MaplePrimes Posts

MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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  • aRandStep2D := proc(X0, Y0, dx, dy)
      local X, Y, P, R;
      P := Array(1 .. 2);
      R := rand(1 .. 8)();
      if R = 1 then X := X0 - dx; Y := Y0 + dy; end if;
      if R = 2 then X := X0; Y := Y0 + dy; end if;
      if R = 3 then X := X0 + dx; Y := Y0 + dy; end if;
      if R = 4 then X := X0 - dx; Y := Y0; end if;
      if R = 5 then X := X0 + dx; Y := Y0; end if;
      if R = 6 then X := X0 - dx; Y := Y0 - dy; end if;
      if R = 7 then X := X0; Y := Y0 - dy; end if;
      if R = 8 then X := X0 + dx; Y := Y0 - dy; end if;
      P[1] := X; P[2] := Y;
      return P;
    end proc 

    SetStart := proc(b)
      local alpha, R, P;
      P := Array(1 .. 2);
      alpha := rand(1 .. b)();
      P[1] := alpha*b;
      P[2] := alpha*b;
      return P;
    end proc 

    RandomFactTpq := proc(N, pb, dx, dy)
      local alpha, X, Y, f, P, counter, B, n, T;
      P := Array(1 .. 2);
      counter := 0; f := 1;
      B := floor(evalf(sqrt(N))); #Set maximal searching steps
      T := floor(evalf(sqrt(N))); #For SetStart's use
      P := SetStart(T);
      X := P[1]; Y := P[2];
      while f = 1 and counter < B do  #loop
        n := pb - X - Y;
        f := gcd(N, n);
        if f > 1then break; end if;
        P := aRandStep2D(X, Y, dx, dy); #A random move
        X := P[1]; Y := P[2];
        if X < 1 or Y < 1 or N - pb - 1 < X or X <= Y then
          P := SetStart(T);       # Restart when out of borders
          X := P[1]; Y := P[2];
        end if;
        counter := counter + 1;    #Counting the searched steps
      end do;
      if  f>1  then print(Find at point (X, Y), found divisor = f, searching steps = counter);
      else print(This*time*finds*no*result, test*again!); end if;
    end proc


    wxbRandWalkTpqNew4.pdf

    Hi
    It's been years since expressions like A %* B %+ C involving inert arithmetic operators used in infix form are correctly understood (parsed) when written on a 1D-Math input line. The idea is simple: have the operators %. %*, %+, %-, %^, %/ work on input as infix operators the same way their active forms: ., *, +, -, ^, / do. This useful functionality, however, remained elusive when using 2D-Math input notation, so one would have to resort to using the functional form of the operators. E.g., input the above as `%+`(`%*`(A, B) ,C), which for me is really ugly. Besides being a bit demoralizing: we do all this fuzz about how great computer algebra and 2D-Math input notation is, and then input things in that way …

    So this is to mention that this elusive functionality of inert arithmetic operators used in infix form within a 2D-Math input line now works. The novelty is present in the latest Maplesoft Physics Updates for Maple 2023, which is version 1490. As usual, to install the Updates open a Maple worksheet and input Physics:-Version(latest).

    Here is an image (worksheet at the end) showing the new thing


    The implementation is pretty new; reports of anything related to these inert operators not displayed/working as you'd expect are much appreciated. 


    Download Inert_arithmetic_operators_in_2D_Math.mw

    Edgardo S. Cheb-Terrab
    Physics, Differential Equations and Mathematical Functions, Maplesoft

    Can’t seem to find the mistake in your math? Instead of painfully combing through each line, let the new “Check my work” operation in Maple Learn help! Now in Maple Learn, you can type out a solution to a variety of math problems, and let Maple Learn check your work! Additionally, by signing on to Maple Learn and the Maple Calculator app, you can take a photo of your handwritten math, import it into Maple Learn, and check your work with the click of a button.

    Whether you’re solving a system of linear equations or an algebra problem, computing an integral or a partial derivative, “Check my work” can help. Maple Learn will tell you which steps are “Ok” and which steps to double-check. If you get a step wrong, Maple Learn will point out which line has an error, then proceed to check whether the rest of your work followed the right procedure.

