MaplePrimes Commons General Technical Discussions

The primary forum for technical discussions.

A simple suggestion...

I would appreciate being able to open multiple help pages simultaneously instead of just one.
This seems to me particularly interesting when you have to browse back and forth between several related items.

Yes, that’s right! You can now add images to your Maple Learn documents! Whether you’re adding a diagram to help visualize a physics concept, inserting the logo or your school or organization, or just adding a cute selfie so that everyone knows how great you looked while making this document, you can add any image you’d like using the image icon on the toolbar. You’ll need to be logged in to access this new feature, but luckily making an account is completely free!

To insert the image, just click the image icon and select the image you want from your computer or tablet. To resize it, highlight the image and click the image icon again. You can also turn the image into a hyperlink by highlight the image and clicking the link button! Now, not only will your document look snazzy, but it can take you anywhere you’d like.

Images aren’t the only exciting new feature in Maple Learn. If you were excited by all the circles in the last set of updates, then you’re going to love this one, because we’ve introduced the Circle command! Just plug in the centre of the circle and the radius, and bam, circle. What’s more, you can easily turn your circle into an arc by adding the angle measures of the two endpoints of the arc. Infinitely customizable round objects, right at your fingertips. To learn more, check out the How-To documents Using the Circle Command and Plotting Arcs.

Ancient Greek mathematicians thought that there was nothing that couldn’t be constructed with only a compass and a straightedge. A wise math professor once tasked my class with using these same tools to draw a pretty picture. With Maple Learn’s Circle function and ability to graph straight lines, you have all the tools you need to complete this same task! We look forward to seeing the results.

 

Guys, this is still the most painful thing i Maple for me, and I hope this gets a high priority for future development.

It is still not possible to compare variables, when one of them could become zero.

with(Units[Standard])

[`*`, `+`, `-`, `/`, `<`, `<=`, `<>`, `=`, Im, Re, `^`, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, evalc, evalr, exp, expand, factor, floor, frac, int, ln, log, log10, log2, max, min, mul, normal, polar, root, round, sec, sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, type, verify]

(1)

a := 15*Unit('kN')

15*Units:-Unit(kN)

(2)

b := 0*Unit('kN')

0

(3)

NULL``

if a < b then "True" else "False" end if

Error, cannot determine if this expression is true or false: 15*Units:-Unit(kN) < 0

 

NULL

Download CompareUnits.mw

As many of you are aware, the Maple Application Center is a very important resource for Maple users. It is a place for authors to share their Maple work, and for users to have access to a rich collection of over 2,500 curated Maple documents covering a wide array of topics and disciplines.

I am very pleased to announce that we have been hard at work on a new version of the Application Center, and it’s at a state where we’re ready to open it up to the public for testing. You can access the new site here: https://www.maplesoft.com/applications_beta . We are looking for feedback, so please give it a try, and let us know what you think!

Here are a few of my favorite features of the new site:

Updated Look & Feel
The interface of the current version of the Application Center has not changed in many years, and it was time for a new paint job. I think you’ll find that the new site is cleaner, modern, and more enjoyable to use.

Easier to Find the Documents you Want
The updated Application Center provides multiple new ways to find content that is relevant for you. Browse user-made collections of documents or use tags (the same tags used in MaplePrimes) to find documents for the topics you are interested in. Alternatively, you can use the search bar to quickly find documents, tags or authors.

Personalize your Experience
If you are logged-in when using the Application Center, you will be able to customize what you see by pinning your favorite collections, authors or tags to your home page.

Community Moderation & Reputation
As with MaplePrimes, the strength of the Application Center comes from the amazing community of individuals who contribute to it. In addition to submitting your own content to the Application Center, users can now edit tags and create collections of content that others can use. Similar to MaplePrimes, community moderation is restricted to members who have a sufficient reputation score. Speaking of reputation, quality contributions to MaplePrimes will now be reflected in your reputation score. When someone likes one of your submissions, your reputation will increase by 5.

