Can anybody post result of provided input to Mathematica?

Questions
,
1

Hello to everybody! Can anybody post result of this input to Mathematica?

Reduce[1/4 (-1 + 4 c E^(-(1/2) t1 v1) + E^(t2 v1)) \[Alpha] - ((-1 + 
       E^(t2 v1)) \[Psi]11)/(2 v1) >= \[Alpha] && \[Alpha] > 0 && 
  v1 > 1 && t1 > 0 && t2 > 0, c, Reals]

What i see

Solve::nsmet: This system cannot be solved with the methods available to Solve. >>

Is it a bug or i just don’t understand something?

2

Same answer, sorry.

3

Hi there, Solve has to be used for polynomial equations, Reduce for transcendental ones. Nevertheless, neither Reduce nor FindInstance succeeded with this. Possibly you should state also something about

Subsuperscript[\[Psi], 1, 1]

shouldn´t you?

4

Also if you would use code without Subscript but using a simpler notation like t1 or v1, the code would look much more readable here on Community posts.

5

I think this expression should work in Mathematica. If I use the simpler notation in the expression, I can rewrite it as

expr = 1/4 (-1 + 4  c  E^(-(1/2) t1 v1) + E^(t2 * v1)) \[Alpha] - ((-1 + E^(t2 *v1)) \[Psi]11)/(2 v1)

This is indeed a simple polynomial in terms of c:

In[93]:= PolynomialQ[expr, c]
Out[93]= True

The coefficients are
coeffL.PNG

Therefore you can either find the solution via:

Solve[expr==\[alpha],c]

Or use the coefficients in the list above (the first over the second).

6

Also, please note that you may have to sepcify the behavior of the coefficient below to solve for the inequality

coeffL2.PNG
coeffL2.PNG423×104 2.26 KB

You may want to replace it with a symbol first and then specify its domain before you reduce the given inequality because the sign of the coefficient of c matters.

7

So, it is a bug, right? (And it does not depend on whether i use Subscript[]s)
P.S. And thanks for advice to use CoefficientList! But also i should note that your usage seems to be erroneous since coefficients start with power 0. So the coefficient at c is always positive. So, it seems to be a bug.

8

Thanks for pointing out the typo, I just corrected it. It seems that Mathematica knows how to handle the equation but the inequality:

reduce.PNG
reduce.PNG518×162 3.58 KB

Probably this is a part that needs improvements.