VerifyTools is a package that has been available in Maple for roughly 24 years, but until now it has never been documented, as it was originally intended for internal use only. Documentation for it will be included in the next release of Maple. Here is a preview:

VerifyTools is similar to the TypeTools package. A type is essentially a predicate that a single expression can either satisfy or not. Analogously, a verification is a predicate that applies to a pair of expressions, comparing them. Just as types can be combined to produce compound types, verifications can also be combined to produce compund verifications. New types can be created, retrieved, queried, or deleted using the commands AddType, GetType (or GetTypes), Exists, and RemoveType, respectively. Similarly in the VerifyTools package we can create, retrieve, query or delete verifications using AddVerification, GetVerification (or GetVerifications), Exists, and RemoveVerification.

The package command VerifyTools:-Verify is also available as the top-level Maple command verify which should already be familiar to expert Maple users. Similarly, the command VerifyTools:-IsVerification is also available as a type, that is,

VerifyTools:-IsVerification(ver);

will return the same as

type(ver, 'verification');

The following examples show what can be done with these commands. Note that in each example where the Verify command is used, it is equivalent to the top-level Maple command verify. (Also note that VerifyTools commands shown below will be slightly different compared to the Maple2024 version):

Download VerificationTools_blogpost.mw

Austin Roche
Software Architect
Mathematical Software
Maplesoft

As AI becomes increasingly relevant in the tech world, Maplesoft has taken steps to integrate AI into our products. We recently launched two new features: Ask AI in Maple Learn and Word Problem Solver in Maple Calculator. 

Ask AI - Maple Learn

As a Math Content Creator at Maplesoft, sometimes I find myself in a creative rut. What documents would be engaging for students? How can I address certain math topics in a fun and interactive way?

I've had the pleasure of creating several collections during my time, including Extreme Value Theorem, Intermediate Value Theorem, and Polynomial Long Division. Nonetheless, each collection took a lot of storyboarding and creativity before I even began drafting them, and I've missed out on creating so many more collections because of this long idea generation process. Having a tool in my back pocket to reignite those creative juices would make it so much easier and faster to create new and exciting Maple Learn documents. 

Luckily, our new Ask AI feature in Maple Learn can help with that! 

Whenever you enter text into a Maple Learn document, a new Context Panel operation called "Ask AI" will pop up. Simply click that button to receive an AI response related to your prompt.

One of my favourite uses of Ask AI is to pick a random subject or phrase and see what the AI responds with. The Ask AI feature is designed to respond with a mathematics-centric answer so it will twist even the least mathematical of concepts into a math problem! The prompt "tacos" resulted in some formulas about sharing tacos with friends, and a prompt of "celebrity gossip" introduced statistical functions to compute the number of celebrity mentions per day. 

I also found that completing part of a tongue twister will result in some funny AI responses!

Here are a couple of my favorites below:

"She sells sea shells..."

Ask AI completes this tongue twister, then offers some formulas to compute the profit of selling S shells!

"How much wood..."

After relating that this tongue twister is not a mathematical problem, Ask AI then builds a simple formula for computing how much wood a woodchuck would (hypothetically) chuck.

There are many more applications of this feature, and I hope you all enjoy exploring them as you create documents on Maple Learn. If you're having trouble inputting text into your documents, or looking for a quick introduction to Maple Learn, check out the Walkthrough Tutorial. Beginner Tutorial (slide 8) addresses adding text to your document. Check out this blog post if you aren't sure how to access the Walkthrough Tutorial. 

Word Problem Solver - Maple Calculator

Maple Calculator now offers support for word problems by leveraging AI. Simply take a picture of your word problem and Maple Calculator will provide a solution generated by AI.

Here is a quick example:

I wrote on paper, “Alice and Bob have 17 apples total. Alice has double the number of apples as Bob plus two. How many apples does Bob have?”. Then I took a picture of this in Maple Calculator, and it gave me a breakdown of the problem using linear equations. See screenshots of my Maple Calculator below.

AI can be an amazing tool, but it can also make mistakes. We ensure that all our tools that incorporate AI clearly indicate its use, so that our users can know when AI is used and choose whether to use it. We're committed to remaining transparent about AI as our journey continues and we are always open to feedback. 

