We are a week away from the submission deadline for the Maple Conference!  
Presentation proposal applications are due July 25, 2025.

We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page.

We hope to see there.

Hi,

Don't laugh.

Some of you are not familair with Wagstaff Prime Numbers

see Wolfram Math World

also, this Maple code is esentially, a loop and the isprime() function

for your edification

b

have a look

just wanted to contribute my two cents to the Maple community

good day

Thank you for your patience and understanding during the recent outage of MaplePrimes. The outage was caused by a server issue. We have obtained and configured a replacement to prevent disruptions moving forward. We are sorry for any inconvenience this may have caused.

Back in 2017, when the concept of Maple Flow was first proposed at Maplesoft, we developed an aspirational brochure to ignite our creative energy. I still have a printed few copies – here’s one that’s sat behind my monitor.

At that time, the product that did not yet exist was called “Maple Whiteboard” and the brochure described what we had gradually come to appreciate that engineers wanted from a calculation tool:

• simplicity at its beating heart – just learn a few basic game mechanics, and then everything else “flows” (ahem). 
• units support from the get-go
• documentation features to describe the analysis
• connectivity with other software
• engineering-focused math functions

The first working version of Maple Whiteboard was crude…but the basic building blocks were in place and the concept worked. This image dates from 2019.

We unveiled Maple Flow to the public in 2021 (coming up with the name was a trial in of itself). Here’s what it looked like.

The target audience loved the new product—they liked what it could do now and were excited about its future potential. Our initial assumptions had been validated!

Maple Flow has evolved dramatically since the fever dream of the initial brochure and early prototypes. Even though it's much more powerful now, we've made sure it’s still simple to use.

Today, I’m delighted to announce the launch of Maple Flow 2025. This release is a major turning point for the product. You'll see a clean, new interface, faster performance, and more tools for documentation and moving your work from other programs.

Let me touch on my personal highlights.

A new interface headlines the release! It’s clean and simple, with logically ordered buttons in organized groups.

The ribbon is contextual; for example, click on an image, and you’ll see tools for adding shapes and text.

There's always room for improvement and refinement. Let me know what you think!.

You can now insert a table of contents into your document. The page numbers automatically update, and headings are hyperlinked – just click and you jump to that part of the worksheet.

Hyperlinks in the table of contents are preserved when you export the worksheet to PDF – that’s an awesome navigation feature when you distribute your work.

This feature gives me a visual dopamine hit every time I use it. Look how easy it is to use!

We've decided to release a tool we’ve been using internally for some time. The Maple Flow Migration Assistant is a free addon that helps you convert your Mathcad 13, 14 and 15 worksheets to Maple Flow. 

You can convert single Mathcad worksheets or point to a folder for bulk conversion. You also get many function translations.

Automatically converting executable code between two different high-level math tools is difficult; some manual reworking is probably needed for anything that’s not simple arithmetic (we documented what the Migration Assistant does here). But if you’ve already decided to make the switch from Mathcad 13, 14 or 15, then the Migration Assistant is a great time saver.

Large worksheets now evaluate faster! These are benchmarks from our internal testing suite.

You can now run Maple Flow worksheets through Excel via a simple function call. You can change parameters and get updated results.

To help you set up that function call, an interface walks you through the process.

You can use this feature to develop a simple spreadsheet reporting dashboard or perform parameter sweeps on your Flow analyses.

Large analysis projects can be difficult to manage. 

• The results of one worksheet might need to be used in another,
• there may be equations that are reused everywhere, 
• or you might need to split your project into small chunks that different people can work on separately

Well, now we’ve made that whole process easier! You can now treat Flow worksheets as “black box” functions that you can call from other Flow worksheets. You can even change parameter values, and return updated results

The AI Formula Assistant made its debut in Maple 2025 and it sparked a lot of interest (and some interesting conversations about the future of AI in math software). 

By popular demand, we've brought this feature into Flow. You can now look up an engineering formula with a simple natural language query,

That's enough of my personal highlights. If you want to know more, visit the What's New pages for a complete rundown and grab a trial.

If you haven’t tried Maple Flow yet, now is the right time to jump in. We have several time-limited launch offers to make the transition to Flow as frictionless as possible; these include offers for users who are

• deploying a small suite of licenses
• switching from other tools
• in large organizations that need a full implementation plan.

As ever, we can only keep Maple Flow on track if you let me know what you want - send all your feedback my way.

We are excited to announce that the Maple Conference will be held Novemeber 5-7, 2025!

Please join us at this free virtual event as it will be an excellent opportunity to meet other members of the Maple community, get the latest news about our products, and hear from the experts about the challenges and opportunities that our technology brings to teaching, learning, and research. More importantly, it's a chance for you to share the work you've been doing with Maple and Maple Learn. 

The Call for Participation is now open. We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. 

You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Applications are due July 25, 2025.

After the conference, all accepted presenters and invited speakers will be invited to submit related content to the Maple Transactions journal for consideration.

