@Muhammad Usman 

Your code is hard to debug because it is not included in a procedure. Without enclosing the code in a procedure Maple's debugger can't be used with its full functionality.

What I have found out so far:

The loop "freezes" at j=3 and i=4 when it either

tries to compute t[3] (which does not happen 
t=", table([0 = 0.6, 1 = 0.002959600326977772952816587148, 2 = 0.0183359320842630459466068924070])    )

or continues without having a numeric value for t[3].

In the second case (which I assume is the most likely) Maple tries to continue with expressions with the indexed name t[3] that does not evaluate to a value. In this case it is not a true freeze but Maple continues with something it cannot finish fast ennough that code errors are visible in the output.

Maybe this helps already. Otherwise I suggest to include the code into a procedure.  

@Carl Love

I see your point but from a user perspective it makes sense to talk about simplifying equations with a certain result in mind.

In this sense I got caught out by "natural language" again when I opted for an extension of simplify. I should have thought of convert or even better isolate in the first place.>

Unsure about my extended use of simplification I asked language models “in math: what is simplification of an equation?” and I got these answers

Simplification of an equation in mathematics refers to the process of rewriting the equation in a simpler or more concise form without changing its solutions. The goal is to make the equation easier to work with or solve … Simplification makes solving equations more manageable and often provides a clearer view of the relationships between variables. (ChatGPT, based on OpenAI's GPT-4 architecture).

… Here's a key takeaway: While simplification in expressions often involves significant transformations, simplification in equations is more about rearranging terms and isolating the variable to gain a clearer understanding of the relationship it represents. (Gemini, no version)

(An observation without drawing any conclusions: Training data sets of both models reflect somehow how people talk and write after school.)

I am getting here of topic but thank you for your feedback.

@Muhammad Usman 

It's still not working. What happens if you cklick on the link?

@acer 

I try to understand the extension mechansim and what it could be good for. In the context of simplify I thought by defining a special procedure the flow of simplification steps could be controlled this way

simplify(expr,Maple_proc,My_proc,Maple_proc)

and by doing so several code lines could be saved.  

Independend from the fact that simplification of equations is not well defined (could be anything) I would have expected from ?simplify,details that only the procedure My_proc is executed because the help page states:

 "Invokes only the simplification procedures specified by the additional names." 
As I see it now, before invoking the procedure there is some preprocessing going on. And this might be annother reason to use command extensions instead of defining an independend procedure.
 

Here is annother example with differnt output that I do not understand

expr:=1/sqrt(2);                            
`simplify/sqrt2` := x -> subs(1/2*sqrt(2) = 1 %/ sqrt(2), x):
simplify(expr, sqrt2);
`convert/sqrt2` := x -> subs(1/2*sqrt(2) = 1 %/ sqrt(2), x):
convert(expr,sqrt2);
                                1  (1/2)
                        expr := - 2     
                                2       

                            1  (1/2)
                            - 2     
                            2       

                           /    (1/2)\
                         %/\1, 2     /

Thank you for the clarification.

@Muhammad Usman 

I still get this

Make sure that your have deleted old links and upload again with 

@Muhammad Usman 

Can you repost the file. I get a page not found message when I click on it.

@mmcdara 

No problem. With your case study the OP should have enought feedback to advance.

There is one else too much or there is soemthing missing

The first if condtion will never be true since

Did you mean v[i-1]? Without the loop and more information about u[i] and v[i] its difficult to tell what else is not working.

@segfault 

This looks similar to the 2k case that I have posted. 

The only way to improve the situation is to try out different display resolutions in combination with font scaling if those things exist on Linux. Zooming in Maple changes on Windows small features sometimes in bigger steps than large features

Graphic cards often come with filters (anti- aliasing for example) that could have a positive effect as well.

It could be that there is a typesetting way to change a displayed symbol to something bigger. I have no idea how this could be applied to operators. 

@acer might know.

In 2d math Output Maple replaces the multiplication symbol with a white space. In the same way 2d math Input does not require a multiplication symbol. A white space is enough. Is that separation not pronounced enough that you prefer a dot instead?

@segfault 

Can you confrim that the canvas background is black on Maple 2002 or did something go wrong with the uplaoded image.

What operating system you are working on?

What happens when you zoom into a worksheet with the control+mouse wheel?

Consider pasting or uploading code. This would make life easier for people who want to help

To better understand the regression that you see: Can you send a screen shot?

This  is how it looks on my screen.
 

4k resolution (150% font scaling recommended by Windows)

2k resolution (100% font scaling - image enlarged for better comparision)

Maples zoom was set for both images to 100%.

@nm 

I can reproduce the above with Maple 2024, Physics 1724 and 1744 but not the original post (see update of my observation)

If I change the unkowns to a set instead of a list in the first attachement, in both cases an empty result is returned.

For the second attachement Maple does also not return an empty result immediately when a set is used. Maple tries "forever".

Update: The oberservation above was made with 2024, Physics 1724.

Attached is 1744 which is also different
why_solve_hangs_with_subscripted_may_15_2024_-_reply_c_r.mw

@ 

Since Maplesoft is not responding, I assume that you have discovered a real bug.

As Maple, MF must have a kind of a parser that translates user input to something that can be processed by a math server (called mserver in windows task manager) that does the math. The user interface then reformats the output from the server to something nice looking. Both Maple and MF use the same mserver. The MF parser must be different since MF input is different from Maple (=  versus   ;enter). It seems that the parser misinterprets the sum. The MF parser also prevents some commands and libraries from beeing used but not basic commands like sum (I would be surprised if not).

Here is my last suggestion. You can try to “smuggle” expressions unevaluated or with delayed evaluation to the  Maple server (replace ; by =)

sum('A^i', i = 0 .. 50);
 50    49    48    47    46    45    44    43    42    41    40
A   + A   + A   + A   + A   + A   + A   + A   + A   + A   + A  

      39    38    37    36    35    34    33    32    31    30
   + A   + A   + A   + A   + A   + A   + A   + A   + A   + A  

      29    28    27    26    25    24    23    22    21    20
   + A   + A   + A   + A   + A   + A   + A   + A   + A   + A  

      19    18    17    16    15    14    13    12    11    10
   + A   + A   + A   + A   + A   + A   + A   + A   + A   + A  

      9    8    7    6    5    4    3    2        
   + A  + A  + A  + A  + A  + A  + A  + A  + A + 1


eval(sum('A^i', i = 0 .. 50));
             [1.81818180244525  0.909090893354340]
             [                                   ]
             [1.51515148892390  2.42424239801481 ]


eval('sum(A^i, i = 0 .. 50)');
                  [1.818181802  0.9090908934]
                  [                         ]
                  [1.515151489  2.424242398 ]

eval(uneval(sum(A^i, i = 0 .. 50)));
                  [1.818181802  0.9090908934]
                  [                         ]
                  [1.515151489  2.424242398 ]

I hope this can serve as a work arround until this issue gets fixed.
You said that entering numeric values is not that good as with Mathcad. Did you used the Tab key to jump from one matrix entry to the next?

The strange looking commands are badly renderd HTML codes closely realated MathML which is the underlying language for math formating. Normally they are not visible

Maples help system is a better reference (if available in MF)
Hope this helps.