hi everyone,

I am trying to find maxima for a multi variable function. As a first step I want to find out partial differentiation and equate each expression to zero.
 

Normally I would expect to solve these equations to get the variable value(s). But I came across a perticular function which cannot be solved as above explained.

Expression :=30*a*sin(theta)+80*cos(theta)*b
variable :=  {a, b, theta} # using indets(Expression,name)

PartialDifferentiationExpressions :={80*cos(theta), 30*sin(theta), 30*a*cos(theta)-80*sin(theta)*b}

How can I find the critical Points from these?

My approach is to find Hessian Matrix and ten find out maxima for the function(at which critical point it happens)

Note Edit: This is an example. I am writing a script which takes an equation as Input and solve for the maxima. Hence, I would like to know how to when this kind of situation arises. Thank You

hello everyone,

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.

For Example:

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.

Thank you

For some reason algsub or applyrule is not performing what they has to do.

I dont understand exactly where the below lines are wrongly declared. Clearly the variable is not substituted

How can one the last value of variable

when I have variables Like C1;C2,C3....., F1,F2,F32,....so on

always number would be at last of the variable.

Depending upon the number in the variable I need to call values from other list. It would be really helpful to know how one can get the number present in variable?