    Here’s an example of a solution to a system of linear equations written out by hand. All I had to do was snap a picture in the Maple Calculator app, and Maple Learn instantly had my equation set ready to go in the Cloud Expressions menu. Then, I just clicked “Check my work” in the Context Panel.

    Screenshot of a handwritten solution to a system with three linear equations and a screenshot of how the expressions appear in Maple Learn through the Cloud Expressions feature.

    Maple Learn identified that I was trying to solve a system with 3 equations, checked my steps, and concluded my solution set was correct.

    Screenshot of the feedback "Check my work" gives to the steps that correctly solve a system of three linear equations. "Ok" for correct steps, and a concluding message once completed.

    What happens if you make a mistake? Here’s an example of evaluating an improper integral with a u-substitution that involves a limit. This time, I directly typed my steps into Maple Learn and pressed “Check my work” in the Context Panel. Check my work recognized the substitution step and noted what step was incorrect; can’t forget to change the limits of integration! After pointing out where my mistake was, Maple Learn continued to evaluate the rest of my steps while taking my error into account. It confirmed that the rest of the process was correct, even though the answer wasn’t.

    Screenshot of incorrect steps in Maple Learn attempting to solve an improper integral. The error is highlighted with the feedback of "Check this step" from "Check my work"

    After making my change in Maple Learn and checking again, I’ve found the correct value.

    Screenshot of the corrected steps to solving the improper integral, with the positive feedback from Check my work indicating these steps are correct.

    Checking your work has never been easier with Maple Learn. Whether you want to type your solution directly in Maple Learn or import math with Maple Calculator, the new “Check my work” feature has you covered. Visit the how-to document for more examples using this new feature and let us know what you think!

     

    Maple introduced "Copy as LaTeX" a few versions ago and I have used this feature exensively when it suddenly stopped working.

    After som experiments I found the root cause and easy (but irritating) workaround for OSX

    Problem:

    "Copy as LaTeX" suddenly stops working ("Copy as MathML" still works fine)

    Cause:

    This problem appears if in “Display Setting”-tab in settings dialogue the “Input display” is set to “Maple Notation

    In that case all attempts on “Copy as LaTeX” will be a null-function and not move anything at all into the copy buffer.

    The “Copy as MathML” is not affected by this in the same way.

    I have confirmed this on OSX in Maple versions 2022, 2023, and 2024

    Workaround:

    Adjusting “Display Setting”-tab in settings dialogue so that the “Input display” is set to “2-D Math” and “Apply Globally” makes it work again.

    A bit annoying as a prefer the maple notation input and I cannot have this setting if I want the copy to latex to work.

    Note:

    in OSX this can also be fixed by removing the Maple preferences file and letting Maple restore it.

    ~/Library/Preferences/Maple/2023/Maple Preferences

    Edit: Added 2024 as affected version.

    Hi everyone,

    I'd like to draw your attention to a package we recently uploaded to the Maple Cloud, here. You can download the package from the linked Cloud page, or directly from here as a workbook file: NaturalLanguage.maple. I'll include a lightly edited version of the "cover sheet" that introduces the package below. I have left the first four sections folded closed - you can see those in the linked Maple Cloud page or the workbook - because I think the last section is the most interesting.
     

    Using natural language models in Maple


    This package explores using large language models such as ChatGPT for processing natural language in Maple. Let's load the package from source, save it in this workbook, and load it.

    restart

    read "this:///lib/NaturalLanguage.mpl"

    savelib('NaturalLanguage', "this://")

    with(NaturalLanguage)

    Warning, the NaturalLanguage package is an experimental package designed as an interface to publicly available large language models such as ChatGPT. Use of this package is entirely at the user's risk. Results may be inconsistent, misleading, or flat out incorrect. 

    [Explain, GetCommand, GetMath, Query, RawQuery]

    (1)

    We note there is a warning: we will see output of large language models, which will often include inaccurate statements. Please keep this in mind - this is not (yet?) technology that you want to use to build a bridge!

    We also note that there are five publically exposed commands. Let's look at them in turn.

    RawQuery

       

    Query

       

    GetMath

       

    GetCommand

       

    Explain

     
    • 

    The Explain command asks the given model to explain the item in the query. After an explanation, you can ask for more detail by issuing the command Explain(more), Explain("go on"), Explain(elaborate), Explain(further), Explain("continue"), or minor variations. The item you ask about can be a mathematical expression, equation, list of equations, or a string.