 

There are many other great new features as well, and we have a roadmap of future updates planned that will make it even better.

I invite you to take a look at the new site and play with it. Browse some content, search, look through tags, and create some collections. Most importantly, I’m really hopeful that you will then use the comments section below to let us know what you think. Did you discover any bugs or issues? What do you like? What do you dislike? What other features would you like to see?

We are hoping to run the Beta for a period of a few weeks, and I’m looking forward to hearing and reading your thoughts. Hope you enjoy it!

https://www.maplesoft.com/applications_beta

Bryon

Do you have a Chromebook?  Are you a student or a teacher looking for the mighty power of Maple, but find yourself limited by your web-only computer? Well, have no fear, because Maple Learn is here!

As a web-based application, Maple Learn is fully supported by Chromebooks. You can create graphs, perform and check calculations, and share documents all within the comfort of your own browser. No need to download any kind of software—just go to learn.maplesoft.com to get started!

Students, if you’re looking for some use for your school-provided Chromebook and wondering how it can help you learn instead of just weighing down your backpack, Maple Learn can help. It’s the perfect, all-inclusive tool to help you learn, visualize, and check your math. And, if you’re looking to brush up on all that math you forgot over the summer, you can check out the Maple Learn Example Gallery, home to hundreds of examples and explanations of a wide variety of math concepts. And it’s all accessible on your Chromebook!

Here's a podcast that covers a few topics that get discussed on MaplePrimes.
 

We all like finding the right tool for the job. In the Sep 2021 episode of the Engineering Matters Podcast “#127 – Tools for Thinking” you can discover how far engineers have come in their quest for better tools.

It features contributions from several members of the Maplesoft team as they discuss how the user experience shapes the adoption of engineering software tools.

The hosts have fun describing some early calculation hacks - from early Sumerian farmers using their fingers as tally counters, to the paper calculus notebooks of the 1850s used by historical engineering figures like Isambard Kingdom Brunel. What starts as a necessity gets improved over time to save them mental effort – all driven by the way users interact with the tool.

This episode gives a behind-the-scenes look at some of the decisions that shaped the engineering product that is now Maple Flow from its roots in Maple. Maplesoft CEO Laurent Bernardin describes the spark of innovation in the late 1970s, when two professors at the University of Waterloo developed Maple. “The two professors got together, realising that there was a need in math education for a tool to help with calculations and setting out to create that tool. And Maple was born quickly, was adopted across universities around the globe.”

As engineers typically work in ways far removed from the regular academic setting, Product Manager Samir Khan weighs in on the shift that comes from a different user base: “Different tools have different design intents,” says Khan. “Some tools are designed for programmers such as code development environments, like Visual Studio. Some environments are aimed at mathematicians, people who need precise control over the mathematical structure of their equations, and some environments are designed for engineers who simply want to throw down a few equations on a virtual whiteboard and manipulate them and get results.”

The conversation also touches on the design of the GUI itself. Margaret Hinchcliffe, Maple’s Senior GUI Developer expresses the importance of smoothing the user experience - drilling down and taking “the typical tasks that people want to do the most, and make those the most immediate. So really focusing on how many keystrokes do they need to do this task?”.

Ironically the idea of the paper notebook still has features that are desirable. Khan muses on the idea that Maplesoft has “taken the first step with having a virtual whiteboard, but Maple Flow still relies on keyboard and mouse input”. He offers suggestions for what may be next in the industry: “It’d be interesting to see if we can take advantage of modern advances in deep learning and AI to imitate what humans are doing and interpreting handwritten mathematics.”

You can listen to the entire podcast (~30 min) here: https://engineeringmatters.reby.media/2021/09/30/the-evolution-of-tools-for-thinking/

From a tweet by Tamás Görbe : plotting Chebyshev polynomials in polar coordinates leads to some interesting pictures.  Screenshot here, link to the worksheet (and some perhaps interesting puzzles) at the end.