Registration for attending the conference will open in July.  Watch for further announcements in the coming weeks.

We hope all of you in the Maple Primes community will join us for this event!

Kaska Kowalska
Contributed Program Co-Chair

Maple 2025.1

We have just released an update to Maple. Maple 2025.1 includes several enhancements to the new interface, as well as various small corrections throughout the product. As always, we recommend that all Maple 2025 users install this update.

In particular, please note that this update includes a fix to the problem where new documents were opening in a new window instead of a new tab.  Thanks for helping us, and other users, by letting us know!

This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2025.1 download page on web site, where you can also find more details.

MapleSim 2025

We are happy to announce that we just released MapleSim 2025. This release includes a new component library to support the modeling of motor drives and updates to several in-product apps that make it even easier to perform optimization and analysis.

See What’s New in MapleSim for details.

claude.ai can write and explain many facits in the feild of prime number theory. Look what was created.

https://claude.ai/public/artifacts/b5b0697c-01a2-4e42-843b-7ddecc63c568

Thanks to @salim-barzani, I became interested in the Laplace Adomian Decompositon method to solve partial differential equations. It produces a sum of analytical components that converge to the exact solution. Probably it is not that efficient for numerical solutions, but the possibility of finding an exact solution to nonlinear PDEs by finding a formula for the components and therefore the infinite sum is interesting.

The version here covers many of the common forms of PDEs, but is still a work in progress. The method for finding the Adomian polynomials could be improved by using one of the reccurence formulas in the literature. Extension to more PDE forms, ODEs etc are possible and I will attempt some of these before uploading an improved version to the application centre. In the meantime, feedback about bugs, usability etc. are appreciated.

Download Laplace_Adomian_Decomposition_procedure8b.mw

First impressions, I have mixed feelings - one being it's cool and new, the other feeling that it's a bit clunky.

In my opinion Maple is starting to look like the interface is being modelled after Microsoft Office, or like the ribbon toolbars of AutoCad or Inventor.  Maple's "uniqueness" is disappearing.  I rather liked the old interface. 

The toolbar icons are larger, taking up more space.

The toolbar layout is indeed simpler, but also less efficient maybe.  I mean there were more useful available icons at once before, more functional is the word I guess.  Now it might be a couple of clicks away to pull up your favorite icon(s).  The icons all look very nice, that's a plus but they could be smaller.  

Perhaps we could make a customized menu toolbar?  That is, allow users to put all the most useful icons we use or would like the most to be displayed?  This would help some of the strange organization of some of the icons and allow us to make our maple "sandbox" feel more at home. 

The link below goes to the Proceedings of the Maple 2024 Conference, which includes several articles that will be of interest to the readers of Maple Primes.

There may be one more paper coming in to the proceedings later as per policy; since most things are ready, away we go!

Proceedings of the Maple 2024 Conferenc

(1) The gray line above the working area is redundant.

(2) Line Style, Color, and the "Delete" key function to delete object are not working properly.

(3) IdentifySequence([1,3,5,7,9]) without the second argument does not work.

(4) IdentifySequence should first identify simple patterns (Arithmetic Progression, Geometric Progression, Arithmetic-Geometric Progression, Harmonic Progression) before attempting to find a more complex formula for the nth term of the sequence.

(5) It would be beneficial if IdentifySequence recognized sequences involving rational, irrational and symbolic numbers.

In Optical-Illusion--Impossible-Prisms, mcarvalho provides a Maple Learn worksheet to illustrate an intriguing optical illusion.  Here I do that illustration in Maple, and in 3D! 

The graphics below shows 4 bars.  Or is it 3 bars?

Download the worksheet, stare at the graphics for short while to grasp the nature of the optical illusion, and then rotate the 3D graph with the mouse and see the illusion fall apart.

optical-illusion.mw

Geometrical entertainment in the form of rolling without slipping, now inside a torus.
You can also print out the corresponding equations - these graphs are # in the text, but it is better to do this separately from the geometric animation, because textplot3d takes up a lot of resources.

Please consider it not as a Maple program, but simply as an idea for a corresponding algorithm.
for_TORUS_IN_TORUS_for.mw
 

The workbook includes the excel data file but I also included the worksheet and data file separate for versions that can't load workbooks.

