Research work

The fractal structure’s researching.

Modeling of the fractal sets in the Maple program.

Municipal Budget Educational Establishment “School # 57” of Kirov district of Kazan

    Author:  Ibragimova Evelina

    Scientific advisor:  Alsu Gibadullina - mathematics teacher

    Translator:  Aigul Gibadullina

In Russian

ИбрагимоваЭ_Фракталы.docx

In English

Fractals_researching.doc

     ( Images - in attached files )

Table of contents:

Introduction

I. Studying of principles of fractals construction

II. Applied meaning of fractals

III. Researching of computer programs of fractals construction

Conclusion

Introduction

We don’t usually think about main point of things, which we have to do with every day. Environmental systems are many-sided, ever–changing and compli­cated, but they are formed by a little number of rules. Fractals are apt example of this – they are complicated, but based on simple regulations. Self – similarity is the main attribute of them.  Just one fractal element contains genetically information about all system.  This information have a forming role for all system. But some­times self – similarity is partial.

Hypothesis of the research. Fractals and various elements of the Universe have general principles of structural organization. It is a reason why the theory of frac­tals is instrument for cognition of the world.

Purpose of the research. Studying  of genetic analogy  between fractals and alive and non-living Universe systems with computer-based mathematical mod­eling in the Mapel’s computer space.

Problems of the research. 

1. studying of principles of fractal’s construction;
2. Detection of  general fractal content of physical, biological and artificial sys­tems;
3. Researching of applied meaning of fractals;
4. Searching of computer programs which can generate all of known fractals;
5. Researching of fractals witch was assigned by complex variables;
6. Formation of innovative ideas of using of fractals in different spaces;

The object of research.  Fractal structures, nature and society objects.

The subject of research. Manifestation of fractality in different objects of the Universe.

Methods of the researching.

1. Studying and analysis of literature of research’s problem;
2. Searching of computer programs which can generate fractals and experimenta­tion with them;
3. Comparative analysis of principles of generating of fractals and structural or­ganizations of physical, biological and artificial systems;
4. Generation and formulation of innovation ways to applied significance of fractals.

Applied significance.

Researching of universality of fractals gives general academic way of cognition of nature and society.

I. Studying of principles of fractal construction

We can see fractal constructions everywhere – from crystals and different accu­mulations (clouds, rivers, mountains, stars etc.) to complex ecosystems and bio­logical objects like fern leafs or human brain. Actually, the idea that frac­tal principles are genetic code of our Universe has been discussed for about fifteen years. The first attempt of modeling of the process of the Universe construction was done by A.D. Linde. We also know that young Andrey Saharov had solved “fractal” calculation problem – it was already half a century ago.

Now therefore, fractal picture of the world was intuitively anticipated by human genius and it inevitably manifested in its activity.

Fractals are divided into four groups in the traditional way: geometric (constructive), algebraical (dynamical), stochastical and natural.

The first group of fractals is geometric. It is the most demonstrative type of fractals, because we can instantly observe the self-similarity in it. This type of fractals is constructed in the basis of original figure by her fragmentation and real­izing of different transformations. Geometrical fractals ensue on repeating of this procedure. They are using in computer-generated graphics for generating the pic­tures of leafs, bush, dimensional structures, etc.

The second large group of fractals -  algebraical. This fractals are constructed by iteration of nonlinear displays, which set by simple formulas. There are two types of algebraical fractals – linear and nonlinear. The first of them are determined by first order equates (linear equates), and the second by nonlinear equates, their na­ture significantly brighter, richer and more diverse than first order equates.

The third known group of fractals – stochastical. It is generated by method of random modification of options in iterative process. Therefore, we get an objects which is similar to nature fractals – asymmetrical trees, rugged coasts, mountain scenery etc. Such fractals are useful in modeling of land topography, sea–surface and electrolysis process etc.