 

ChebyshevRose.mw

Dear all,

Reversion of series---computing a series for the functional inverse of a function---has been in Maple since forever, but many people are not aware of how easy it is.  Here's an example, where we are looking for "self-reverting" series---which I called "ambiverts".  Anyway have fun.

 

https://maple.cloud/app/5974582695821312/Series+Reversion%3A+Looking+for+ambiverts

PS There looks to be some "code rot" in the branch point series for Lambert W in Maple, which we encounter in that worksheet.  Or, I may simply have not coded it very well in the first place (yeah, that was mine, once upon a time).  Checking now.  But there is a workaround (albeit an ugly one) shown in that worksheet.

 

... and two suggestions to the development team

POINT 1
In ?DiscreteValueMap (package Statistics) it's given an example concerning rhe Geometric distribution along with this comment:
"The Geometric distribution is discrete but it necessarily assumes integer values, so (bold font is mine) it also does not have a DiscreteValueMap"

This sentence seems to indicate that "because a distribution is discrete over the set of integers, it cannot have a DiscreteValueMap", some sort of logical implication...

But my feeling is that the Geometric distribution (or any other discrete distribution) does not have a DiscreteValueMap because this attribute has just not been specified when defining the distribution.

restart:
with(Statistics):

GeomRV := RandomVariable(Geometric(1/2)):
f := unapply(ProbabilityFunction(GeomRV, n), n):

AnotherGeomRV := Distribution(
      'ProbabilityFunction'=f,
      'Support'=0..infinity,
      'DiscreteValueMap'=(n->n),
      'Type'=discrete
):
DiscreteValueMap(AnotherGeomRV , n);

Thus having the set of natural numbers as support doesn't imply that DiscreteValueMap cannot exist.

Suggestion 1: modify the ?DiscreteValueMap help page so that it no longer suggests that some discrete distributions cannot have a .DiscreteValueMap 

______________________________________________________________________________________

POINT 2
I think there exists a true problem with the definition of discrete distributions in Maple: the ProbabilityFunction of a (discrete) random variable) takes non zero values outside their definition set.
For instance

ProbabilityFunction(GeomRV, Pi);  # something non null


To ivercome this problem I defined a new Geometric distribution this way (not entirely satisfying):

restart:
with(Statistics):

GeomRV := RandomVariable(Geometric(1/2)):
f := unapply(ProbabilityFunction(GeomRV, n), n):
g := n -> (1-ceil(n-floor(n)))*f(n)    # (1-ceil(n-floor(n))) = 1 if n in Z, 0 otherwise

AnotherGeomRV := Distribution(
      'ProbabilityFunction'=g,
      'Support'=0..infinity,
      'DiscreteValueMap'=(n->n),  # is wanted
      'Type'=discrete
):
ProbabilityFunction(AnotherGeomRV, 2);
                 1/8
ProbabilityFunction(AnotherGeomRV, Pi);
                  0

PS: None of the statistics based upon the  ProbabilityFunction (Mean, Variance, ... ) is correctly computed with the previous construction. This could be easily overcome by completing this definition, just as its done in Maple, for all the requires statistics, for instance 

AnotherGeomRV := Distribution(
      ....
      'Mean'=1   # or more generally (1-p)/p form Geometric(p)
):


Suggestion 2: modify the way discrete distributions are defined in Maple in order to avoid ProbabilityFunction to return wrong values.

I am a high school Teacher in Denmark, who have been using Maple since version 12, more than 12 years ago. I suggested it for my school back then and our math faculty finally decided to purchase a school license. We are still there. We have watched Maple improve in a lot of areas (function definitions, context panels, graphically etc., etc ). Often small changes makes a big difference! We have been deligted. We we are mostly interested in improvements in GUI and lower level math, and in animations and quizzes. I have also been enrolled as a beta tester for several years yet. 

One of the areas, which is particually important is print and export to pdf, because Danish students have to turn in their papers/solutions at exams in pdf format! I guess the Scandinavian countries are ahead in this department. They may quite possible be behind in other areas however, but this is how it is. 