Average_World_Temperature_workbook-.maple

Average_World_Temperature_since_1850_worksheet.mw

HadCRUT5.zip

Last week, DeepMind announced their new AlphaEvolve software along with a number of new results improving optimization problems in a number of areas. One of those results is a new, smaller, tensor decomposition for multiplying two 4 × 4 matrices in 48 scalar multiplications, improving on the previous best decomposition which needed 49 multiplications (Strassen 1969). While the DeepMind paper was mostly careful about stating this, when writing the introduction, the authors mistakenly/confusingly wrote:

For 56 years, designing an algorithm with rank less than 49 over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find a rank-48 algorithm to multiply two 4 × 4 complex-valued matrices

This gives the impression that this new result is the way to multiply 4 × 4 matrices over a field with the fewest number of field multiplications. However, it's not even the case that Strassen's 1969 paper gave a faster way to multiply 4 × 4 matrices. In fact, Winograd's 1968 paper on computing inner products faster could be applied to 4 × 4 matrix multiplication to get a formula using only 48 multiplications. Winograd uses a trick 

which changes two multiplications of ab's into one multiplication of ab's and two multiplications involving only a's or only b's. The latter multiplications can be pre-computed and saved when calculating all the innerproducts in a matrix multiplication

    # i=1..4, 4*2 = 8 multiplications
    p[i] := -A[i, 1]*A[i, 2] - A[i, 3]*A[i, 4];
    # 4*2 = 8 multiplications
    q[i] := -B[1, i]*B[2, i] - B[3, i]*B[4, i];

    # i=1..4, j=1..4, 4*4*2 = 32 multiplications
    C[i,j] = p[i] + q[j] 
            + (A[i,1]+B[2,j])*(A[i,2]+B[1,j])
            + (A[i,3]+B[4,j])*(A[i,4]+B[3,j])

It is simple to verify that C[i,j] = A[i,..] . B[..,j] and that the above formula calculates all of the entries of C=A.B with 8+8+32=48 multiplications.

So, if Winograd achieved a formula of 48 multiplications in 1968, why is the DeepMind result still interesting? Well, the relative shortcoming of Winograd's method is that it only works if the entries of A and B commute, while tensor decomposition formulas for matrix multiplication work even over noncommutative rings. That seems very esoteric, but everyone's favorite noncommutative ring is the ring of n × n matrices. So if a formula applies to a matrix of matrices, that means it gives a recursive formula for matrix multiplication - an tensor decomposition formulas do just that.

The original 1969 Strassen result gave a tensor decomposition of 2 × 2 matrix multiplication using only 7 scalar multiplications (rather than the 8 required by the inner product method) and leads to a recursive matrix multiplication algorithm using O(N^log[2](7)) scalar multiplications. Since then, it has been proved that 7 is the smallest rank tensor decompostion for the 2 × 2 case and so researchers have been interested in the 3x3 and larger cases. Alexandre Sedoglavic at the University of Lille catalogs the best tensor decompositions at https://fmm.univ-lille.fr/ with links to a Maple file with an evaluation formula for each.

The previous best 4 × 4 tensor decomposition was based on using the 2 × 2 Strassen decomposition recursively (2 × 2 matrix of 2 × 2 matrices) which led to 7 2 × 2 matrix multiplications each requiring 7 scalar multiplications, for a total of 49. The new DeepMind result reduces that to 48 scalar multiplications, which leads to a recursive algorithm using O(N^log[4](48)) scalar multiplications: O(N^2.7925) vs. O(N^2.8074) for Strassen. This is a theoretical improvment over Strassen but in 2024 the best known multiplication algorithm has much lower complexity: O(N^2.3713) (see https://arxiv.org/abs/2404.16349). Now, there might be some chance that the DeepMind result could be used in practical implementations, but its reduction in the number of multiplications comes at the cost of many more additions. Before doing any optimizations I counted 1264 additions in the DeepMind tensor, compared to 318 in the unoptimized 4×4 Strassen tensor (which can be optimized to 12*7+4*12=132). Finally, the DeepMind tensor decomposition involves 1/2 and sqrt(-1), so it cannot be used for fields of characteristic 2, or fields without sqrt(-1). Of course, the restriction on characteristic 2 is not a big deal, since the DeepMind team found a 4 × 4 tensor decomposition of rank 47 over GF2 in 2023 (see https://github.com/google-deepmind/alphatensor).

Now if one is only interested in 4 × 4 matrices over a commutative ring, the Winograd result isn't even the best possible. In 1970, Waksman https://ieeexplore.ieee.org/document/1671519 demonstrated an improvement of Winograd's method that used only 46 multiplications as long as the ring allowed division by 2. Waksman's method has since been improved by Rosowski to remove the divisions see https://arxiv.org/abs/1904.07683. Here's that nice compact straight-line program that computes C = A · B in 46 multiplications.

And, here attached are five Maple worksheets that create the explicit formulas for the 4 × 4 matrix methods mentioned in this post, and verify their operation count, and that they are correct.

Strassen_444.mw  Winograd.mw  DM_444.mw Waksman.mw Rosowski.mw

If you are interested in some of the 2022 results, I posted some code to my GitHub account for creating formulas from tensor decompositions, and verifying them on symbolic matrix multiplications: https://github.com/johnpmay/MapleSnippets/tree/main/FastMatrixMultiplication

The clear followup question to all of this is:  does Maple use any of these fast multiplication schemes?  And the answer to that is mostly hidden in low level BLAS code, but generally the answer is: No, the straightforward inner-product scheme for multiplying matrices optimized memory access thus usually ends up being the fastest choice in most cases.