First a summary of the general problem I'm trying to solve: I want to get a set of inequalities for a very complex function (If you are interested is the no-arbitrage conditions Black-Scholes equation with a volatility given by an SVI function)
So basically I'm trying to find the parameters that best fit a model given some conditions.
Long story short these are my problems:
1) I want only ONE set of inequalities, Reduce and Solve give me many solutions but in doing so take a little to much time. (This shouldn't be difficult)
2) Only get "general" inequalities: (this is the hard one). I have parameters and variables: I can set the parameters but the variables are independant. There, I need solutions that don't depend on the variables, but only on the parameters.
As an easy example, let's say my model is:
a*b*(1+x^2), where x is a Real variable and a and b are my variables. Note, if my condition is something like:
f(a,b,x)>2 I want this result:
Instead of this result which is what I got:
The second term depends on x^2 so it doesn't give me defined boundaries for my conditions which I can use to fit the model to the data (As I need general terms of a and b that should fit any x)
EDIT: I found of the function
ForAll which solves my simple example, but doesn't work for me on the actual problem as I have also conditions on x (Is there any similar command with no such conditions?)
Thanks in advance for your time, and sorry if this is simple, I couldn't find a solution within this site.