The fourth group of fractals is nature, they are dominate in our life. The main difference of such fractals is that they can’t demonstrate infinite self-similarity. There is “physical fractals” term in the classification concept for nature fractals, this term notes their naturalness. These fractals are created with two simple opera­tions: copy and scaling. We can indefinitely list examples of nature fractals: hu­man’s circulatory system, crowns and leafs of trees, lungs, etc.  It is impossible to show all diversity of nature fractals.

II. Applied meaning of fractals

Fractals are having incredibly widespread application nowadays.

In the medicine. Human’s organism is consists from fractal structures: circulatory system, bronchus, muscle, neuron system, etc. So it’s naturally that fractal algorithms are useful in the medicine. For example, assessment of rhythm of fractal dimension while electric diagrams analyzing allows to make more infor­mative and accurate view on the beginning of specific illnesses. Also fractals are using for high–quality processing of  X–ray images (in the experimental way). There are designing of new methods in the gastroenterology which allows to ex­plore gastrointestinal tract organs qualitative and painlessly. Actually, there are discoveries of application of fractal methods for diagnosis and treatment of cancer.

In the science. There are no scientific and technical areas without fractal calcu­lations nowadays. It happens due to the fact that majority of nature objects have fractal structures and dimension: coasts of the continents; natural resources alloca­tion; magnetic field anomaly; dissemination of surges and vibrations in an elastic environments; porous, solid and fungal bodies; crystals; turbulence; dynamic of complicated systems in general, etc. Fractals are useful in geology, geophysics, in the oil sciences… It’s impossible to list all the spaces of adaptability.

Modeling of chaotic processes, particularly, in description of population models.

In telecommunications. It’s naturally that fractals are popular in this area too. Natan Coen is person, who had started to use fractal antennas. Fractal antenna has very compact form which provides high productivity. Due to this, such antennas are used in marine and air transport, in personal devises. The theory of fractal an­tennas has become an independent, well-developed apparatus of synthesis and analysis of electric small antenna (ESA) nowadays. There are developments of possibility of fractal compression of the traffic which is transmitted through the web. The goal of this is more effective transfer of information.

In the visual effects. The theory of fractals has penetrated area of formation of different kinds of visualizations and creation of special effects in the computer graphics soon. This theory are very useful in modeling of nature landscapes in computer games. The film industry also has not been without fractal geometry. All the special effects are based in fractal structure: mountain landscape, lava, flame, fog, large flows and the same. In the modern level of the cinema creation of the special effects is impossible without modeling of fractals.

In the economics. The Veirshtrass’s function is famous example of stochastic fractals. Analysis of graph of the function in interactive mathematic environment Maple allows to make sure in fractal structure of function by way of entry of dif­ferent ranges of graphic visualization. In any indefinitely small area of the part graph of the function absolutely looks like area of this part in the all . The property of function is used in analysis of stock markets.

In the architect. Notably, fractal structures have become useful in the architect more earlier than B. Mandelbrode had discovered them. S.B. Pomorov, Doctor of Architecture, Professor, member of Russian Architect Union, talks about applica­tion of fractal theory in the architect in his article. Let’s see on the part of this arti­cle:

“Fractal structures were found in configuration of African tribal villages, in an­cient Vavilon’s ziggurats, in iconic buildings of ancient India and China, in gothic temples of ancient Russia .

We can see the high fractal level in Malevich’s Architectons. But they were cre­ated long before emergence of the notion of fractals in the architect. People started to use fractal algorithms on the architect morphogenesis consciously after Mandel­brot’s publications. It was made possible to use fractal geometry for analyzing of architectural forms.

Fractals had become available to the majority of specialists due to the comput­erization.  They had been incredibly attractive for architectors, designers and town planners in aesthetic, philosophical and psychological way. Fractal theory was per­ceived on emotional, sensual level in the first phase. The constant repression lead­ing to loss of sensuality.

Application of fractal structures is effective on the microenvironment designing level: interior, household items and their elements. Fractal structures introduction allows creating a new surroundings for people with fractal properties on all levels. It corresponds to nesting spaces.