For our community of educators, a valuable exercise for students might be to show examples where AI makes mistakes and encourage students to find and explain the errors.

As an example, here is an algebra problem answered by Ask AI in Maple Learn – but it made a mistake! See if your students can spot where it went wrong and explain what should happen instead.

Building these skills will translate into good critical thinking skills that will benefit students inside and outside the classroom. For example, these exercises aim to help students identify their own mistakes in math and critically evaluate online sources. We would love to hear feedback about these exercises if you try them.

We hope these features will come in handy next time you use Maple Learn and Maple Calculator! 

I’m thrilled to introduce the updated Q&A Cards Creator! Michael Barnett had created the original Flash Cards Creator, inspired by the quiz creators in the Maple Learn gallery. I added some of the features (mentioned later in this post) that will help you use this tool to make more comprehensive quizzes. Students can use the creator to quiz themselves before a test, and instructors can integrate more practice quizzes into their lesson plans. One feature I particularly love is the ability to link full solutions to the back of each card, allowing users to understand the answers in depth (as shown in this document). Additionally, you can link a general solutions package (as seen here) if individual solutions aren’t necessary for each question. Below is an example of what the Q&A cards can look like from the users point of view.
This creator is a great example of the Maple Learn documents you can create through scripting in Maple. With a single script, you can create an infinite amount of content and quizzes. If you are interested in Maple scripting, here is a link to the Q&A cards script. If this script looks intimidating, feel free to check out this blog post on the basics of Maple scripting!


If you are interested in creating your own Q&A quiz, you can go to this document to get started. If you get stuck at any point creating your card set, check out the instructions included in the document for clarification. We hope you enjoy creating some quizzes with this document!

Dear Maple Community,

It has been a year since the passing of Stefan Vorkoetter, who started contributing to the Maple project in the 80s and was a long term member of our development team. 

Here are a few recently published articles about Stefan, that I'd like to share with you:

https://mapletransactions.org/index.php/maple/article/view/18269
https://mapletransactions.org/index.php/maple/article/view/18681

we shall not forget

We are pleased to announce that the registration for the Maple Conference 2024 is now open.

Like the last few years, this year’s conference will be a free virtual event. Please visit the conference page for more information on how to register.

This year we are offering a number of new sessions, including more product training options and an Audience Choice session.
You can find an overview of the program on the Sessions page. Those who register before September 10th, 2024 will have a chance to vote for the topics they want to learn more about during the Audience Choice session.

We hope to see you there!

Maple Learn has so much to offer, but it can be tricky to know where to start! Even for those experienced with Maple Learn, sometimes, we miss an update with new features or fall out of practice with older ones. Luckily, we have the perfect solution for you–and it shows up right when you open your first document.

Introducing our brand-new Walkthrough Tutorial!

The tutorial covers all the main features of Maple Learn: from assigning functions, to using the Plot commands and Context Panel operations, all the way to creating your own visualizations with the Geometry commands. Stuck? Hints are provided throughout, or just click "Next" and the step will be completed automatically. 

If you're just starting out with Maple Learn, try the Beginner tutorial and work up to Advanced. This will introduce you to a holistic view of Maple Learn's capabilities along with some Maple Learn terminology. If you have some experience, starting with the Beginner tutorial is still a great option, but you may wish to begin with the Intermediate and Advanced tutorials. The Intermediate and Advanced sections cover how to use newer features of Maple Learn and you might discover something you haven't seen before!

How do I access the tutorial?

The tutorial will automatically launch when you open a new document. Head to https://learn.maplesoft.com and click "Open new document".

If the tutorial doesn't open automatically, it may have been disabled. You can manually open it by clicking the "Help" button in the top right, then clicking "Walkthrough Tutorial". 

