I am trying to optimize expressions symbolically. I need to find out the maximum value possible for an variable, so that the expressoin still have a valid solution.
expr:=a-b/b-a^3; # a=(0,10), b=(0,10)
In this eypression b=a^3 is the only case where undefined solution is possible, for a given interval of variables
This looks fine for simple expression. But in reality there are complex equations to solve with more than 2 varibles.
1) first thing is to find out all values of a variable resulting in undeifined output(or infinite)
2) assign a symbolic value(variable < or > some value) to the variable so that the undefined result can be eliminated.
I need to optimize the given expression so that it does not have any undefined cases when solving. I understood that when optimizing, there always be a condition on variables(in this case variable max is the condition, maximum value the variable can take). output of an expression is always a real value
OptimizedExpr:=a-b[max]/b[max]-a^3 --> b[max]>a^3 or b[max]<a^3
(it is easy to to say b[max] is not equal to a^3 , also a^3 is the limiting value. In some case it is more resonable to just ignore other part of limiting value. Hence, I would like to optimize using greaterthan or lessthan of limiting value).
I would be very glad to know how I can find Optimized expressions. I tried using the solve function but observed that expressions are equalled to zero and solving. which is completely opposite to what I was looking. I really do not know is there any way to find out undefined cases in expressions and on what varibale at what values.
I tried to explain the situation at my best and I welcome for any suggested edits or furthur information required.