Fractal formations are not a panacea or a new era in the architect history. But it’s a new way to design architect forms which enriches the architectural theory and practice language. The understanding of na­ture fractal impacts on architectural view of urban environment. An attempt to de­velop the method of architectural designing which will base in an in-depth fractal forms is especially interesting. Will this method base only on mathematics? Will it be different methods and features symbiosis? The practice experiments and re­searches will show us. It’s safe to say that modern fractal approach can be useful not only for analysis, but also for harmonic order and nature’s chaos, architect which may be semantic dominant in nature and historic context.”

Computer systems. Fractal data compression is the most useful fractal applica­tion in the computer science. This kind of compression is based on the fact that it’s easy to describe the real world by fractal geometry. Nevertheless, pictures are compressed better than by other methods (like jpeg or gif). Another one advantage is that picture isn’t pixelateing while compressing. Often picture looks better after increase in fractal compressing.

Basic concept for fractal computer graphics is “Fractal triangle”. Also there are “Fractal figure”, “Fractal object”, “Fractal line”, “Fractal composition”, “Parent object” and “Heir object”. However, it should be noted that fractal computer graphics has recently received as a kind of computer graphics of 21th century.

 The opportunities of fractal computer graphics cannot be overemphasized. It allows creating abstract compositions where we can realize a lot of moves: hori­zontal and vertical, diagonal directions, symmetry and asymmetry etc. Only a few programmers from all over the world know about fractal graphics today.  To what can we compare fractal picture? For example, with complex structure of crystal or with snowflake, the elements of which line up in the one complex composition. This property of fractal object can be useful in ornament creating or designing of decorative composition. Algorithms of synthesis of fractal rates which allows to reproduce copy of any picture too close to the original are developed today.

III. Researching of computer programs of fractal construction

Strict algorithms of fractals are really good for programming. There are a lot of computer programs which introduce fractals nowadays. Computer mathematic systems are stand out from over programs, especially, Maple. Computer mathe­matics is mathematic modeling tool. So programming represents genetic structure of fractal in these systems and we can see precise submission of fractal structure in the picture while we enter a number of iterations . This is the reason why mathematic fractals should be studied with computer mathematics.  The last dis­covery in fractal geometry has been made possible by powerful, modern com­puters. Fractal property researching is almost completely based on computer cal­culations. It allows making computer experiments which reproduce processes and phenomenon which we can’t experiment in the real world with.

Our school has been worked with computer mathematics Maple package more than 10 years. So we have unique opportunity to experiment with mathematic fractals, thanks to that we can understand how initial values impact on outcome   (it is stochastic fractal). For example, we have understood the meaning of the fact that color is the fourth dimension: color changing leads to changing of physical char­acteristics. That is what astrophysics mean talking about “multicolored” of the Universe. While fractal constructing in interactive mathematic environment we re­ceived graphic models which was like A. D. Linde’s model of the Universe. Perhaps, it demonstrates that Universe has fractal structure.

Conclusion

Scientists and philosophers argue, can we talk about universality of fractals in recent years. There are two groups of two opposite positions. We agree with the fact that fractals are universal. Due to the fact that movement is inherent property of material also we always have fractals wherever we have movement.  

We are convinced that fractal is genetic property of the Universe, but it is not mean that all the Universe elements to the one fractal organization. In deployment process fractal structure is undergoing a lot of fluctuations (deviations) and a lot of points of bifurcation (branching) lead grate number of fractal development varie­ties.  

Therefore, we think that fractals are general academic method of real world re­searching. Fractals give the methodology of nature and community researching.

In transitional, chaotic period of society development social life become harder. Different social systems clash. Ancient values are exchanged for new values literally in all spaces. So it’s vitally important for science to develop behavior strategies which allow to avoid tragic mistakes. We think that fractals play important role in developing of such technologies. And – synergy is theory of evolving systems self- organization. But evolution happens on fractal principles, as we know now.

P.S.  Images - in attached files

This is still a work in progress, but might be of use to anybody interested in Maxwell's Equations :-)

Examining_Maxwells_Equations.mw

Since we are getting many questions on how to create Math apps to add to the Maple Cloud. I wanted to go over the different GUI aspects of how you go about creating a Math App in Maple. The following Document also includes some code examples that are used in the the Math App but doesn't go into them in detail. For more details on the type of coding you do in a Math App see the DocumentTools package help page.