Now my point: Maplesoft is lacking terrible behind when regarding screen look in comparison with print/export to pdf. 

I am very frustrated, because I have been pinpointing this problem in several versions of Maple, both on Mapleprimes and in the beta groups. Some time you have corrected it, but it has always been bouncing back again and again! I have come to the opinion that you are not taking it seriously? Why?

Students may loose grades because of missing documentations (marking on graphs etc.). 

I will be reporting yet another instance of this same problem. When will it stop?

Erik

 

Wirtinger Derivatives in Maple 2021

Generally speaking, there are two contexts for differentiating complex functions with respect to complex variables. In the first context, called the classical complex analysis, the derivatives of the complex components ( abs , argument , conjugate , Im , Re , signum ) with respect to complex variables do not exist (do not satisfy the Cauchy-Riemann conditions), with the exception of when they are holomorphic functions. All computer algebra systems implement the complex components in this context, and computationally represent all of abs(z), argument(z), conjugate(z), Im(z), Re(z), signum(z) as functions of z . Then, viewed as functions of z, none of them are analytic, so differentiability becomes an issue.

 

In the second context, first introduced by Poincare (also called Wirtinger calculus), in brief z and its conjugate conjugate(z) are taken as independent variables, and all the six derivatives of the complex components become computable, also with respect to conjugate(z). Technically speaking, Wirtinger calculus permits extending complex differentiation to non-holomorphic functions provided that they are ℝ-differentiable (i.e. differentiable functions of real and imaginary parts, taking f(z) = f(x, y) as a mapping "`&Ropf;`^(2)->`&Ropf;`^()").

 

In simpler terms, this subject is relevant because, in mathematical-physics formulations using paper and pencil, we frequently use Wirtinger calculus automatically. We take z and its conjugate conjugate(z) as independent variables, with that d*conjugate(z)*(1/(d*z)) = 0, d*z*(1/(d*conjugate(z))) = 0, and we compute with the operators "(&PartialD;)/(&PartialD; z)", "(&PartialD;)/(&PartialD; (z))" as partial differential operators that behave as ordinary derivatives. With that, all of abs(z), argument(z), conjugate(z), Im(z), Re(z), signum(z), become differentiable, since they are all expressible as functions of z and conjugate(z).

 

 

Wirtinger derivatives were implemented in Maple 18 , years ago, in the context of the Physics package. There is a setting, Physics:-Setup(wirtingerderivatives), that when set to true - an that is the default value when Physics is loaded - redefines the differentiation rules turning on Wirtinger calculus. The implementation, however, was incomplete, and the subject escaped through the cracks till recently mentioned in this Mapleprimes post.

 

Long intro. This post is to present the completion of Wirtinger calculus in Maple, distributed for everybody using Maple 2021 within the Maplesoft Physics Updates v.929 or newer. Load Physics and set the imaginary unit to be represented by I

 

with(Physics); interface(imaginaryunit = I)

 

The complex components are represented by the computer algebra functions

(FunctionAdvisor(complex_components))(z)

[Im(z), Re(z), abs(z), argument(z), conjugate(z), signum(z)]

(1)

They can all be expressed in terms of z and conjugate(z)

map(proc (u) options operator, arrow; u = convert(u, conjugate) end proc, [Im(z), Re(z), abs(z), argument(z), conjugate(z), signum(z)])

[Im(z) = ((1/2)*I)*(-z+conjugate(z)), Re(z) = (1/2)*z+(1/2)*conjugate(z), abs(z) = (z*conjugate(z))^(1/2), argument(z) = -I*ln(z/(z*conjugate(z))^(1/2)), conjugate(z) = conjugate(z), signum(z) = z/(z*conjugate(z))^(1/2)]

(2)

The main differentiation rules in the context of Wirtinger derivatives, that is, taking z and conjugate(z) as independent variables, are

map(%diff = diff, [Im(z), Re(z), abs(z), argument(z), conjugate(z), signum(z)], z)

