# Hiding trivial conditions when using Reduce

I use Reduce to find conditions on some parameters such that certain inequalities are fulfilled. An additional condition is that all parameters are positive. The first problem is that I have to mention all those conditions when calling Reduce, and the second is that they appear in the result and make it less readable.

I tried to use Assumptions, but it doesn't change the result.

I wonder if it is possible to hide these trivial conditions or at least suppress them in the output?

$Assumptions = Flatten[{Thread[{r, p, h, K} > 0], Element[{r, p, h, K}, Reals]}] Reduce[K*(r - h)/r > 0 && (p*h)/(r - h) < p && K >0 && p>0 && h>0 && r>0,h]  • MemberQ[Keys[Options[Reduce]], Assumptions] returns False, so it is inappropriate to use $Assumptions with Reduce[]. – J. M.'s technical difficulties Jan 22 at 9:23
• Dmitry, apply Simplify to the result of Reduce. – Henrik Schumacher Jan 22 at 9:24
• @HenrikSchumacher, this seems to be the most simple and efficient solution so far. Thank you! – Dmitry Jan 22 at 9:38
• You're welcome! – Henrik Schumacher Jan 22 at 9:45

conds = K > 0 && p > 0 && h > 0 && r > 0;

• Then you can use Simplify[], which does take assumptions: With[{conds = K > 0 && p > 0 && h > 0 && r > 0 && ρ > 0}, Assuming[conds, Simplify[Reduce[K*(r - h)/r > 0 && (p*h)/(r - ρ - h) < p && conds, h, Reals]]]]. – J. M.'s technical difficulties Jan 22 at 9:42