Some of the graphical features of the Math app don't display on Maple Primes so I'd recommend downloading this worksheet from here: HowToMathApp.mw to follow along.

How to make a Math App (An example of using the Document Tools).   This Document will provide a beginners guide on one way to make a Math app in Maple. It will contain some coding examples as well as where to find different options in the user interface. Step 1 Insert a Table     •  When making a Math App in Maple I often start with a table. You can enter a table by going to Insert > Table...      •  I often make the table 1 x 2 to start with as this gives an area for input and an area for the output (such as plots).   Add a plot component to one of the cells of the table     •  From the Components  Palette you can add a Plot Component . Add it to the table by clicking and dragging it over.     Add another table inside the other cell     •  In the other cell of the table I'll add another table to organize my use of buttons, sliders, and other components. Add some components to the new table     •  From the Components Palette I'll add a slider, or dial, or something else for interaction.   •  You may also want a Math region for an area to enter functions and a button to tell Maple to do something with it.   Arrange the Components to look nice     •  You can change how the components are placed either by resizing the tables or changing the text orientation of the contents of the cells.   Write some code for the interaction of the buttons.     •  Using the DocumentTools  package there are lots of ways you can use the components. I often will start writing my code using a code edit region  as it provides better visualization for syntax. On MaplePrimes these display as collapsed so I will also include code blocks for the code.   Let's write something that takes the value of the slider and applies it to the dial     •  Note that the names of the components will change in each section as they are copies of the previous section.   with(DocumentTools): with(DocumentTools): sv:=GetProperty('Slider2',value); SetProperty('Dial2',value,sv); •  This code will only execute when run using the  button. Change the value of the slider below then run the code above to see what happens.   Move the code 'inside' the slider     •  Instead of putting the code inside the code edit region where it needs to be executed, we'll next add the code to the value changed code of the slider.   •  Right click the Slider then select "Edit Value Changed Code".     •  This will open the code editor for the Slider     •  Enter your code (ensuring you're using the correct name for the slider and dial).   •  Notice that you don't need to use the with(DocumentTools): command as "use DocumentTools in ... end use;" is already filled in for you.   •  Save the code in the Slider and hit the  button inside it once. •  Now move the slider.   •  On future uses of the App you won't need to hit  as the code will be run on startup. Add some more details to your App     •  Let's make this app do something a bit more interesting than change the contents of a dial when a slider moves.   •  The plan in the next few steps is to make this app allow a user to explore parameters changing in a sinusoidal expression.   •  I'm going to add a second Math Component, put the expression into both then uncheck the box in the context panel that says "Editable".   •  To make the Math containers fit nicely I'll check the Auto-fit container box and set the Minimum Width Pixels to 200.   Add code to change the value of phi in the second Math Container when the Slider changes     Note: Maple uses Radians for trigonometric functions so we should convert the value of phi to Radians. use DocumentTools in   use DocumentTools in phi_s:=GetProperty(Slider5,value); expr:= GetProperty(MathContainer6,expression); new_expr:=algsubs(phi=phi_s*Pi/180,expr); SetProperty(MathContainer7,expression,new_expr); end use: Make the Dial go from 0 to 360°     •  Click the Dial and look at the options in the context panel on the right.   •  Update the values in the Dial so that the highest position is 360 and the spacing makes sense for the app.   Have the Dial update the theta value of the expression     •  Add the following code to the Dial   use DocumentTools in use DocumentTools in theta_d:=GetProperty(Dial7,value); phi_s:=GetProperty(Slider7,value); #This is added so that phi also has the value updated expr:= GetProperty(MathContainer10,expression); new_expr0:=algsubs(theta=theta_d*Pi/180,expr); new_expr:=algsubs(phi=phi_s*Pi/180,new_expr0); #This is added so that phi also has the value updated SetProperty(MathContainer11,expression,new_expr); end use:   •  Update the value in the slider to include the value from the dial   use DocumentTools in   use DocumentTools in theta_d:=GetProperty(Dial7,value); #This is added so that theta also has the value updated phi_s:=GetProperty(Slider7,value); expr:= GetProperty(MathContainer10,expression); new_expr0:=algsubs(theta=theta_d*Pi/180,expr); #This is added so that theta also has the value updated new_expr:=algsubs(phi=phi_s*Pi/180,new_expr0); SetProperty(MathContainer11,expression,new_expr); end use:   Notice that the code in the Dial and Slider are the same     •  Since the code in the Dial and Slider are the same it makes sense to put the code into a procedure that can be called from multiple places.   