[%diff(Im(z), z) = -(1/2)*I, %diff(Re(z), z) = 1/2, %diff(abs(z), z) = (1/2)*conjugate(z)/abs(z), %diff(argument(z), z) = -((1/2)*I)/z, %diff(conjugate(z), z) = 0, %diff(signum(z), z) = (1/2)/abs(z)]

(3)

Since in this context conjugate(z) is taken as - say - a mathematically-atomic variable (the computational representation is still the function conjugate(z)) we can differentiate all the complex components also with respect to  conjugate(z)

map(%diff = diff, [Im(z), Re(z), abs(z), argument(z), conjugate(z), signum(z)], conjugate(z))

[%diff(Im(z), conjugate(z)) = (1/2)*I, %diff(Re(z), conjugate(z)) = 1/2, %diff(abs(z), conjugate(z)) = (1/2)*z/abs(z), %diff(argument(z), conjugate(z)) = ((1/2)*I)*z/abs(z)^2, %diff(conjugate(z), conjugate(z)) = 1, %diff(signum(z), conjugate(z)) = -(1/2)*z^2/abs(z)^3]

(4)

For example, consider the following algebraic expression, starting with conjugate

eq__1 := conjugate(z)+z*conjugate(z)^2

conjugate(z)+z*conjugate(z)^2

(5)

Differentiating this expression with respect to z and conjugate(z) taking them as independent variables, is new, and in this example trivial

(%diff = diff)(eq__1, z)

%diff(conjugate(z)+z*conjugate(z)^2, z) = conjugate(z)^2

(6)

(%diff = diff)(eq__1, conjugate(z))

%diff(conjugate(z)+z*conjugate(z)^2, conjugate(z)) = 1+2*z*conjugate(z)

(7)

Switch to something less trivial, replace conjugate by the real part ReNULL

eq__2 := eval(eq__1, conjugate = Re)

Re(z)+z*Re(z)^2

(8)

To verify results further below, also express eq__2 in terms of conjugate

eq__22 := simplify(convert(eq__2, conjugate), size)

(1/4)*(z^2+z*conjugate(z)+2)*(z+conjugate(z))

(9)

New: differentiate eq__2 with respect to z and  conjugate(z)

(%diff = diff)(eq__2, z)

%diff(Re(z)+z*Re(z)^2, z) = 1/2+Re(z)^2+z*Re(z)

(10)

(%diff = diff)(eq__2, conjugate(z))

%diff(Re(z)+z*Re(z)^2, conjugate(z)) = 1/2+z*Re(z)

(11)

Note these results (10) and (11) are expressed in terms of Re(z), not conjugate(z). Let's compare with the derivative of eq__22 where everything is expressed in terms of z and conjugate(z). Take for instance the derivative with respect to z

(%diff = diff)(eq__22, z)

%diff((1/4)*(z^2+z*conjugate(z)+2)*(z+conjugate(z)), z) = (1/4)*(2*z+conjugate(z))*(z+conjugate(z))+(1/4)*z^2+(1/4)*z*conjugate(z)+1/2

(12)

To verify this result is mathematically equal to (10) expressed in terms of Re(z) take the difference of the right-hand sides

rhs((%diff(Re(z)+z*Re(z)^2, z) = 1/2+Re(z)^2+z*Re(z))-(%diff((1/4)*(z^2+z*conjugate(z)+2)*(z+conjugate(z)), z) = (1/4)*(2*z+conjugate(z))*(z+conjugate(z))+(1/4)*z^2+(1/4)*z*conjugate(z)+1/2)) = 0

Re(z)^2+z*Re(z)-(1/4)*(2*z+conjugate(z))*(z+conjugate(z))-(1/4)*z^2-(1/4)*z*conjugate(z) = 0

(13)

One quick way to verify the value of expressions like this one is to replace z = a+I*b and simplify "assuming" a andNULLb are realNULL

