlinearVariables" /. 
    "SimplificationOptions" /. 
       SystemOptions["SimplificationOptions"]

Simplify[x > (a + b + c)/e, x < (a + b + c)/e]

 x > (a + b + c)/e

Simplify[x > (a + b + c + z)/e, x < (a + b + c + z)/e]

 x > (a + b + c + z)/e

ClearSystemCache[]
SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 7}];

Simplify[x > (a + b + c)/e, x < (a + b + c)/e]

False

Simplify[x > (a + b + c + z)/e, x < (a + b + c + z)/e]

False

Answered by kglr on October 2, 2021

Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?

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