    • 

    The default model is GPT-4; you can select the other model by using the model = ChatGPT option, or forcing use of the GPT-4 model by using the model = GPT4 option. Note that OpenAI may deprecate and disable models, so the set of models supported may change in the future.

    display(Explain(x^2+y^2=1));display(Explain(x^2+y^2 = 1))

    This equation represents a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane.

     

    display(Explain(more));display(Explain(more))

    The equation x^2 + y^2 = 1 represents a circle in a two-dimensional plane (specifically, a Cartesian plane).

    The center of the circle is at the origin of the coordinates (0,0) and its radius is 1. This is because any point (x, y) on the circle is a distance r (the radius) away from the center, and by the Pythagorean theorem, this distance is given by the square root of (x^2 + y^2). The fact that x^2 + y^2 = 1 implies that the radius r = sqrt(1) = 1.

    This fundamental equation is also the unit circle in trigonometry, where angles are measured in radians. The coordinates (x, y) represent the cosine and sine of the angle respectively. The unit circle is a crucial concept in trigonometry, complex number theory, and calculus. It simplifies many mathematical concepts and provides a geometric interpretation of a variety of phenomena in physical sciences and engineering.

     

    display(Explain(Re(exp(x*I + y*I)) = Re(exp(x*I)) * Re(exp(y*I)) - Im(exp(x*I)) * Im(exp(y*I))));display(Explain(Re(exp(I*x+I*y)) = Re(exp(I*x))*Re(exp(I*y))-Im(exp(I*x))*Im(exp(I*y))))

    The equation seems to be using Euler's formula, which states that e^(ix) = cos(x) + i*sin(x). The 'Re' refers to the real part of a complex number, and 'Im' refers to the imaginary part. So, if you put Euler's formula in there your equation is equivalent to cos(x + y) = cos(x)cos(y) - sin(x)sin(y), which is basically the well-known trigonometric formula for the cosine of a sum. In a nutshell, it's dealing with the trigonometric identities and properties of exponential functions with complex numbers.

     

    display(Explain("go on", model = ChatGPT));display(Explain("go on", model = ChatGPT))

    The given equation appears to be dealing with the real part of a complex exponential expression. Let's break it down step by step to understand its meaning:

    1. The equation involves the expression e^(i*x+i*y), where e represents Euler's number (~2.718), i is the imaginary unit (√(-1)), and x and y are real numbers.
    2. The expression e^(i*x+i*y) can be rewritten using Euler's formula: e^(i*x+i*y) = cos(x+y) + i*sin(x+y). This is a complex number in the form a + bi, where 'a' represents the real part (Re) and 'b' represents the imaginary part (Im).
    3. The real part of e^(i*x+i*y) is, therefore, Re(e^(i*x+i*y)) = cos(x+y).
    4. The right side of the equation consists of the product of two complex exponential expressions: Re(e^(i*x))*Re(e^(i*y))-Im(e^(i*x))*Im(e^(i*y)).
    5. The expression Re(e^(i*x)) represents the real part of e^(i*x), which is cos(x), and Im(e^(i*x)) represents the imaginary part of e^(i*x), which is sin(x).
    6. Similarly, Re(e^(i*y)) represents the real part of e^(i*y), which is cos(y), and Im(e^(i*y)) represents the imaginary part of e^(i*y), which is sin(y).
    7. Therefore, the right side becomes: (cos(x)*cos(y)) - (sin(x)*sin(y)).

    So, the equation Re(e^(i*x+i*y)) = Re(e^(i*x))*Re(e^(i*y))-Im(e^(i*x))*Im(e^(i*y)) essentially states that the real part of e^(i*x+i*y) (i.e., cos(x+y)) is equal to the real part of e^(i*x) (i.e., cos(x)) multiplied by the real part of e^(i*y) (i.e., cos(y)), minus the imaginary part of e^(i*x) (i.e., sin(x)) multiplied by the imaginary part of e^(i*y) (i.e., sin(y)).

    In simpler terms, the equation is connecting the real part of the sum of two complex exponential expressions with the product of the real parts and the difference of the imaginary parts of those individual expressions.