There you have it! I had been using Maple Learn for the past few months and only recently discovered these two incredible features:

Silencing Groups (Intermediate - 6/7)

Live Sessions (Advanced - 6/6)

I found these features thanks to the Walkthrough Tutorial and my experience on Maple Learn hasn't been the same since! The Walkthrough Tutorial is a great introduction for new users, and a quick refresher for experts, but isn't the end of exploring Maple Learn's capabilities. See our How to Use Maple Learn (maplesoft.com) collection and our Getting Started with Maple Learn (youtube.com) video for more. You can also challenge The Treasure of Maple Learn (maplesoft.com) – a collection of documents designed to gamify exploring Maple Learn's features. Check out our blog post on The Case of the Mysterious Treasure - MaplePrimes to learn more about this collection. 

Hope you enjoy our new tutorial and let us know what you think!

We have just released an update to Maple. Maple 2024.1 includes improvements to the math engine, PDF export, the Physics package, command completion, and more. As always, we recommend that all Maple 2024 users install this update. In particular, please note that this update includes fixes to ODESteps and simplifying integrals, as reported on Maple Primes. Thanks for helping us, and other users, by letting us know!

At the same time, we have also released an update to MapleSim. MapleSim 2024.1.1 includes improvements to FMU import/export, plotting, co-simulation, and more, as well as enhancements to the Web Handling Library.

These updates are available through Tools>Check for Updates in Maple or MapleSim, and are also available from the Download Product Updates section of our web site, where you can find more details.

I’m excited to announce that we’ve just launched MapleSim 2024.

The new release has tools that are designed to drive innovation, and overall save you time when creating and developing simulations.

At Maplesoft we are looking to continually enhance our engineering software with new features based on customer feedback, and I’m pleased to share some of the fruits of that labor, and thank the developers, product management team, and  customers that contributed.

The new offering  helps engineers to

• Rapidly Tune Parameters
• Explore Design Concepts
• Expand Modeling Capabilities

For example, the new Rerun panel allows you to significantly cut the time between simulations as you quickly apply different parameter values, initial conditions and even simulation settings between runs. It does this by skipping the formulation steps when there are no structural changes made to the model, and you can even see the plots and results of the different iterations side by side.
You can see it in action in this short demo video.

There is now support for the latest Modelica feature set, so you can import Modelica Libraries that make use of MSL 4.0.0 features, and adds a range of new modeling components to the standard MapleSim libraries (electrical, 1-D mechanical, signal block and more).

MapleSim 2024 also includes more components in the Hydraulic library to support modeling of flow restrictions and adds a Scripting button to add and organize Maple worksheets.

We’ve also applied a whole series of updates to our MapleSim add-on products, including:

• The MapleSim Web Handling Library has new tools for modeling heavier webs, winding of multiple rolls on the same drum, and adding a Switching Nip Roller to swing the web contact points between rollers.
• The MapleSim Connector for FMI can now import and export FMI 3.0.
• The MapleSim CAD Toolbox supports recent software releases from NX™, SOLIDWORKS®, Solid Edge®, Parasolid®, and other CAD tools.
• The MapleSim Heat Transfer Library has gained a new T-junction component for the Water subpackage to improve flow/pressure-drop calculations for systems with branches.

We have an upcoming webinar for you to see the new 2024 features in MapleSim Web Handling Library – you can sign up to register here.

You can find out more about the other new features at the MapleSim What’s New web page, and as always, we are happy to hear your comments and product suggestions.

And if you are new to MapleSim and would like to try building and running a model yourself, you can request a free trial, or contact Maplesoft sales team with any questions.

We've just launched Maple Flow 2024!

You're in the driving seat with Maple Flow - each new feature has a straight-line connection to a user-driven demand to work faster and more efficiently.

Head on over here for a rundown of everything that's new, but I thought I'd share my personal highlights here.

If your result contains a large vector or matrix, you can now scroll to see more data. You can also change the size of the matrix to view more or fewer rows and columns.

You can resize rows and columns if they're too large or small, and selectively enable row and column headers.

If the vector or matrix in your result contains a unit, you can now rescale units with the Context Panel (for the entire matrix) or inline (for individual entries).

A few releases ago, we introduced the Variables palette to help you keep track of all the user-defined parameters at point of the grid cursor.

You can now insert variables into the worksheet from the Variables palette. Just double-click on the appropriate name.

Maple Flow already features command completion - just type the first few letters of a command, and a list of potential completions appears. Just pick the completion you need with a quick tap of the Tab key.

