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

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

A way of cutting holes on an implicit plot. This is from the field of numerical parameterization of surfaces. On the example of the surface  x3 = 0.01*exp (x1) / (0.01 + x1^4 + x2^4 + x3^4)  consider the approach to producing holes. The surface is locally parameterized in some suitable way and the place for the hole and its size are selected. In the first example, the parametrization is performed on the basis of the section of the initial surface by perpendicular planes. In the second example, "round"  parametrization. It is made on the basis of the cylinder and the planes passing through its axis. Holes can be of any size and any shape. In the figures, the cut out surface sections are colored green and are located above their own holes at an equidistant to the original surface.
HOLE_1.mwHOLE_2.mw

In maple plot, very many symbols like, diamond, star, solidcircle are available. Many of them may have been used also for teaching purposes.

Recently, someone encountered the need to draw graphs with arrowheads and many solutions may be available as well. But it requires a thorough understanding of maple's features which are infinitely many. My feeling was that an arrow symbol also could be added in the symbol feature so that the option can be used as a plot point in the graph at the graph end points very easily. It can be just like adding a solidbox symbol at any point on the curve.

Hope my suggestions are in order.

Thanks.

Ramakrishnan V

The following puzzle prompted me to write this post: "A figure is drawn on checkered paper that needs to be cut into 2 equal parts (the cuts must pass along the sides of the squares.)" (parts are called equal if, after cutting, they can be superimposed on one another, that is, if one of them can be moved, rotated and (if need to) flip so that they completely coincide) (see the first picture below). 
I could not solve it manually and wrote a procedure called  CutTwoParts  that does this automatically (of course, this procedure applies to other similar puzzles). This procedure uses my procedure  AreIsometric  published earlier  https://www.mapleprimes.com/posts/200157-Testing-Of-Two-Plane-Sets-For-Isometry  (for convenience, I have included its text here). In the procedure  CutTwoParts  the figure is specified by the coordinates of the centers of the squares of which it consists).

I advise everyone to first try to solve this puzzle manually in order to feel its non-triviality, and only then load the worksheet with the procedure for automatic solution.


For some reason, the worksheet did not load and I was only able to insert the link.

Cuttings.mw



 

With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.

First_equilibrium_condition.zip

Lenin AC

Ambassador of Maple

When discussing Maple programming, we often refer to for-loops, while-loops, until-loops, and do-loops (the latter being an infinite loop). But under the hood, Maple has only two kinds of loop, albeit very flexible and powerful ones that can combine the capabilities of any or all of the above, making it possible to write very concise code in a natural way.

Before looking at some actual examples, here is the formal definition of the loops' syntax, expressed in Wirth Syntax Notation, where "|" denotes alternatives, "[...]" denotes an optional part, "(...)" denotes grouping, and Maple keywords are in boldface:

[ for  ] [ from  ] [ by  ] [ to  ]
    [ while  ]
do
    
( end do | until  )

[ for  [ , variable ] ] in 
    [ while  ]
do
    
( end do | until  )

In the first form, every part of the loop syntax is optional, except the do keyword before the body of the loop, and either end do or an until clause after the body. (For those who prefer it, end do can also be written as od.) In the second form, only the in clause is required.

The simplest loop is just:

do
    
end do

This will repeat the forever, unless a break or return statement is executed, or an error occurs.

One or two loop termination conditions can be added:

• A while clause can be written before the do, specifying a condition that is tested before each iteration begins. If the condition evaluates to false, the loop ends.
• An until clause can be written instead of the end do, specifying a condition that is tested after each iteration finishes. If the condition evaluates to true, the loop ends.

A so-called for-loop is just a loop to which iteration clauses have been added. These can take one of two forms:

• Any combination of for (with a single variable), from, by, and to clauses. The last three can appear in any order.
• A for clause with one or two variables, followed by an in clause.

The following for-loop executes 10 times:

for  from 1 to 10 do
    
end do

However, if the doesn't depend on the value of , both the for and from clauses can be omitted:

to 10 do
    
end do

In this case, Maple supplies an implicit for clause (with an inaccessible internal variable), as well as an implicit "from 1" clause. In fact, all of the clauses are optional, and the infinite loop shown earlier is understood by Maple in exactly the same way as:

for  from 1 by 1 to infinity while true do
    
until false

When looping over the contents of a container, such as a one-dimensional array A, there are several possible approaches. The one closest to how it would be done in most other programming languages is (this example and those that follow can be copied and pasted into a Maple session):

 := Array([,"foo",42]);
for  from lowerbound() to upperbound() do
    print([],[])
end do;

If only the entries in the container are of interest, it is not necessary to loop over the indices. Instead, one can write:

 := Array([,"foo",42]);
for  in  do
    print()
end do;

If both the indices and values are needed, one can write:

 := Array([,"foo",42]);
for ,  in  do
    print([],)
end do;

For a numerically indexed container such as an Array, this is equivalent to the for-from-to example. However, this method also works with arbitrarily indexed containers such as a Matrix or table:

 := LinearAlgebra:-RandomMatrix(2,3);
for ,  in  do
    print([],)
end do;

 := table({1="one","hello"="world",=42});
for ,  in eval() do
    print([],)
end do;

(The second example requires the call to eval due to last-name evaluation of tables in Maple, a topic for another post.)