     

    display(Explain(Re(sigma) < 0));display(Explain(Re(sigma) < 0))

    The inequality "Re(sigma) < 0" is a statement in complex number theory. It is saying that the real part (Re) of a complex number sigma is less than zero. This means that the complex number is to the left of the imaginary axis in the complex number plane. This kind of inequality is often used in the study of complex functions, in areas such as control systems or signal processing in electrical engineering, and also in number theory and the study of dynamical systems in mathematics.

     

    display(Explain(continue));display(Explain(continue))

    The inequality "Re(sigma) < 0" is typically related to the field of complex numbers. Here, "Re" stands for the real part of a complex number and "sigma" is usually used to represent a complex number. So, "Re(sigma) < 0" is saying that the real part of the complex number sigma is negative.

    Complex numbers are usually written in the form a + bi, where a and b are real numbers and i is the imaginary unit. The "Re" in "Re(sigma)" refers to the a part of this form, i.e. the real part of the complex number.

    This inequality is often found in fields like control systems engineering or signal processing. For instance, in control systems, all the poles of a stable system must have a negative real part. Another context you might come across this inequality is in complex analysis, one might examine the region where the real part of a complex function is negative. So, the inequality "Re(sigma) < 0" expresses that a complex number is in the left half of the complex plane, which is often crucial for the stability of many systems in engineering.

     

    display(Explain("The Maple command simplify"));display(Explain("The Maple command simplify"))

    The Maple command "simplify" is used to simplify mathematical expressions. In Maple, this command applies various rules to reduce an equation or expression to its simplest or most compact form.

    For example, if you have an equation like `(x^3 - x^2)/x^2`, using the simplify command would reduce it to `x - 1`. It simplifies algebraic expressions, performs factorization, combines like terms, cancel out common factors, etc.

    The general syntax is `simplify(expr)`, where `expr` is the expression that you want to simplify. The simplified expression is returned as output.

    Please note that the simplifications made by this command are based on general rules and may not always give the expected results for some specific expressions due to the complexity of mathematical simplifications.

     

    display(Explain(continue, model=ChatGPT));display(Explain(continue, model = ChatGPT))

    The Maple command "simplify" is used to simplify mathematical expressions. It takes an expression as input and attempts to find a simplified form by applying various algebraic rules and simplification techniques.

    When you use the "simplify" command, Maple applies a series of simplification steps, which can include:

    1. Expanding and factoring polynomials: This step expands products of terms and factors out common terms.
    2. Simplifying fractions: The command simplifies fractions by canceling common factors in the numerator and denominator.
    3. Simplifying trigonometric expressions: Maple applies trigonometric identities to simplify expressions involving trigonometric functions.
    4. Simplifying logarithmic and exponential expressions: The command applies rules of logarithms and exponents to simplify expressions with these functions.
    5. Simplifying square roots and radicals: It simplifies square roots by expressing them in simplest radical form.
    6. Simplifying expressions involving absolute values: Maple simplifies absolute value expressions by considering different cases based on the sign of the argument.
    7. Applying mathematical identities and rules: The command uses various mathematical identities and rules to simplify expressions further.

    The "simplify" command in Maple is very powerful and can handle a wide range of mathematical expressions. However, it may not always produce the most simplified form, as simplification can sometimes be a subjective task. In such cases, you can try using other commands or options available in Maple to refine the simplification process.

    To use the "simplify" command in Maple, you can simply type "simplify(expression)" where "expression" represents the mathematical expression you want to simplify.

     

    display(Explain("Weight of a W10X54 beam?"))

    The weight of a W10X54 beam refers to the weight specification of a beam in the W Beam series, commonly used in construction and engineering projects. The nomenclature "W10X54" is decoded as follows:

    - W: it stands for 'wide flange', a type of structural steel beam where the flanges are parallel to each other.
    - 10: it indicates the nominal depth of the wide flange, which is about 10 inches.
    - 54: it indicates the weight of the beam per linear foot, which is about 54 pounds.

    So, a W10X54 beam weighs 54 pounds per foot.

     

    display(Explain(further))

    "Weight of a W10X54 beam" refers to the weight of a specific kind of structural steel beam used in construction and architecture. The "W" stands for "wide flange", which is a particular type of I-beam.

