sometimes I get intermediate expressions generated from other operations that contain terms such as exp(x)^n in them. As an example, exp(x)^3.  In Mathematica, it automatically replaces these by exp(3*x). But in Maple I need to force this change.

For purposes of Latex only, I like to change these terms to exp(3*x) before converting the whole expression to Latex, as it is looks much better that way.

expr:=exp(x)^3;
Physics:-Latex(expr)

                \left({\rm e}^{x}\right)^{3}

expr:=exp(3*x);
Physics:-Latex(expr)

                {\rm e}^{3 x}

I found that doing simplify(expr,exp)  does the trick. It changes exp(x)^n to exp(n*x). But I am worried about applying this whole simplification command to the whole expression, which can be very large, and do not want to change it all yet.

I just want to change any occurance of exp() there, and nothing more.

I tried using subsindent to do that, but it does not work on terms in denominator

restart;
expr:=exp(x)^3*sin(x)+3/(exp(x)^n);
subsindets(expr,'exp(anything)^anything',f->simplify(f,exp))

I tried

subsindets(expr,'1/exp(anything)^anything',f->simplify(f,exp))

and it did not work.

I am still not good at subsindent. How to make it change all exp(x)^n to exp(n*x) everywhere?

What is the best way to handle this?  Many times one wants to return an expression from inside a proc, which uses local symbls, back to the user (global context).

The problem is, if one tries to simplify this returned expression, adding assumptions on some of the symbols in the expression, it does not work. Since the symbol used in the assuming is global, while the symbol inside the returned expression was local to the proc.

Even though the symbols look the same on the screen, they are actually different symbols, so the simplify does not work as expected.

Here is a simple example

restart;
foo:=proc()
local x;
  return exp(2*sqrt(1/x^2)*x*ln(x)) + exp(sqrt(1/x^2)*x*ln(x)) ;
end proc;

sol:=foo();

simplify(sol) assuming x>0

The above does not work. Since the "x" in assuming x>0 is global, while the "x" in the expression was local to the proc. So even though they look same, they are different symbols.

The standard way to handle this, is to pass the "x" to be used to build the solution, from the user to the proc(), so that when the expression is returned, the "x" used will be the global one. Like this

restart;
foo:=proc(x)
  return exp(2*sqrt(1/x^2)*x*ln(x)) + exp(sqrt(1/x^2)*x*ln(x)) ;
end proc;

sol:=foo(x);

simplify(sol) assuming x>0

Now it works:

But this method is not practical all the time. Suppose the local proc wants to generate an expression with other symbols in it, that the user does not know about. Say alpha, beta, z, eta, and so on. The user does not care about having to pass every possible symbol down on each call.  

Is there a way to tell assuming, that the symbols in assumptions command, are to be taken from the expression itself, and not to be global ones?    i.e. when doing 

simplify(sol) assuming x>0

I want Maple to take that "x" in assuming to be the "x" inside the expression only, and not a global "x".  

This will make life much simpler.  I remember seeing other use of assuming where this could be done, but I can't find it yet.

edit:

This is  just one example, where returning expression with new symbol from local proc can be required sometimes.

This is similar to using constant of integrations _C1 by dsolve when it returns a solution.

But those _C1 are all predefined as system/global symbols. But there can be cases where one needs to use new symbols. 

An example is where int() timesout or it does not produce result.

In this case, instead of leaving it as is (since I need to use the result and do not want Maple to keep evaluating it in the expression it is in), so  I replace int(integrand,x) with Int( new_integrand , alpha=0...x) where new_integrand is the same as integrand but with each x in it, is replaced by new symbol alpha

This symbol alpha has to be local to the proc (it was not passed down by user). 

Maple uses _Z sometimes for such a cases, which I do not like. (it looks bad in Latex)

Here is an example

foo:=proc(x)
local int_result,alpha;
local integrand:=1/ln(x^2+1);

int_result:= int(integrand,x);
if has(int_result,'int') then  #did not integrate
   int_result:=Int(subs(x=alpha,integrand),alpha=0..x);
fi;

  return int_result;
end proc:

int_result:=foo(x)

The expression returned contains symbol alpha, which is local to the proc.  Only way around this, is to have the user pass in alpha as well as x, just in case it is needed, which is not practical to do.

This is just one example of many. Another example is when doing some transformation internally (change of variables) to convert the ode from one form to another, and I need to return those intermediate results back to caller. These substitutions use local symbols.

As I said, I could have used _Z or some other system/global known symbol for this. But I do not like how this looks in Latex. And if I need another symbol for another case, I have to look for another one.  Instead, I just make my own local symbols and use them in the expression. (Except for constant of integrations, I use those _C1,_C2, etc....

I solved this linear constant coefficients ode by hand, and wanted to use Maple to check my solution.

dsolve works with no problem. I wanted to check the particular solution on its own, so called DEtools:-particularsol(ode,y(x)); but was surprised it hangs.

Why would DEtools:-particularsol(ode,y(x)); hang, when dsolve gives the complete solution (including particular solutin ofcourse) right away?  It is 7th order ODE. But nothing special. Linear and constant coefficients. Since dsolve solves it right away, I expected DEtools:-particularsol to have no problem as well.

restart;
ode:=diff(y(x),x$7)-2*diff(y(x),x$6)+9*diff(y(x),x$5)-16*diff(y(x),x$4)+24*diff(y(x),x$3)-32*diff(y(x),x$2)+16*diff(y(x),x)=exp(2*x)+x*sin(x)+x^2;

dsolve(ode);  #no problem.

#this hangs. Why?
DEtools:-particularsol(ode,y(x));

Download particular_sol.mw

I was saying to myself today, that one nice thing in Maple, is that it has good type system so one can check type of arguments aginst wrong types being used in the call.

So I was surprised when I called ArrayTools:-AllNonZero  using list as argument, where this function is supposed to accept only Matrix,Vector or Array. And it worked.  But it gave wrong answer at the same time.

Am I doing something wrong here? Should not have this call failed to go through?

restart;
interface(warnlevel=4);
kernelopts('assertlevel'=2):

A:=[0,0,0];
ArrayTools:-AllNonZero(A)

Maple replied 

                       true

But 

A:=Array([0,0,0]);
ArrayTools:-AllNonZero(A)

Now Maple gives the expected result  false

The question is why Maple did not detect the wrong type? Should it have detected wrong type?

And why it even gave wrong answer (but this is not as important, since the call should not be allowed in first place).

btw, this applied to all the other API's listed

I found a new strange thing with odetest that I have not seen before.

Would you say that these two solutions are the same or not?

They look the same to me.  One just have all the terms on one side, that is all.

Why would Maple odetest verify the first one but not the second? I did not know that all terms have to be on one side before. Is this documented somewhere?

Please see worksheet below.

Download odetest_issue_oct_18_2020.mw