We've supercharged this feature to give potential arguments for many popular functions. Type a function name followed by an opening bracket, and a list appears.

In case you've missed it, the argument completion list also features (when they make sense) user-defined variables.

You can now link to different parts of the same worksheet. This can be used to create a table of contents that lets you jump to different parts of larger worksheets.

This page lists everything that's new in the current release, and all the prior releases. You might notice that we have three releases a year, each featuring many user-requested items. Let me know what you want to see next - you might not have to wait that long!

This Maplesoft guest blog post is from Prof. Dr. Johannes Blümlein from Deutsches Elektronen-Synchrotron (DESY), one of the world’s leading particle accelerator centres used by thousands of researchers from around the world to advance our knowledge of the microcosm. Prof. Dr. Blümlein is a senior researcher in the Theory Group at DESY, where he and his team make significant use of Maple in their investigations of high energy physics, as do other groups working in Quantum Field Theory. In addition, he has been involved in EU programs that give PhD students opportunities to develop their Maple programming skills to support their own research and even expand Maple’s support for theoretical physics.

The use of Maple in solving frontier problems in theoretical high energy physics

For several decades, progress in theoretical high energy physics relies on the use of efficient computer-algebra calculations. This applies both to so-called perturbative calculations, but also to non-perturbative computations in lattice field theory. In the former case, large classes of Feynman diagrams are calculated analytically and are represented in terms of classes of special functions. In early approaches started during the 1960s, packages like Reduce [1] and Schoonship [2] were used. In the late 1980s FORM [3] followed and later on more general packages like Maple and Mathematica became more and more important in the solution of these problems. Various of these problems are related to data amounts in computer-algebra of O(Tbyte) and computation times of several CPU years currently, cf. [4].

Initially one has to deal with huge amounts of integrals. An overwhelming part of them is related by Gauss’ divergence theorem up to a much smaller set of the so-called master integrals (MIs). One performs first the reduction to the MIs which are special multiple integrals. No general analytic integration procedures for these integrals exist. There are, however, several specific function spaces, which span these integrals. These are harmonic polylogarithms, generalized harmonic polylogarithms, root-valued iterated integrals and others. For physics problems having solutions in these function spaces codes were designed to compute the corresponding integrals. For generalized harmonic polylogarithms there is a Maple code HyperInt [5] and other codes [6], which have been applied in the solution of several large problems requiring storage of up to 30 Gbyte and running times of several days. In the systematic calculation of special numbers occurring in quantum field theory such as the so-called β-functions and anomalous dimensions to higher loop order, e.g. 7–loop order in Φ⁴ theory, the Maple package HyperLogProcedures [7] has been designed. Here the largest problems solved require storage of O(1 Tbyte) and run times of up to 8 months. Both these packages are available in Maple only.

A very central method to evaluate master integrals is the method of ordinary differential equations. In the case of first-order differential operators leading up to root-valued iterative integrals their solution is implemented in Maple in [8] taking advantage of the very efficient differential equation solvers provided by Maple. Furthermore, the Maple methods to deal with generating functions as e.g. gfun, has been most useful here. For non-first order factorizing differential equation systems one first would like to factorize the corresponding differential operators [9]. Here the most efficient algorithms are implemented in Maple only. A rather wide class of solutions is related to 2^nd order differential equations with more than three singularities. Also here Maple is the only software package which provides to compute the so-called ₂F₁ solutions, cf. [10], which play a central role in many massive 3-loop calculations

The Maple-package is intensely used also in other branches of particle physics, such as in the computation of next-to-next-to leading order jet cross sections at the Large Hadron Collider (LHC) with the package NNLOJET and double-parton distribution functions. NNLOJET uses Maple extensively to build the numerical code. There are several routines to first build the driver with automatic links to the matrix elements and subtraction terms, generating all of the partonic subprocesses with the correct factors. To build the antenna subtraction terms, a meta-language has been developed that is read by Maple and converted into calls to numerical routines for the momentum mappings, calls to antenna and to routines with experimental cuts and plotting routines, cf. [11].