    The "10" means the nominal depth of the beam in inches (also known as its height when standing upright).

    The "54" represents the beam's weight per foot in pounds. In other words, for every foot of length the beam has, it weighs 54 pounds.

     So if you have a W10X54 beam that is 10 feet long, its total weight would be 540 pounds (10 feet times 54 pounds per foot).

    Please note that these are nominal dimensions and may not exactly match the true dimensions of the beam due to manufacturing variables.

     

    NULL

     

    What do you think? Will this be an important part of mathematical software in the near future, or are we still far away from that point? We'd love to hear your opinions.

    What was established in 1788 in Prussia, is derived from the Latin word for “someone who is going to leave”, and can be prepared for using the many capabilities of Maple Learn? Why, it’s the Abitur exam! The Abitur is a qualification obtained by German high school students that serves as both a graduation certificate and a college entrance exam. The exam covers a variety of topics, including, of course, mathematics.

    So how can students prepare for this exam? Well, like any exam, writing a previous year’s exam is always helpful. That’s exactly what Tom Rocks Math does in his latest video—although, with him being a math professor at Oxford University, I’d wager a guess that he’s not doing it as practice for taking the exam! Instead, with his video, you can follow along with how he tackles the problems, and see how the content of this particular exam differs from what is taught in other countries around the world.

    Oh, but what’s this? On question 1 of the geometry section, Tom comes across a problem that leaves him stumped. It happens to the best of us, even university professors writing high school level exams. So what’s the next step?  Well, you could use the strategy Tom uses, which is to turn to Maple Learn. With this Maple Learn document, you can see how Maple Learn allows you to easily add a visualization of the problem right next to your work, making the problem much easier to wrap your head around. What’s more, you don’t have to worry about any arithmetic errors throwing your whole solution off—Maple Learn can take care of that part for you, so you can focus on understanding the solution! And that’s just what Tom does. In his video, after he leaves his attempt at the problem behind, he turns to this document to go over the full solution, making it easy for the viewer (and any potential test-takers!) to understand where he went wrong and how to better approach problems like that in the future.

    A screenshot of a Maple Learn document, showing a 3D plot depicting the intersection of 2 spheres. A text box describes how the plot relates to the problem.

    So to all you Abitur takers out there—that’s just one problem that can be transformed with the power of Maple Learn. The next time you find yourself getting stuck on a practice problem, why not try your hand at using Maple Learn to solve it? After that, you’ll be able to fly through your next practice exam—and that’ll put you one step ahead of an Oxford math professor, so it’s a win all around!

    Maple's fsolve command can quickly solve expressions involving large floating point numbers where the (symbolic) solve command can take much longer attempting to solve the equivalent rational expression. For example, consider the following worksheet:

    restart;

    sys := {a + b^0.2784982189 = c+1, b + c^0.9575068354 = a+2, c + a^0.1576130817 = b+3};

    {a+b^.2784982189 = c+1, b+c^.9575068354 = a+2, c+a^.1576130817 = b+3}

    (1)

    fsolve_start:=time[real]():

    fsolve(sys);

    {a = 3.561242843, b = 1.994950678, c = 3.773320855}

    (2)

    fsolve_elapsed_seconds:= time[real]()-fsolve_start;

    0.50e-1

    (3)

    solve_start:=time[real]():

    ###warning, the following command may crash and/or execute indefinitely###

    solve(sys);

    solve_elapsed_hours:=(time[real]()-solve_start)/3600;


     

    Download solve-fsolve-primes.mw

    We have just released updates to Maple and MapleSim.

    Maple 2023.1 includes improvements to the math engine, Plot Builder, import/export, and moreWe recommend that all Maple 2023 users install this update.

    This update is available through Tools>Check for Updates in Maple, and is also available from the Maple 2023.1 download page, where you can find more details.

    In particular, please note that this update includes fixes to problems with Quantifier Elimination and Group  Theory, and improves performance after a period of inactivity, all of which were reported on MaplePrimes. Thanks for the feedback!

    At the same time, we have also released an update to MapleSim, which contains a variety of improvements to MapleSim and its add-ons. You can find more information on the MapleSim 2023.1 download page.

    Sometimes, it’s the little things. Those little improvements that make a good tool even better. Sometimes, it’s as simple as an easy shorthand notation that allows you to create and label points on a graph with a single command. Just to pick a totally random example.