`assuming`([eval(Re(z)^2+z*Re(z)-(1/4)*(2*z+conjugate(z))*(z+conjugate(z))-(1/4)*z^2-(1/4)*z*conjugate(z) = 0, z = a+I*b)], [a::real, b::real])

a^2+(a+I*b)*a-(1/2)*(3*a+I*b)*a-(1/4)*(a+I*b)^2-(1/4)*(a+I*b)*(a-I*b) = 0

(14)

normal(a^2+(a+I*b)*a-(1/2)*(3*a+I*b)*a-(1/4)*(a+I*b)^2-(1/4)*(a+I*b)*(a-I*b) = 0)

0 = 0

(15)

The equivalent differentiation, this time replacing in eq__1 conjugate by abs; construct also the equivalent expression in terms of z and  conjugate(z) for verifying results

eq__3 := eval(eq__1, conjugate = abs)

abs(z)+abs(z)^2*z

(16)

eq__33 := simplify(convert(eq__3, conjugate), size)

(z*conjugate(z))^(1/2)+conjugate(z)*z^2

(17)

Since these two expressions are mathematically equal, their derivatives should be too, and the derivatives of eq__33 can be verified by eye since z and  conjugate(z) are taken as independent variables

(%diff = diff)(eq__3, z)

%diff(abs(z)+abs(z)^2*z, z) = (1/2)*conjugate(z)/abs(z)+z*conjugate(z)+abs(z)^2

(18)

(%diff = diff)(eq__33, z)

%diff((z*conjugate(z))^(1/2)+conjugate(z)*z^2, z) = (1/2)*conjugate(z)/(z*conjugate(z))^(1/2)+2*z*conjugate(z)

(19)

Eq (18) is expressed in terms of abs(z) = abs(z) while (19) is in terms of conjugate(z) = conjugate(z). Comparing as done in (14)

rhs((%diff(abs(z)+abs(z)^2*z, z) = (1/2)*conjugate(z)/abs(z)+z*conjugate(z)+abs(z)^2)-(%diff((z*conjugate(z))^(1/2)+conjugate(z)*z^2, z) = (1/2)*conjugate(z)/(z*conjugate(z))^(1/2)+2*z*conjugate(z))) = 0

(1/2)*conjugate(z)/abs(z)-z*conjugate(z)+abs(z)^2-(1/2)*conjugate(z)/(z*conjugate(z))^(1/2) = 0

(20)

`assuming`([eval((1/2)*conjugate(z)/abs(z)-z*conjugate(z)+abs(z)^2-(1/2)*conjugate(z)/(z*conjugate(z))^(1/2) = 0, z = a+I*b)], [a::real, b::real])

(1/2)*(a-I*b)/(a^2+b^2)^(1/2)-(a+I*b)*(a-I*b)+a^2+b^2-(1/2)*(a-I*b)/((a+I*b)*(a-I*b))^(1/2) = 0

(21)

simplify((1/2)*(a-I*b)/(a^2+b^2)^(1/2)-(a+I*b)*(a-I*b)+a^2+b^2-(1/2)*(a-I*b)/((a+I*b)*(a-I*b))^(1/2) = 0)

0 = 0

(22)

To mention but one not so famliar case, consider the derivative of the sign of a complex number, represented in Maple by signum(z). So our testing expression is

eq__4 := eval(eq__1, conjugate = signum)

signum(z)+z*signum(z)^2

(23)

This expression can also be rewritten in terms of z and  conjugate(z) 

eq__44 := simplify(convert(eq__4, conjugate), size)

z/(z*conjugate(z))^(1/2)+z^2/conjugate(z)

(24)

This time differentiate with respect to conjugate(z),

(%diff = diff)(eq__4, conjugate(z))

%diff(signum(z)+z*signum(z)^2, conjugate(z)) = -(1/2)*z^2/abs(z)^3-z^3*signum(z)/abs(z)^3

(25)

Here again, the differentiation of eq__44, that is expressed entirely in terms of z and  conjugate(z), can be computed by eye

(%diff = diff)(eq__44, conjugate(z))