In lattice gauge calculations there is a wide use of Maple too. An important example concerns the perturbative predictions in the renormalization of different quantities. Within different European training networks, PhD students out of theoretical high energy physics and mathematics took the opportunity to take internships at Maplesoft for several months to work on parts of the Maple package and to improve their programming skills. In some cases also new software solutions could be obtained. Here Maplesoft acted as industrial partner in these academic networks.

References

[1] A.C. Hearn, Applications of Symbol Manipulation in Theoretical Physics, Commun. ACM 14 No. 8, 1971.

[2] M. Veltman, Schoonship (1963), a program for symbolic handling, documentation, 1991, edited by D.N. Williams.

[3] J.A.M. Vermaseren, New features of FORM, math-ph/0010025.

[4] J. Blümlein and C. Schneider, Analytic computing methods for precision calculations in quantum field theory, Int. J. Mod. Phys. A 33 (2018) no.17, 1830015 [arXiv:1809.02889 [hep-ph]].

[5] E. Panzer, Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals, Comput. Phys. Commun. 188 (2015) 148–166 [arXiv:1403.3385 [hep-th]].

[6] J. Ablinger, J. Blümlein, C .Raab, C. Schneider and F. Wissbrock, Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms, Nucl. Phys. 885 (2014) 409-447 [arXiv:1403.1137 [hep-ph]].

[7] O. Schnetz, φ⁴ theory at seven loops, Phys. Rev. D 107 (2023) no.3, 036002 [arXiv: 2212.03663 [hep-th]].

[8] J. Ablinger, J. Blümlein, C. G. Raab and C. Schneider, Iterated Binomial Sums and their Associated Iterated Integrals, J. Math. Phys. 55 (2014) 112301 [arXiv:1407.1822 [hep-th]].

[9] M. van Hoeij, Factorization of Differential Operators with Rational Functions Coefficients, Journal of Symbolic Computation, 24 (1997) 537–561.

[10] J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C. G. Raab, C. S. Radu and C. Schneider, Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams, J. Math. Phys. 59 (2018) no.6, 062305 [arXiv:1706.01299 [hep-th]].

[11] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and T.A. Morgan, Precise QCD predictions for the production of a Z boson in association with a hadronic jet, Phys. Rev. Lett. 117 (2016) no.2, 022001 [arXiv:1507.02850 [hep-ph]].

     Happy Easter to all those who celebrate! One common tradition this time of year is decorating Easter eggs. So, we’ve decided to take this opportunity to create some egg-related math content in Maple Learn. This year, a blog post by Tony Finch inspired us to create a walkthrough exploring the four-point egg. The four-point egg is a method to construct an egg-shaped graph using just a compass and a ruler, or in this case, Maple Learn. Here's the final product: 

     The Maple Learn document, found here, walks through the steps. In general, each part of the egg is an arc corresponding to part of a circle centred around one of the points generated in this construction. 

     For instance, starting with the unit circle and the three red points in the image below, the blue circle is centred at the bottom point such that it intersects with the top of the unit circle, at (0,1). The perpendicular lines were constructed using the three red points, such that they intersect at the bottom point and pass through opposite side points, either (-1,0) or (1,0). Then, the base of the egg is constructed by tracing an arc along the bottom of the blue circle, between the perpendicular lines, shown in red below.

     Check out the rest of the steps in the Maple Learn Document. Also, be sure to check out other egg-related Maple Learn documents including John May’s Egg Formulas, illustrating other ways to represent egg-shaped curves with mathematics, and Paige Stone’s Easter Egg Art, to design your own Easter egg in Maple Learn. So, if you’ve had your fill of chocolate eggs, consider exploring some egg-related geometry - Happy Easter!  

To celebrate this day of mathematics, I want to share my favourite equation involving Pi, the Bailey–Borwein–Plouffe (BBP) formula:

This is my favourite for a number of reasons. Firstly, Simon Plouffe and the late Peter Borwein (two of the authors that this formula is named after) are Canadian! While I personally have nothing to do with this formula, the fact that fellow Canadians contributed to such an elegant equation is something that I like to brag about.