     

    A screenshot of a Maple Learn document containing a math cell and a plot. The math cell reads 'A(1,2)'. The plot show a point plotted at (1,2) with the label 'A'.

    Okay, maybe it’s not totally random. Maybe this new point notation is one of our newest features in Maple Learn, and maybe it’s now easy and quick for you to create labeled points to your heart’s content. Maybe you could learn more about all the ins and outs of this new feature by checking out the how-to document.

    But I can’t make any guarantees, of course.

    That said, if this hypothetical scenario were true, you would also be able to see it in action in our new document on the proof of the triangle inequality.

    A screenshot of a Maple Learn document. The left side shows an explanation of how the triangles are constructed for Euclid's proof of the triangle inequality. The right side shows an adjustable graph of said triangles.

    With this document, you can explore a detailed (and interactive!) visualization of the proof using Euclidean geometry. You can adjust the triangles to see for yourself that the sum of the lengths of any two sides must be greater than the third side, read through the explanation to see the mathematical proof, and challenge yourself with the questions it leaves you to answer. And those points on those triangles? Labeled. Smoothly and easily. I wonder how they might have done it?

    We hope you enjoy the new update! Let us know what other features you want to see in Maple Learn, and we’ll do our best to turn those dreams into reality.

    This is a reminder that we are seeking presentation proposals for the Maple Conference.

    Details on how to submit your proposal can be found on the Call for Participation page. Applications are due July 11, 2023.

    We would love to hear about your work and experiences with Maple! Presentations about your work with Maple Learn are also welcome.

    We’re now coming to the end of Pride Month, but that doesn’t mean it’s time to stop celebrating! In keeping with our celebration of queer mathematicians this month, we wanted to take some time to highlight the works of LGBT+ mathematicians throughout history. While it’s impossible to say how some of these individuals would have identified according to our modern labels, it’s still important to recognize that queer people have always existed, and have made and continue to make valuable contributions to the field of mathematics. It’s challenging to find records of LGBT+ people who lived in times when they would have been persecuted for being themselves, and because of that many contributions made by queer individuals have slipped through the cracks of history. So let’s take the time to highlight the works we can find, acknowledge the ones we can’t, and celebrate what the LGBT+ community has brought to the world of mathematics.

    If you ask anyone to name a queer mathematician, chances are—well, chances are they won’t have an answer, because unfortunately the LGBT+ community is largely underrepresented in mathematics. But if they do have an answer, they’ll likely say Alan Turing. Turing (1912-1954) is widely considered the father of theoretical computer science, largely due to his invention of the Turing machine, which is a mathematical model that can implement any computer algorithm. So if you’re looking for an example of his work, look no further than the very device you’re using to read this! He also played a crucial role in decoding the Enigma machine in World War II, which was instrumental in the Allies’ victory. If you want to learn more about cryptography and how the field has evolved since Turing’s vital contributions, check out these Maple MathApps on Vigenère ciphers, password security, and RSA encryption. And as if that wasn’t enough, Turing also made important advances in the field of mathematical biology, and his work on morphogenesis remains a key theory in the field to this day. His mathematical model was confirmed using living vegetation just this year!

    In 1952, Turing’s house was burgled, and in the course of the investigation he acknowledged having a relationship with another man. This led to both men being charged with “gross indecency”, and Turing was forced to undergo chemical castration. He was also barred from continuing his work in cryptography with the British government, and denied entry to the United States. He died in 1954, from what was at the time deemed a suicide by cyanide poisoning, although there is also evidence to suggest his death may have been accidental. Either way, it’s clear that Turing was treated unjustly. It’s an undeniable tragedy that a man whose work had such a significant impact on the modern era was treated as a criminal in his own time just because of who he loved.

    An image of Alan Turing next to a diagram of a Turing machine computing the busy beaver problem.

