@acer 

I have just seen the the print extension. This is close to what I was looking for when I initially tried convert. I really think that this should be considered as a permanent extension to convert and the context panel. Really good!!!

@dharr 
Looks like. Unfortuneatly that is not what we find in text books.

And: Why a two argument function?

2*polar(1,Pi)-polar(2,Pi);
simplify(%)
                 2 polar(1, Pi) - polar(2, Pi)

                               0

Euler would turn over in his grave if he saw how wasteful we are with screen space.

But maybe an different looking inert e could be a solution.

e^(Pi*I)
                             Pi I
                            e      

alias(e=%exp): #that is not working
e(I*Pi);       # but should describe the idea I have in mind
simplify(%)

                            e(Pi I)
                            -1

@acer
I see. Automatic simplification...

I am surprised that there is nothing provided for students.
The exponential form is so important when it comes to multiplication and division of complex numbers by hand.

It would be nice to demonstrate stepwise calcualtions/simplifications with Maple.

Brilliant ideas are needed.

Thanks

@vv 

IMO it should because it converts without ICs to the expected from.

odetest((lhs-rhs)(mysol),ode);

If this was intentionally implemented it should also work with ICs.

I would report it as a product improvement.

The reduction in size is impressive.
 👍

When plotting, some smart_int results differ from Maples default output. Which one to chose?
The choice is probably less imporant in the context of ODEs since integration constants must be determined anyway

x*arctan(x)^2*ln(x^2+1);
simplify(int(%,x)-smart_int(%,x)):
plot(%,x=-Pi..Pi);

x/(-x^2+5)/(-x^2+3)^(1/2);
simplify(int(%,x)-smart_int(%,x));
plot(%,x=0..Pi);

@Carl Love 

Elegant but not fully clear to me. Can you explain the yellow part and its purpose?

I understand

type([[-2.71396014591046, 0], [-2.66663223217829, 0], [-2.66663223217829, 0.0132214378482131], [-2.71396014591046, 0.0132214378482131]],4 &under nops)

Here is what I do not

[[-2.71396014591046, 0], [-2.66663223217829, 0], [-2.66663223217829, 0.0132214378482131], [-2.71396014591046, 0.0132214378482131]] &under nops;
eval(%);# tried also value...

How should I read the code?

an expression of "type listlist(numeric) having 4 operands"

or

an expression of type listlist(numeric) and of type 4 under application of nops

I analysed:

Statistics:-TallyInto(
        A, 
        map(
            b-> b[1,1]..b[2,1],
            [indets(op(1,Q), And(listlist(numeric), 4 &under nops))[]]))

@aroche 

Thank you for the fix and the explanations. Very helpful.

@Ronan 

Yes, I wanted to give a nicer alternative for the second code line but forgot to mention that intersect has to be used

indets(eqn) minus indets(eqn,name);
% intersect indets(eqn, `^`);
rpl:=[A,B,C,`&D;`,E,F]:
Subs2:=[seq(subexpr[i]=rpl[i], i=1..nops(subexpr))]:
simplify(subs(Subs2,eqn));

@Ronan 

In my example I showed a complicated way to filter for roots and powers because I could not find this straight away:

indets(a+sqrt(b), `^`)

Looks to me that the solution Maple finds is not compatible with the IC

infolevel[dsolve]:=5;
dsolve(ode);
subs(x=0,ic,%);
%/(-2);
tan(lhs(%))=tan(rhs(%))

I remember a similar case we discussed but cannot find it right away.

@acer 

Thank you very much for the answers. Very satisfying!

@acer 

Does this mean that when I see "enter unknown" Maple refers exclusively to an anonymous procedure? In the below Maple seems to assign a "procedure without name" to the name "unknown".Is this intentional or an unfortunate coincidence?

@Carl Love 

Probably the way to go. If I understand correctly, there are command specific extenstion rules.  

?simplify,details is silent about any details in which order options are processed.

Without knowing them I cannot expect 

simplify(expr,Maple_proc1,My_proc,Maple_proc2)

to process from left to right.

Thanks for the one-liner. Always a pleasure to see those.

@Carl Love 

I do not get a plot from the above code

@acer I used 2024. With 2023 I have to paste to 1D to make it work