Note: The changes in the code such as local and the single quotes are not needed but make the code easier to read and less likely to run into errors if edited in the future (for example if you create a variable called dial8 it won't interfere now that the names are in quotes).     UpdateMath:=proc()  UpdateMath:=proc() local theta_d, phi_s, expr, new_expr, new_expr0; use DocumentTools in theta_d:=GetProperty('Dial8','value'); #Get value of theta from Dial phi_s:=GetProperty('Slider8','value'); #Get value of phi from slider expr:= GetProperty('MathContainer12','expression'); new_expr0:=algsubs('theta'=theta_d*Pi/180,expr); # Put value of theta in expression new_expr:=algsubs('phi'=phi_s*Pi/180,new_expr0); # Put value of phi in expression SetProperty('MathContainer13','expression',new_expr); # Update expression end use: end proc:   •  Now change the code in the components to call the function using .   •  Since the code above is only defined there it will need to be run once (but only once) before moving the components. Instead of leaving it here you can add it to the Startup code by clicking  or going to Edit > Startup code.  This code will run every time you open the Math App ensuring that it works right away.   •  The startup code isn't defined in this document to allow progression of these steps.   Make the button initialize the app     •  Since the startup code isn't defined in this document we are going to move this function into the button.   UpdateMath:=proc()   UpdateMath:=proc() local theta_d, phi_s, expr, new_expr, new_expr0; use DocumentTools in theta_d:=GetProperty('Dial9','value'); #Get value of theta from Dial phi_s:=GetProperty('Slider9','value'); #Get value of phi from slider expr:= GetProperty('MathContainer14','expression'); new_expr0:=algsubs('theta'=theta_d*Pi/180,expr); # Put value of theta in expression new_expr:=algsubs('phi'=phi_s*Pi/180,new_expr0); # Put value of phi in expression SetProperty('MathContainer15','expression',new_expr); # Update expression end use: end proc: •  First click the button to rename it, you'll see the  option in the context panel on the right. Then add the code above to the button in the same way as the Slider an Dial (Right click and select Edit Click Code).   Now it is easy to add new components     •  Now if we want to add new components we just have to change the one procedure.  Let's add a Volume Gauge to change the value of A.   •  Click in the cell containing the Dial, the context panel will show the option to Insert a row below the Dial. •  Now drag a Volume Gauge into the new cell.   •  Click in the cell and choose the alignment (from the context panel) that looks best to you. In this case I chose center:     Update the procedure code for the Gauge     •  Add two lines for the volume gauge to get the value and sub it into the expression UpdateMath:=proc() UpdateMath:=proc() local theta_d, phi_s, expr, new_expr, new_expr0; use DocumentTools in theta_d:=GetProperty('Dial11','value'); #Get value of theta from the Dial phi_s:=GetProperty('Slider11','value'); #Get value of phi from the Slider A_g:=GetProperty('VolumeGauge1','value'); #Get value of A from the Guage expr:= GetProperty('MathContainer18','expression'); new_expr0:=algsubs('theta'=theta_d*Pi/180,expr); # Put value of theta in expression new_expr1:=algsubs('phi'=phi_s*Pi/180,new_expr0); # Put value of phi in expression new_expr:=algsubs('A'=A_g,new_expr1); # Put value of A in expression SetProperty('MathContainer19','expression',new_expr); # Update expression end use: end proc: •  Now add UpdateMath();   to the Gauge.   Plot the changing expression     •  Make a procedure to get the value in the second Math Container and plot it   PlotMath:=proc() PlotMath:=proc() local expr, p; use DocumentTools in expr:=GetProperty('MathContainer21','expression'); p:=plot(expr,'t'=-Pi/2..Pi/2,'view'=[-Pi/2..Pi/2,-100..100]): SetProperty('Plot14','value',p) end use: end proc: •  Put this procedure in the Initialize button and the call to it in the components.   Tidy up the app     •  Now that we have an interactive app let's tidy it up a bit.   •  The first thing I'd recommend in your own app is moving the code from the initialize button to startup code. In this document we choose to use the button instead to preserve earlier versions.   •  You can also remove the borders around the components by clicking in the table and selecting "Interior Borders" > "None" and "Exterior Borders" > "None" from the context panel. Now you have a Math App     •  You can upload your Math App to the Maple Cloud to share with others by going to "File" > "Save to Cloud".   •  I'd recommend also including a description of what your app does. You can do this nicely using another table and Text mode.

