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Good morning, I'm new in the world of Mathematica, so I'm sorry if my question isn't very relevant. I'm trying to solve a system of 5 equations withs many parameters. To be clear, I will hit the core of my problem. Here is my code :

$Assumptions = q > 1;
C1[a_, q] := -(7/5) + (7 a)/5 + 2 q; //** here a is a real number and q is a real number strictly grater than 1
Reduce[C11[a, q] <= 0, a]

The answer that I got is "q ∈ $\mathbb{R}$ && a <= 1/7 (7 - 10 q). This means that my code didn't take the assumption on q. Please could you propose a method to solve this issue ?

Of course my system contains a lot of parameters with different constraints to be injected (bit I avoid it here) Thank you for helping

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  • $\begingroup$ @cvgmt I want to reduce the expression with respect to a. When I wrote what you proposed, I get " q>1 is not a valid variable" $\endgroup$
    – A H
    Jul 19, 2022 at 13:25
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    $\begingroup$ You need to specify the condition inside Reduce like: Reduce[{C1[a, q] <= 0, q > 1}, a] $\endgroup$
    – Daniel Huber
    Jul 19, 2022 at 13:31
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    $\begingroup$ Clear[C1, a, q]; C1[a_, q_] = -(7/5) + (7 a)/5 + 2 q; Reduce[{C1[a, q] <= 0, q > 1}, a] $\endgroup$
    – cvgmt
    Jul 19, 2022 at 13:38
  • $\begingroup$ @DanielHuber @@cvgmt Thank you for your answers. With your help, I got q >1 && a <= 1/7 (7 - 10 q) $\endgroup$
    – A H
    Jul 19, 2022 at 13:44
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    $\begingroup$ Note that FreeQ[Options[Reduce], Assumptions] gives True, so of course Reduce[] is not going to be affected by setting $Assumptions. $\endgroup$
    – J. M.'s persistent exhaustion ♦
    Jul 19, 2022 at 14:51

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