I found it finally. No crash any more with the attached. Maple 2023 requires right single quotes.

The GUI crash is another matter. Should not happen with incorrect input (IMO).

plot3d_in_2023_not_working_solved.mw

On a different PC:

No freeze before installing the lastest Physics package. Conversion to 1d works.

Preview in context pannel indicates ndash

After installation: Expected preview but freeze when doing right clikc convert to 1d input

@Christopher2222 

I was wondering if the type of graphic card could be retrieved as well. Is that possible?

@vv 

That is a nice debugging trick. (Copy paste in a startup code region works as well.) I will use it to track down at which point my original worksheet changed or changes.

What I know so far is that the ndash originates from Maple output (i.e. I never entered it). It might be related to the use of equation labels and it only manifest in Maple 2023. It can be that Maple 2023 generates a ndash when executing a document. I will send an update if I find something.

It's the first time I could not debug with lprint or convert to 1d (and the Maple GUI crashes). Thank you for your help!

All outputs removed and Maple GUI frozen.

(I am experiencing upload and editing problems. So I have to reply to myself to update the post)

1. Open the attachment above in 2023.

2. do

3. Try to execute the whole document

@sursumCorda 

I am mouth open for two reasons:

• First, I stopped my “elliptic investigations” at the point where I felt the need to transform moduli but could not find any reliable reference. I overlooked the connection formulas…
• Second, I did not know that eval can be used this way.

What is missing in your Maple trick is a formula connecting E(z,k) with I*E(z,k). I checked Maple’s function advisor for it. Perhaps it is not general enough to be listed there but it can probably be found in DLMF (If ones know where to look…).

You use two times 1/… in f which is not required. I would remove it.

Consider making your reply an answer to nm. It is at least a complex trick using assumptions and formulas not(?) available in Maple. It is the best way I have seen so far how to simplify with Maple such complex output.
 

Excellent!

PS.: The assumptions in your simplification match my complex3D plot above

Same for me. I try to upload an image

@nm 
I do not know MMA. Can I assume that FullSimplify is fully implemented in the complex domain?

Maple cannot simplify the intermediate result (simplify,symbolic can)

sqrt(sin(x))*csgn(sin(Pi/4 + x/2))

without the assumption

(0 <= x, x <= Pi/2)

Can FullSimplify do this? If it can and if this simplification is possible without assumptions, it would be desirable that Maple can do it as well.

Interesting to note that the derivation performed with Maple returns the substitution you mentionned but with a complex sign term.

sqrt(1 - 2*cos(Pi/4 + x/2)^2)*csgn(sin(Pi/4 + x/2))

Something does not fit together. Either the substitution cannot be applied in the complex domain (and hence the short result does not apply for the complex domain) or Maple could be improved when dealing with expressions without assumptions.

It looks like that MMA does more than Maple. To your original question about Maple tricks to shorten it would be interesting to see whether MMA can simplify Maples complex result. My guess would be no because of nonexisting(?) theorems and identities (see my reply to @sursumCorda).

Update:

Plotting the difference between Maple's differentiation and the original integrand in the complex plane reveals the domain where the expression are equal. Beyond that, the magnitude of the expressions is the same but the argument is different

plots:-complexplot3d(sqrt(sin(z))*csgn(sin(Pi/4 + z/2)) - sqrt(sin(z)), z = -2*Pi - (2*Pi)*I .. 2*Pi + 2*I*Pi, orientation = [35, 25, 0], title = sqrt(sin(z))*csgn(sin(Pi/4 + z/2)) - sqrt(sin(z)))

Taking the derivative of Maples output results in the integrand of the original integral

int(sqrt(sin(x)), x);
simplify(diff(%, x));
           1          /            (1/2)                (1/2) 
 - ------------------ |(sin(x) + 1)      (-2 sin(x) + 2)      
                (1/2) \                                       
   cos(x) sin(x)                                              

            (1/2) /           /            (1/2)  1  (1/2)\
   (-sin(x))      |2 EllipticE|(sin(x) + 1)     , - 2     |
                  \           \                   2       /