    Antonia J. Jones (1943-2010) was a mathematician and computer scientist. She worked at a variety of universities, including as a Professor of Evolutionary and Neural Computing at Cardiff University, and lived in a farmhouse with her partner Barbara Quinn. Along with her work with computers and number theory, she also wrote the textbook Game Theory: Mathematical Models of Conflict. If you want to learn more about that field, check out this collection of Maple Learn documents on game theory. As a child, Jones contracted polio and lost the use of both of her legs. This created a barrier to her work with computers, as early computers were inaccessible to individuals with physical disabilities. Luckily, as the technology developed and became more accessible, she was able to make more contributions to the field of computing. And that’s especially lucky for banks who like having their money be secure—she then exposed several significant security flaws at HSBC! That just goes to show you the importance of making mathematics accessible to everyone—who knows how many banks’ security flaws aren’t being exposed because the people who could find them are being stopped by barriers to accessibility?

    An image of Antonia J. Jones next to the cover of the textbook she wrote: Game Theory: Mathematical models of conflict.

    James Stewart (1941-2014) was a gay Canadian mathematician best known for his series of calculus textbooks—yes, those calculus textbooks, the Stewart Calculus series. I’m a 7th edition alumni myself, but I have to admit the 8th edition has the cooler cover. To give you a sense of his work, here’s an example of an optimization problem that could have come straight from the pages of Stewart Calculus. Questions just like this have occupied the evenings of high school and university students for over 25 years. I suspect not all of those students really appreciate that achievement, but nonetheless his works have certainly made an impact! Stewart was also a violinist in the Hamilton Philharmonic Orchestra, and got involved in LGBT+ activism. In the early 1970s, a time where acceptance for LGBT+ people was not particularly widespread (to put it lightly), he brought gay rights activist George Hislop to speak at McMaster University. Stewart is also known for the Integral House, which he commissioned and had built in Toronto. Some may find the interior of the house a little familiar—it was used to film the home of Vulcan ambassador Sarek in Star Trek: Discovery!

    An image of James Stewart next to the cover of the 8th edition Stewart Calculus textbook.

    Agnes E. Wells (1876-1959) was a professor of mathematics and astronomy at Indiana University. She wrote her dissertation on the relative proper motions and radial velocities of stars, which you can learn more about from this document on the speed of orbiting bodies and this document on linear and angular speed conversions. Wells was also a woman’s rights activist, and served as the chair of the National Woman’s Party. In her activism, she argued that the idea of women “belonging in the home” overlooked unmarried women who needed to earn a living—and women like her who lived with another woman as their partner, although she didn’t mention that part. There is a long-standing prejudice against women in mathematics, and it’s the work of women like Wells that has helped our gradual progress towards eliminating that prejudice. To be a queer woman on top of that only added more barriers to Wells’ career, and by overcoming them, she helped pave the way for all queer women in math.

    An image of Agnes E. Wells next to a table from her dissertation on the movement of stars.

    Now, there is a fair amount of debate as to whether or not our next mathematician really was LGBT+, but there is sufficient possibility that it’s worth giving Sir Isaac Newton a mention. Newton (1642-1727) is most known for his formulation of the laws of gravity, his invention of calculus (contended as it is), his work on optics and colour, the binomial theorem, his law of temperature change… I could keep going; the list goes on and on. It’s unquestionable that he had a significant impact on the field of mathematics, and on several other fields of study to boot. While we can’t know how Newton may have identified with any of our modern labels, we do know that he never married, nor “had any commerce with women”[a], leading some to believe he may have been asexual. He also had a close relationship with mathematician Nicolas Fatio de Duillier, which some believe may have been romantic in nature. In the end, we can never say for sure, but it’s worth acknowledging the possibility. After all, now that more and more members of the LGBT+ community are feeling safe enough to tell the world who they are, we’re getting a better sense of just how many people throughout history were forced to hide. Maybe Newton was one of them. Or maybe he wasn’t, but maybe there’s a dozen other mathematicians who were and hid it so well we’ll never find out. In the end, what matters more is that queer mathematicians can see themselves in someone like Newton, and we don’t need historical certainty for that.

    An image of Isaac Newton next to a Maple Learn document depicting how light passing through a prisim becomes a rainbow.

    So there you have it! Of course, this is by no means a comprehensive list, and it’s important to recognize who’s missing from it—for example, this list doesn’t include any people of colour, or any transgender people. Sadly, because of the historical prejudices and modern biases against these groups, they often face greater barriers to entry into the field of mathematics, and their contributions are frequently buried. It’s up to us in the math community to recognize these contributions and, by doing so, ensure that everyone feels like they can be included in the study of mathematics.