Secondly, I find it fascinating how Plouffe first discovered this formula using a computer program. It can often be debated whether mathematics is discovered or invented, but there’s no doubt here since Plouffe found this formula by doing an extensive search with the PSLQ integer relation algorithm (interfaced with Maple). This is an example of how, with ingenuity and creativity, one can effectively use algorithms and programs as powerful tools to obtain mathematical results.

And finally (most importantly), with some clever rearranging, it can be used to compute arbitrary digits of Pi!

Digit 2024 is 8
Digit 31415 is 5
Digit 123456 is 4
Digit 314159 is also 4
Digit 355556 is… F?

That last digit might look strange… and that’s because they’re all in hexadecimal (base-16, where A-F represent 10-15). As it turns out, this type of formula only exists for Pi in bases that are powers of 2. Nevertheless, with the help of a Maple script and an implementation of the BBP formula by Carl Love, you can check out this Learn document to calculate some arbitrary digits of Pi in base-16 and learn a little bit about how it works.

After further developments, this formula led to project PiHex, a combined effort to calculate as many digits of Pi in binary as possible; it turns out that the quadrillionth bit of Pi is zero! This also led to a class of BBP-type formulas that can calculate the digits of other constants like (log2)*(π^2) and (log2)^5.

Part of what makes this formula so interesting is human curiosity: it’s fun to know these random digits. Another part is what makes mathematics so beautiful: you never know what discoveries this might lead to in the future. Now if you’ll excuse me, I have a slice of lemon meringue pie with my name on it 😋

References
BBP Formula (Wikipedia)
A Compendium of BBP-Type Formulas
The BBP Algorithm for Pi

     On International Women’s Day we celebrate the achievements of women around the world. One inspiring story of women in STEM is that of Sophie Germain (1776-1831), a French mathematician and physicist who made groundbreaking strides in elasticity theory and number theory. She learned mathematics from reading books in her father’s library, and while she was not permitted to study at the École Polytechnique, due to prejudice against her gender, she was able to obtain lecture notes and decided to submit work under the name Monsieur LeBlanc. Some prominent mathematicians at the time, including Joseph-Louis Lagrange and Carl Friedrich Gauss, with whom Germain wrote, recognized her intellect and were supportive of her work in mathematics. 

     Sophie Germain is remembered as a brilliant and determined trailblazer in mathematics. She was the first woman to win a prize from the Paris Academy of Sciences for her contributions in elasticity theory and was among the first to make significant contributions toward proving Fermat’s Last Theorem. Among her many accomplishments, one special case of Fermat’s Last Theorem she was able to prove is when the exponent takes the form of what is now known as a Sophie Germain prime: a prime, p, such that 2p+1 is also a prime. The associated prime, 2p+1, is called a safe prime. 

     To mark International Women’s Day, I’ve created a document exploring the Ulam spiral highlighting Sophie Germain primes and safe primes, as an adaptation of Lazar Paroski’s Ulam spiral document. The image below displays part of the Ulam spiral with Sophie Germain primes highlighted in red, safe primes highlighted in blue, primes that are both a Sophie Germain prime and safe prime highlighted in purple, and primes that are neither in grey. 

     The document also contains small explorations of these types of prime numbers. For instance, one interesting property of safe primes is that they must either be 5, 7 or take the form 12k-1 for some k≥1. This can be shown from the fact a safe prime q must equal 2p+1 for some prime, p (a Sophie Germain prime), by definition. Then, since q and p are prime, for q > 7 we can determine through contradiction that q ≡ 3 (mod 4) and q ≡ 5 (mod 6), to conclude q ≡ 11 (mod 12) ≡ -1 (mod 12). And so, q = 12k-1 for some k≥1. The Maple Learn document can be found here along with its Maple script. The document also includes a group where you can test whether some positive integer of your choice, n, is a Sophie Germain prime or a safe prime. Alternatively, given n, a button press will display the next Sophie Germain prime greater than n, using Maple’s NextSafePrime command in the number theory package.  

     In mathematics, there is no shortage of interesting rabbit holes to dive into; many of which are the result of past and present women in mathematics, like Sophie Germain, who have persevered despite their hardships. 

