Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

If I compare Maple 2024 and Maple 2022 on the exact same worksheet, Maple 2022 executes twice as fast as Maple 2024.

For my kind of work this is very serious. I have programs that can take 10 or more days to complete calcuations, therefore what Maple 2022 will calculate in 10 days, Maple 2024 takes 20 days. It has wasted a LOT of my time, whatever the reason is.

Here is the code: 
1) MM must be a high order series expansion with complex arguments so that simplification is not trivial. Use any such asymptotic expansion.
NOTE: I can supply an expansion for a developer through official Maple support, but cannot release it publicly as it is part of a future publication. It is easy enough for anyone to create a complex expansion, with difficult simplification.
2) The simplification of the expansion must at least take a couple of minutes at e.g. Order=10 for the comparison to make sense.
3) Then run the program for Maple 2022 and Maple 2024 respectively and note execution time.
4) This was run on Linux.

As you will see the Maple 2024 calculation takes twice as long as the Maple 2022 calculation. 
SEE RESULTS AT END OF PROGRAM.

testorder:=6;                             # Enter the expansion order here.
MM:=??:                                   # Enter the expansion here.
series(MM, x = 0, testorder):
convert(%, polynom):
map(simplify, %):
#collect(%, x, simplify):
simplify(%):

                        testorder := 6

RESULTS:

OPTION1 Calculation time for series MM,

Maple 2024
O(4):   Linux Wall-Clock Time: 1.000 seconds
O(6):   Linux Wall-Clock Time: 11.000 seconds
O(8):   Linux Wall-Clock Time: 153.000 seconds
O(10): Linux Wall-Clock Time: 2135.000 seconds 
O(12): Linux Wall-Clock Time:  19593.000 seconds

Maple 2022
O(4):   Linux Wall-Clock Time: 0.000 seconds
O(6):   Linux Wall-Clock Time: 9.000 seconds
O(8):   Linux Wall-Clock Time: 88.000 seconds
O(10): Linux Wall-Clock Time: 1062.000 seconds 
O(12): Linux Wall-Clock Time: 8987.000 seconds

I tried to copy a snippet of a maple command from a worksheet and paste it elsewhere in the worksheet and it was transformed into document form. I could not figure out how to fix that.It was worthless to me. For example, in the command I had "eval(f, [y=1,d=3])" and it became f| with the subscript y=1,d=3.

Also, I wrote "parametr" in a procedure and Maple rejected the command with a vague complaint. OK, my bad; garbage in garbage out, parameter not parametr, etc. BUT this is 2026! Autocorrect features have been around for years. Underlining of strange spellings are standard on word processors, phones , etc. Can't Maple catch up? 

With thanks for the advice regarding quadratic Diophantine equations and tabulation, here is a little puzzle:
For a rectangular cuboid, the length of the space diagonal is known to be 90 cm and its surface area 8800 cm². Determine its integer edge lengths.

Is Maple 2026 compatible with Mac OS27.1 ___________________________________________________________

In the attached file, I would like to create a table of values ​​(k,f(k),g(k)) for the functions f and g for, e.g., k=1..10. I would appreciate your help with this, as f and g refer to reciprocity in their expressions.

test.mw

I want to do some timing tests on a bunch of procedures in a module, some of which call others, so I do not get the true timing I want - see attached.

Download Timing.mw

How to solve this Diophantine equation?

x^2-12*x*y+6*y^2+4*x+12*y-3=0    ?

I would appreciate some advice.

I am attaching two worksheets.  The first worksheet titled testflaw shows the original state of a module. The module in the startup code area contained two exported variables which were never implemented. The module had been used in testing the code.  The second worksheet testflaw2 shows the result after deleting the exported variables. (AsTable and TestAssociativity).  Note that when the worksheet opens a typesetting error code occurs.  It appears that the typesetting routines retain knowledge of the exported variables even after a Restart command.  

testflaw.mw    

testflaw.mw

I would like to have a list of sets and parallelize the same operation performed on each list. Any suggestions on how to do this? Thanks in advance.

Asking the small model (without including a worksheet)

what does x || (a, b, c) := y =~ x ^~ (1, 2, 3)

throws this error

Is that error message reproducible on other installations? Should be. 
Warning: The same question to the large model ate up 100000 credits. I added two more questions about operator precedence:

Reminds me of playing pinball when I was young. Either it tilts or you run out of money pretty quickly ;-)

Joking asside, any suggestions to improve my prompting to make the small model produce a correct answer?

A bundle of planes is here defined as the set of all planes in Cartesian (x, y, z)-space that intersect along the same straight line. This line is commonly referred to as the axis of the bundle. Is there an efficient method in Maple to model a bundle of planes in a simple, symbolic way?
The background to my request for advice is the following problem (for those interested in the puzzle), dating back to 1965:
Let a surface be given in Euclidean space. Suppose that every planar section of the surface is a circle, provided the section contains more than one point. Prove that the surface is a sphere.

edited:

Simple deductions are sufficient to solve the puzzle. Complex calculations are not necessary.

how we can find the X1 and X2 in such system with high degree power 

aaaa.mw

A Blog Post reminded me of an old problem from my Mathcad-days:
Given a torus and two points, P and Q, on its surface, calculate and graphically represent the shortest path from P to Q.

edited:
Can Mathcad worksheets (MC14) be converted into functional worksheets for Maple?

I've reported a Maple 2026 bug, that Maple becomed unresponsive, when using a Nvidia driver later than version 610. I described in detail, what happens and I described, that I can break down this issue to the release of the Nvidia driver.

And now I get a message, that a moderator deleted my post as SPAM? Wow! Maple is considering SPAM, when a technical issue is reported? I am completely disappointed.

deleted post:

https://www.mapleprimes.com/questions/243789-Maple-Gets-Unresponsive-With-Nvidia?sp=243789

I am delighted to share that the ExaktAI Workspace now also provides a full-featured mathematical document interface for Lean, the theorem prover and proof assistant, integrated directly with computer algebra system (CAS) computation.

The Workspace, including its Lean integration, is in free beta testing and open to everybody.

Lean files (.lean) open as Lean documents, proofs are checked step by step with goals shown under each step, CAS computations can be inserted inside proofs, and a class of CAS results can be turned into Lean theorem candidates that Lean then independently checks.



The Workspace also includes a Lean tutorial, intended to make this accessible to users who are not yet familiar with Lean syntax and workflow.

CAS computations can be inserted between Lean proof steps. A class of CAS results can also be turned into Lean theorem candidates that Lean independently checks.



Edgardo S. Cheb-Terrab
ExaktAI, Canada
Research Fellow Emeritus at Maplesoft.

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