I need to count how many times a special function shows up in an expression.

The problem is that indets returns a set. So if the same function shows up more than one time in the original expression, with same arguments, only one of these will show up in the result. So I would not know if there were mmore than one of these.

Here is a simple example, using sin(x) here.

restart;
expr:=sin(x)+3*cos(x)*sin(x)+1/sin(2*x);
indets(expr,'specfunc(anything,sin)')

#gives
#   {sin(x), sin(2*x)}

So when I do nops() on the above, it gives 2 and not 3.

How to obtain number of times a function shows in an expression, even it if is repeated?

in a worksheet, typing

r:=(x^2 - 2*x - 1)/4;

Maple returns

But when typing

r:=(x^2 - 2*x - 1)/(4*x);

Now it does not expand terms and gives what is expected

Is there a way to make the first example remain unexpanded? Same with Mathematica:

I know this only affects the display only. But it is annoying, as I want to see the numerator and denominator on the screen as I put them there and not have them change.

I tried changing the typesetting level, but this had no effect.

I used to like Maple becuase it does not change anything unless asked to, and everything is explicit, which is better.

Now I am starting to change my mind on this aspect of Maple.

Is there an assumption or some other way I can tell Maple to avoid such errors when using odetest, as I get many of them.

I think the solution Maple gives is correct. But odetest generates these strange innternal error that it does not know the sign of a complex number.

restart;
ode:=x^2*diff(y(x), x$2) + (cos(x)-1)*diff(y(x), x) + exp(x)*y(x) = 0;
sol:=dsolve(ode,y(x),series):
odetest(sol,ode,series,point=0);

Error, (in odetest/series) need to determine the sign of I*3^(1/2)

I've seen such error many times before and it is still not fixed in release after release.

I am using Maple 2022.1 on windows 10.

Is there a problem with Maple primes?  

When I want to ask a question, the input panel is disabled and not possible to type into it. Here is screen shot.

Same when I wanted to make a reply to an answer. I can not type into the window that shows. It is like disabled.

I found I only can write here, in the post section.

What is the problem?  

Every time I convert Mathematica expressions to Maple in order to use them there, I have to spend hrs by hand adding () around places in the input Mathematica expression because Maple complains about a^b^c.

The problem is that Mathematica has no problem with this, as it always takes a^b^c as a^(b^c). Here is an example to illustrate

But in Maple

MmaTranslator:-FromMma("E^x^2")

So I have to edit the input by hand

MmaTranslator:-FromMma("E^(x^2)")

The problem is that this is how Mathematica produces the expressions, and I have no way to tell Mathematica to put an extra () around to clear this ambiguity,

So I am hoping there is a way in Maple to do it. May be using some option? I know even using Maple own expressions, it complains about this:

x^y^z

But in Mathemtica it accepts this

If there is no way to change this behavior maple, else it means I have to spend hrs again editing all the Mathematica input by hand before using MmaTranslator:-FromMma each time. There are 100's of these in each file.

I think Maple here is not behaving the same as other CAS system. In Fricas it also works as is

(1) -> x^y^z

          z
         y
   (1)  x

Same in Maxima

(%i2) x^y^z;  
                                        z
                                       y
(%o2)                                x

Same in Giac

0>> x^y^z
x^(y^z)

And in every other CAS system I tried. It is only Maple who complain about this.

Any suggestions for workaround?