%diff(z/(z*conjugate(z))^(1/2)+z^2/conjugate(z), conjugate(z)) = -(1/2)*z^2/(z*conjugate(z))^(3/2)-z^2/conjugate(z)^2

(26)

Eq (25) is expressed in terms of abs(z) = abs(z) while (26) is in terms of conjugate(z) = conjugate(z). Comparing as done in (14),

rhs((%diff(signum(z)+z*signum(z)^2, conjugate(z)) = -(1/2)*z^2/abs(z)^3-z^3*signum(z)/abs(z)^3)-(%diff(z/(z*conjugate(z))^(1/2)+z^2/conjugate(z), conjugate(z)) = -(1/2)*z^2/(z*conjugate(z))^(3/2)-z^2/conjugate(z)^2)) = 0

-(1/2)*z^2/abs(z)^3-z^3*signum(z)/abs(z)^3+(1/2)*z^2/(z*conjugate(z))^(3/2)+z^2/conjugate(z)^2 = 0

(27)

`assuming`([eval(-(1/2)*z^2/abs(z)^3-z^3*signum(z)/abs(z)^3+(1/2)*z^2/(z*conjugate(z))^(3/2)+z^2/conjugate(z)^2 = 0, z = a+I*b)], [a::real, b::real])

-(1/2)*(a+I*b)^2/(a^2+b^2)^(3/2)-(a+I*b)^4/(a^2+b^2)^2+(1/2)*(a+I*b)^2/((a+I*b)*(a-I*b))^(3/2)+(a+I*b)^2/(a-I*b)^2 = 0

(28)

simplify(-(1/2)*(a+I*b)^2/(a^2+b^2)^(3/2)-(a+I*b)^4/(a^2+b^2)^2+(1/2)*(a+I*b)^2/((a+I*b)*(a-I*b))^(3/2)+(a+I*b)^2/(a-I*b)^2 = 0)

0 = 0

(29)

NULL


 

Download Wirtinger_Derivatives.mw

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

I’m very pleased to announce that the Maple Calculator app now offers step-by-step solutions. Maple Calculator is a free mobile app that makes it easy to enter, solve, and visualize mathematical problems from algebra, precalculus, calculus, linear algebra, and differential equations, right on your phone.  Solution steps have been, by far, the most requested feature from Maple Calculator users, so we are pretty excited about being able to offer this functionality to our customers. With steps, students can use the app not just to check if their own work is correct, but to find the source of the problem if they made a mistake.  They can also use the steps to learn how to approach problems they are unfamiliar with.

Steps are available in Maple Calculator for a wide variety of problems, including solving equations and systems of equations, finding limits, derivatives, and integrals, and performing matrix operations such as finding inverses and eigenvalues.

(*Spoiler alert* You may also want to keep a look-out for more step-by-step solution abilities in the next Maple release.)

If you are unfamiliar with the Maple Calculator app, you can find more information and app store links on the Maple Calculator product page.  One feature in particular to note for Maple and Maple Learn users is that you can use the app to take a picture of your math and load those math expressions into Maple or Maple Learn.  It makes for a fast, accurate method for entering large expressions, so even if you aren’t interested in doing math on your phone, you still might find the app useful.

I make a maple worksheet for generating Pythagorean Triples Ternary Tree :

Around 10,000 records in the matrix currently !

You can set your desire size or export the Matrix as text ...

But yet ! I wish to understand from you better techniques If you have some suggestion ?

the mapleprimes Don't load my worksheet for preview so i put a screenshot !

Pythagoras_ternary.mw

Pythagoras_ternary_data.mw

Pythagoras_ternary_maple.mw

 

 

 

The order in which expressions evaluate in Maple is something that occasionally causes even advanced users to make syntax errors.

I recently saw a single line of Maple code that provided a good example of a command not evaluating in the order the user desired.

The command in question (after calling with(plots):) was

animate(display, [arrow(<cos(t), sin(t)>)], t = 0 .. 2*Pi)