HowToMathApp.mw

When re-initializing a module (for example, while executing its ModuleApply), you'd likely want to re-initialize all of the remember tables and caches of its procedures. Unfortunately, forget(thismodule) (a direct self reference) doesn't work (I wonder why not?), and it doesn't even tell you that it didn't work. You could do forget(external name of module) (an indirect self reference), but I consider that not robust because you'd need to change it if you change the external name. Even less robust is forget~([procedure 1, procedure 2, submodule 3, ...]). Here's something that works and is robust:

forget~([seq(x, x= thismodule)])[]

Or, using Maple 2019 or later syntax,

forget~([for local x in thismodule do x od])[]

Both of these handle submodules and ignore non-procedures. Both handle both locals and exports.

There is an interesting preprint here, on a method for integration of some pseudo-elliptic integrals.

It was mentioned in a (sci.math.symbolic) usenet thread, which can be accessed via Google Groups here.

Inside the paper, the author mentions that the following is possible for some cases -- to first convert to RootOf form.

Download int_pe.mw

I’m extremely pleased to introduce the newest update to the Maple Companion. In this time of wide-spread remote learning, tools like the Maple Companion are more important than ever, and I’m happy that our efforts are helping students (and some of their parents!) with at least one small aspect of their life.  Since we’ve added a lot of useful features since I last posted about this free mobile app, I wanted to share the ones I’m most excited about. 

(If you haven’t heard about the Maple Companion app, you can read more about it here.) 

If you use the app primarily to move math into Maple, you’ll be happy to hear that the automatic camera focus has gotten much better over the last couple of updates, and with this latest update, you can now turn on the flash if you need it. For me, these changes have virtually eliminated the need to fiddle with the camera to bring the math in focus, which sometimes happened in earlier versions.

If you use the app to get answers on your phone, that’s gotten much better, too. You can now see plots instantly as you enter your expression in the editor, and watch how the plot changes as you change the expression. You can also get results to many numerical problems results immediately, without having to switch to the results screen. This “calculator mode” is available even if you aren’t connected to the internet.  Okay, so there aren’t a lot of students doing their homework on the bus right now, but someday!

Speaking of plots, you can also now view plots full-screen, so you can see more of plot at once without zooming and panning, squinting, or buying a bigger phone.

Finally, if English is not you or your students’ first language, note that the app was recently made available in Spanish, French, German, Russian, Danish, Japanese, and Simplified Chinese. 

As always, we’d love you hear your feedback and suggestions. Please leave a comment, or use the feedback forms in the app or our web site.

Visit Maple Companion to learn more, find links to the app stores so you can download the app, and access the feedback form. If you already have it installed, you can get the new release simply by updating the app on your phone.