Attention Maple enthusiasts! It gives me great pleasure to announce Maple 2024! Maple 2024 brings together a collection of new features and enhancements carefully designed to enrich your mathematical explorations. Maple 2024 is the result of a lot of hard work by a lot of people, and there is far more in it than I can cover here. But I’d like to share with you some of my favorite features in this release.

AI Formula Assistant

The AI Formula Assistant in Maple 2024 is undoubtedly the feature that excites me the most, especially considering how often I’m asked the question: 'When will Maple include AI features?' This assistant serves as your new mathematical companion and will change the way you look up and enter formulas and equations. Driven by advanced AI technology, it presents a range of relevant options based on your search query. Alongside suggestions, you'll also receive detailed explanations for each formula and its parameters so you can select the one you need, and then you can insert the formula into your document at a click of a button, as a proper Maple expression.

NaturalLanguage Package

The Formula Assistant is built on top of the new NaturalLanguage package, which integrates powerful language models like GPT-4 and ChatGPT from OpenAI into Maple. With this feature, you can leverage large language models to process natural language within Maple. Ask the AI to explain concepts, provide additional details, find specific Maple commands, and more. Of course, since this is a Maple package, you can also use it as a basis to build your own AI-powered applications inside Maple. We’re really looking forward to seeing what you will do with it!

Argument Completion
We’ve had a lot of requests from people who wanted Maple’s command completion features to do even more, and I’m happy to say that Maple 2024 delivers. The new argument completion feature in Maple 2024 is poised to significantly enhance your experience with commands. For many users, including myself, not being aware of all the options a command takes is a challenge, often leading me to refer to help pages for clarification. With argument completion, that's no longer a concern. Just enter the command with the help of the existing command completion feature, then automatic argument completion takes over to guide you through the rest. Give it a try with the 'plot' command!

Check My Work

A personal favorite feature that's gotten even better in Maple 2024 is Check My Work. As someone who has tutored students, I vividly recall their stress before exams, often receiving emails and text messages from them seeking last-minute help. At the time, I found myself wishing the students had a way to check their work themselves, so we would all be less stressed! So I was super excited when we added the first Check My Work feature a couple of years ago, and am very happy that it gets better ever year. In Maple 2024, we’ve expanded its capabilities to support problems involving factoring, simplification, and limits.

Scrollable Matrices:
This feature will definitely resonate with many of the engineers in the Maple Primes community. If you're someone who works with worksheets containing large matrices, you've likely wished that you could scroll the matrices inside your document instead of having to launch a separate matrix browser. With Maple 2024, your wish has come true.

Color Bars

And finally, for those of you who appreciated the addition of color bars in Maple 2023 but wanted to see them extended to more 2D and 3D plots, you'll be delighted to know that this is exactly what we’ve done. We’ve also added new customization options, providing you with greater control over appearance.

This is just a partial glimpse of what's new in Maple 2024. For a comprehensive overview, visit What’s New in Maple 2024.

The Lunar New Year is approaching and 2024 is the Year of the Dragon! This inspired me to create a visualization approximating the dragon curve in Maple Learn, using Maple. 

The dragon curve, first described by physicist John Heighway, is a fractal that can be constructed by starting with a single edge and then continually performing the following iteration process:  

Starting at one endpoint of the curve, traverse the curve and build right triangles on alternating sides of each edge on the curve. Then, remove all the original edges to obtain the next iteration. 

This process continues indefinitely, so while we can’t draw the fractal perfectly, we can approximate it using a Lindenmayer system. In fact, Maple can do all the heavy lifting with the tools found in the Fractals package, which includes the LSystem subpackage to build your own Lindenmayer systems. The subpackage also contains different examples of fractals, including the dragon curve. Check out the Maple help pages here: 

Overview of the Fractals Package  

Overview of the Fractals:-LSystem Subpackage 

Using this subpackage, I created a Maple script (link) to generate a Maple Learn document (link) to visualize the earlier iterations of the approximated dragon curve. Here’s what iteration 11 looks like: 

You can also add copies of the dragon curve, displayed at different initial angles, to visualize how they can fit together. Here are four copies of the 13th iteration: 

Mathematics is full of beauty and fractals are no exception. Check out the LSystemExamples subpackage to see many more examples. 

Happy Lunar New Year!