               /            (1/2)  1  (1/2)\\\
    - EllipticF|(sin(x) + 1)     , - 2     |||
               \                   2       ///


                                (1/2)
                          sin(x)     

Now the same with MMA output

MmaTranslator:-FromMma(`-2*EllipticE[1/2*(Pi/2-x),2]`);
simplify(diff(%,x));
combine(%,trig)assuming x>0,x<Pi/2 ;

                         /   /1      1  \         \
             -2 EllipticE|sin|- Pi - - x|, sqrt(2)|
                         \   \4      2  /         /

                              (1/2)                      
      /                     2\                           
      |         /1      1  \ |          /   /1      1  \\
      |1 - 2 cos|- Pi + - x| |      csgn|sin|- Pi + - x||
      \         \4      2  / /          \   \4      2  //

                                (1/2)
                          sin(x)     

The required restriction to a part of the real domain is an indication that the MMA response may be too short for the complex domain.

I have not found a way to use the assumptions on the original integral to shorten the output.

If this is perhaps a win in terms of correctness for Maple it would still be nice to evaluated the integral to something shorter if assumptions can be made.

@sursumCorda 

I have spend guite a while on the question why Maple is unable to simplify such expressions without finding an answer. Here is where I stopped:

Technically, to reduce such output, addition theorems or identities would be required that allow elliptic integrals of the first and second kind to be combined (with one of the them having a coefficient). I did not find any suitable theoremes or identities neither in Maple nor in DLMF (I did not look any further).

An essential technical step to simplify elliptic expressions would be to include the coefficient of an elliptic integral in the argument (i.e. transforming the elliptic integral with a coefficient into an elliptic integral without coefficient). I could not find identities that would allow for this in general. It might be possible in cases where the coeffient, the argument and the module depend on each other in a certain way.

So my guess is that there are no simple ways to simplify algorithmically and smart substitutions as here are not applied before evaluation of an integral. I assume that Mathematica provides lookup tables for such integrals and Maple does not do the same in this case.

Integration is still an art.

@AHSAN 

If I understand correctly you are interesed in solutions of the kind x=x(lambda) and not in the inverse, which is trivial

subs(h = x^2 + 1, solve(Expression = 0, [lambda])[][])

In case you are interested in x=x(lambda) the problem gets worse since we are now dealing with a polynom of 10th degree.

Taking random values for the "constants" will not change the situation. Maple will allways return a RootOf expression because it cannot provide a general solution for a polynom of 5th degree. Try for example

allvalues(subs(m = 1, Br = 0.2, N = 5, beta = 45, k = 2, lambda = 6, solve(Expression = 0, h)))

Maple returns the five indexed solutions that can only be found numerically (see ?RootOf).

If you can find a combination of values for the "constants" that make the coefficient of h^5 zero

(-210*N + (50*Br + 140)*m)*k + 210*N + (-40*Br - 70)*m = 0

you will get geenral solutions.

I think the hardware should be powerful enough.

Your observations are GUI related. Maples GUI is implemented on Java and it communicates with a Maple server that does the computations. The Java GUI uses resources from the operating system which is Linux in your case. Do you have Java installed on your machine? Perhaps Maples Java interferes  with an existing installation (this is just a guess).

If no Linux&Windows user shares his experience, I would do a comparison with Windows to see if the experience is the same.

@AHSAN 

There is no general solution for polynoms of fifth order accoridng to Abel-Ruffini Theoreme. For this reason I ttought that you wanted "somehow" identify and factor out one root and solve the remaining polynom of fourth-order. Without any assumptions on the indeterminants there is little hope that you will get a symbolic solution.

Solve sometimes can find solutions with assumptions that are not necessarily numeric. Q could be larger than m for example. Looking at the complex coefficients, I don't think that assumptions of this kind will change the situation.

Do you mean by separating a value: Factoring out a root of the ploynom?

Are all the other indeterminats {Br, N, Q, beta, k, lambda, m} real valued?

Can you give values for their ranges that could be used as assumptions for solve?