As with a simple do-loop, a while and/or until clause can be added. For example, the following finds the first negative entry, if any, in a Matrix (traversing the Matrix in storage order):

 := LinearAlgebra:-RandomMatrix(2,3);
for ,  in  do
    # nothing to do here
until  < 0;
if  < 0 then
    print([],)
end if;

Notice that the test, < 0, is written twice, since it is possible that the Matrix has no negative entry. Another way to write the same loop but only perform the test once is as follows:

 := LinearAlgebra:-RandomMatrix(2,3);
for ,  in  do
    if  < 0 then
	print([],);
	break
    end if;
end do;

Here, we perform the test within the loop, perform the desired processing on the found value (just printing in this case), and use a break statement to terminate the loop.

Sometimes, it is useful to abort the current iteration of the loop and move on to the next one. The next statement does exactly that. The following loop prints all the indices but only the positive values in a Matrix:

 := LinearAlgebra:-RandomMatrix(2,3);
for ,  in  do
    print(=[]);
    if  < 0 then
	next
    end if;
    print(=);
end do;

(Note that a simple example like this would be better written by enclosing the printing of the value in an if-statement instead of using next. The latter is generally only used if the former is not possible.)

Maple's loop statements are very flexible and powerful, making it possible to write loops with complex combinations of termination conditions in a concise yet readable way. The ability to use while and/or until in conjunction with for means that break statements are often unnecessary, further improving clarity.

The binary search algorithm is used to obtain the index of a given number by dividing the search bound in half over iteration. If the value entered in the array a message pop up telling that ''value is not present in the array". Please see the code. 
 

Download BINARY_SEARCH1.mw

FeynmanDiagrams_and_the_Scattering_Matrix.PDF

FeynmanDiagrams_and_the_Scattering_Matrix.mw

FeynmanDiagrams_-_help_page.mw

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

Application of MapleSim in Science and Engineering: a simulationbased approach

In this research work I show the methods of embedded components together with modeling and simulation carried out with Maple and MapleSim for the main areas of science and engineering (mathematics, physics, civil, mechanical etc); These two latest scientific softwares belonging to the company Maplesoft. Designed to be generated and used by teachers of education, as well as by university teachers and engineers; the results are highly optimal since the times saved in calculations are invested in analyzes and interpretations; among other benefits; in this way we can use our applications in the cloud since web technology supports Maple code with procedural and component syntax.

FAST_UNT_2020.pdf

kinematics_curvilinear_updated_2020.mw

Lenin AC

Ambassador of Maple

 The Joint Mathematics Meetings are taking place next week (January 1518) in Denver, CO. This meeting is a must-attend for anyone interested in learning about innovative mathematical research, advancing mathematical achievement, providing the communication and tools to progress in the field, encouraging mathematical research, and connecting with the mathematical community.

Maplesoft will at booth #1100  in the networking area (located just outside the exhibit hall doors). Stop by our booth or the networking area to chat with me and other members of the Maplesoft team, pick up some free Maplesoft swag or win some prizes. We’ve got some good ones!

There are also several interesting Maple-related talks and events happening this week. 

Attend our Workshop - Maple: Math Software for Teaching, Learning and Research

Thursday January 16th, 2020

Centennial Ballroom AHYATT Denver Colorado

Catered Reception: 6:00PM6:30PM
Training Workshop: 6:30PM8:00PM

Are you new to the Maple world and interested in finding out what Maple can do for you? Are you an old hand at Maple but curious about the many new features we’ve added in the past few years? Come join us for an interactive workshop that will guide you through Maple’s capabilities, with an emphasis on our latest additions.

The topics we’ll be covering include:

• Our natural math notation for input and output
• Tools for creating interactive documents that incorporate math, text and graphics
• An overview of our vast library containing packages for advanced mathematics research scientific and engineering applications
• A brief look at Maple’s powerful programming language|
• Online and mobile tools that augment the Maple experience

Register herewww.com/ 

We are also 3 show floor talks, at the end of Aisle 600 inside the exhibits:

If you are attending the Joint Math Meetings and plan on presenting anything on Maple, please let me know and I'll add it to our list!

See you there!

Charlotte 

Here is two solutions with Maple of the problem A2 of  Putnam Mathematical Competition 2019 . The first solution is entirely based on the use of the  geometry  package; the second solution does not use this package. Since the triangle is defined up to similarity, without loss of generality, we can set its vertices  A(0,0) , B(1,0) , C(x0,y0)  and then calculate the parameters  x0, y0  using the conditions of the problem. 

Download Putnam.mw