    Some texts distinguish between unary and binary negation signs, using short dashes for unary negation and a longer dash for binary subtraction. How important is this distinction to users of Maple?

    Some earlier versions of Maple used to have short dashes for negation (in some places). Maple 2023 has apparently abandoned the short dash for unary negation, and all such signs are now a long dash.

    How about math books? Do all texts make this short-long distinction? The typesetters for my 2001 Advanced Engineering Math book also opted for all long dashes and that book was set from the LaTeX exported from Maple 20+ years ago. But I also have texts in my library that use a short dash for unary negation, on the grounds that -a, the additive inverse of "a" is a complete symbol unto itself, the short dash being part of the symbol for that additive inverse.

    Apparently, this issue bugs me. Am I making a tempest in a teapot?

    What do you think is the acceptable limit to the effort required to answer a question?

    At what point does the question-and-answer game between two contributors become unreasonable?

    How do you, the most highly ranked, deal with situations that last for days?

    We all know that math is beautiful in and of itself—but sometimes students might need a little convincing. What better way to do that then sprucing up your math with a little colour? With Maple Learn, plot colours are fully customizable. We have several colour palettes to choose from—want your document to evoke the delicate tones of springtime? Looking for a palette that’s colourblind friendly? Or maybe you’re just nostalgic for the colours of Maple V? All these options and more are available for making your graphs colourful and coordinated. But maybe you’re the kind of person who wants to go against the grain, and you laugh in the face of predetermined colour coordination. Don’t worry, we’ve got you covered too! With our colour selector, you can also choose your own custom colours. The full colour spectrum is right at your fingertips. To learn more about how to customize the colours on your document, check out this How-To guide.

    And of course, the potential for colour inevitably leads to the potential for art. Our Maple Learn Art Gallery has plenty of fun and colourful works you can admire and contemplate (and maybe even draw inspiration from!). One of our most recent and most colourful additions is this document showcasing the history of the rainbow pride flag, in honour of June being Pride Month. You can use the slider to move through time, letting you see how the colours on the flag evolved and read about the meanings behind them. And, thanks to the colour selector, the colours match the precise shades used for the original flags! That’s the magic of hexadecimal colours for you.


    Hold on—the magic of hexadecimal colours, I hear you ask? What an enticing concept. If only we had some kind of document, perhaps one made in Maple Learn, that explained how hexadecimal colours worked and included an interactive example so that you could easily see how the red, green, and blue colour values blend together to create any given colour… Too bad we don’t!

    Just kidding. Of course we do.

    If all these colours have inspired you, be sure to check out our Call for Creative Works for the upcoming Maple Conference! Maybe your colourful creation could be this year’s winner.

    If you've seen Paulina's announcement then you know that we are once again holding a virtual Maple Conference this year.  As well, we are once again going to have a virtual gallery featuring artwork and creative projects submitted by the Maple community!

    Last year we had a number of great submissions to our Maple Art Gallery and our Maple Learn Creative Showcase.  These were our excellent prize winners.

    From left to right we have A visualization of all the primitive roots of 10037 created by Simon Plouffe, winner of the Judge’s Choice, Mother’s Day Rose created with Maple plots by Greg Wheaton, winner of the People’s Choice, and Mona Lisa in Maple Learn created by Paul DeMarco (with help from Leonardo DaVinci), the winner of the People’s Choice for the Maple Learn Showcase.

    This year we are expanding the Gallery into two collections to encourage more people to submit.  They are

    • The Art Gallery - A small gallery to highlight high effort, mathematically interesting works (with stricter criteria)

    • The Creative Works Showcase - A larger showcase for nearly any interesting visual works created with Maplesoft products like Maple Learn and Maple

    Feel free to submit nearly anything cool for the Creative Works Showcase, if we find it particularly impressive we might even ask you to let us consider it for the gallery.  Also, do not be intimidated by the title "Art Gallery" we're looking for anything that has taken some artistic effort and tells a mathematical story.

    For more information on critera and how to submit, please visit our Call for Creative Works.  The important deadline to know is the September 14th deadline for submission of works with virtual gallery reception and awards ceremony durring the conference October 26-27.

    I look forward to seeing all the submissions for the Maple community again this year!

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