Download log_misinterpretation2.mw

One of the forums asked a question: what is the maximum area of a triangle inscribed in a given ellipse x^2/16 + y^2/3 - 1 = 0? It turned out to be 9, but there are infinitely many such triangles. There was a desire to show them in one of the possible ways. This is a complete (as far as possible) set of such triangles.
(This is not an example of Maple programming; it is just an implementation of a Maple-based algorithm and the work of the Optimization package).
MAX_S_TRIAN_ANINATION.mw

This app shows the modeling and simulation of DNA carried out entirely in Maple. The mathematical model is inserted through the combination of trigonometric functions. It shows the graphs of the curvature vs time for its interpretation. Made for engineering and health science students.

MV_AC_R3_UNI_2020.mw

Lenin Araujo Castillo

Ambassador of Maple

I have recently taken some questions about MaplePrimes reputation scores, and coincidentally, there was a discussion about it within MaplePrimes yesterday. I wanted to address these issues, and thought that doing so as a separate post made sense.

Reputation was added back in 2010 as a mechanism to track how fellow users value your contributions, and I believe it has largely worked. It's become a great way to acknowledge the time and effort our members put into the community, and I know that many of you greatly value the scores that you have earned. I also know that it is never fun to see it drop, even by just a few points.

To be clear, there are only two ways to lose reputation:

• If someone upvoted your answer/reply and then later rescinded the upvote
• If someone marked your answer as the "best" answer, and then later changed their vote to another answer

This means you can only lose reputation points if someone undoes an action that gave you points in the first place. This is going to happen occasionally. For example, the user may have voted your answer “best”, but as the discussion continued, someone else posted a different solution that the user felt was even better. So you can expect to see small fluctuations from day to day, but the overall trend will be upward. 

That said, members get understandably concerned when their reputation drops, and want to know why. We have always been able to track when reputation changed, but “why it changed” was obscured. Starting today, we have added enhanced logging for reputation shifts. This will allow us to better diagnose the causes when a member is concerned about a change to their reputation points. As well, in the very unlikely event that there is malicious behavior on MaplePrimes, this will give also us the data we need to take action to protect the community.  

With the new features added to the Student[LinearAlgebra] package I wanted to go over some of the basics on how someone can do Linear Algebra in Maple without require them to do any programming.  I was recently asked about this and thought that the information may be useful to others.
 

This post will be focussed towards new Maple users. I hope that this will be helpful to students using Maple for the first time and professors who want their students to use Maple without needing to spend time learning the language.
 

In addition to the following post you can find a detailed video on using Maple to do Linear Algebra without programming here. You can also find some of the tools that are new to Maple 2020 for Linear Algebra here.

The biggest tools you'll be using are the Matrix palette on the left of Maple, and the Context Panel on the right of Maple.

First you should load the Student[LinearAlgebra] package by entering:

with(Student[LinearAlgebra]);

Once you have a Matrix you can use the context panel on the right to apply a variety of operations to it:

The Student Linear Algebra Menu will give you many linear algebra commands.

You can also access Maple's Tutors from the Tools Menu

Tools > Tutors > Linear Algebra

?Student[LinearAlegbra]

Maple_for_Beginners.mw

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

Over the past weeks, we have spoken with many of our academic customers throughout the world, many of whom have decided to continue their academic years online. As you can imagine, this is a considerable challenge for instructors and students alike. Academia has quickly had to pivot to virtual classrooms, online testing and other collaborative technologies, while at the same time dealing with the stress and uncertainty that has resulted from this crisis.

We have been working with our customers to help them through this time in a variety of ways, but we know that there are still classes and students out there who are having trouble getting all the resources they need to complete their school year. So starting today, Maple Student Edition is being made free for every student, anywhere in the world, until the end of June. It is our hope that this action will remove a barrier for instructors to complete their Maple-led math instruction, and will help make things a bit more simple for everyone.

If you are a student, you can get your free copy of Maple here.

In addition, many of you have asked us about the best way to work on your engineering projects from home and/or teaching and learning remotely during this global crisis. We have put together resources for both that you can use as a starting point, and I invite you to contact us if you have any questions, or are dealing with challenges of your own. We are here to support you, and will be very flexible as we work together through these uncertain times.

I wish you all the best,

Laurent
President & CEO

Download Vectors_and_Spherical_coordinates_in_tensor_notation.mw

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