Posts - MaplePrimes

Choose Your Own Adventure, for Students New to...

by: eithne 2072 Product: Maple

August 29 2017

3 0

I was asked if I would put together a list of top resources to help students who are using Maple for the first time. An awful lot of students will be cracking Maple open in the next few weeks (the ones who are keeping up with their assignments, at least – for others, it sometimes takes little longer :-), so it seemed like a good idea.

So then I had to decide what to do. I know Top N lists are very popular (Ten Things that Will Shock You about Your Math Software!), and there are tons of Maple training resources available to fill such a list without any difficulties. But personally, I don’t always like Top N lists. What are the chances that there are exactly N things you need to know, for nice values of N? And how often you are really interested in all N items? I just want to get straight to the points I care about.

I decided I’d try a matrix. So here you go: a mini “choose your own adventure” guide for getting to know Maple. Pick the row that corresponds to what you want to do, and the column for how you want to do it. All on a single, page, and ad-free!

And best of luck for the new school year.

	I like words	I like videos	Just let me try it
Product Overview	Inside Maple, from the Help menu, select Take a Tour of Maple then click on the Ten Minute Tour button. (Okay, even though I like words, too, you might also want to watch the video in the next column. The whole “picture is worth a thousand words” does have some truth to it, much as I don’t always like to admit it. J)	Watch Clickable Math. Keep in mind that if you prefer to use commands instead of these Clickable Math tools, you can do that too. Personally, I mix and match.	You’ll figure it out.
Getting Started Info	Read the Maple Quick Start Tutorial Guide, as a PDF, or from the Help system. To access this guide from within Maple, start Maple, click on the Getting Started icon the left, then select the Quick Start Guide (first icon in the second row).	Watch the Maple Quick Start Tutorial Video.	The most important things to remember are Right click on your math expression to bring up a menu of things you can do, like plotting or integrating or solving your expression If you have just entered an exponent or the denominator of a fraction, use the right arrow key to get out of it.
How do I? Essentials	Look at the “How do I” section of the Maple Portal (Start Maple, click on the Getting Started icon, click on the Maple Portal icon; or search for “MaplePortal” in the help system). Also look at the Maple Portal for Students, using the button from the Maple Portal.	Check out the dozens of videos in the Maple Training Video collection.	You can do a lot with the context menus and the various tools you’ll find on the Tools menu. But when in doubt, look at the list of “How do I” tasks from the Maple Portal described in the “words” column and pull out what you need from there.
What now?	The help system is your friend. Not only does it have help pages for every feature and every command, but it includes both the Maple User Manual and the Maple Programming Guide (also available as PDFs).	Check out the collection of videos on the Maplesoft YouTube channel. (And the help system is your friend, too. We can’t make videos to cover every last thing, and if we did, you wouldn’t have time to watch them all!)	Maple comes with many examples and applications you can look at and modify. You can browse through the Start page resources, or search for “examples,index” in the help system to see the full list. And yes, the help system is your friend, too. But don’t worry, no one is going to make you read the manual.

Report Generation with Experimental Data Received...

by: Ramakrishnan 404 Product: Maple 2017

August 28 2017

3 0

Download New_ReportGeneration_with_ExcelData.mw

Dear Users,

I have received a congratulations from a Mapleprime user for my post (on Finite Element Analysis - Basics) posted two years earlier. I did not touch that subject for two years for obvious reasons. Now that a motivation has come, I have decided to post my second application using embedded components. This I was working for the past two years and with the support from Maplesoft technical support team and Dr.RobertLopez. I thank them here for this workbook has come out well to my satisfaction and has given me confidence to post it public.

About the workbook

I have tried to improve the performance of a 2-Stroke gasoline engine to match that of a four stroke engine by using exhaust gas recirculation. Orifice concept is new and by changing the orifice diameter and varying the % of EGR, performance was monitored and data stored in Excel workbook. These data can be imported to Maple workbook by you as you want for each performance characteristic. The data are only my experimental and not authentic for any commercial use.

This Maple workbook generates curves from data for various experiments conducted by modifying the field variables namely Orifice diameter, % Exhaust gas Recirculation and Heat Exchanger Cooling. Hence optimum design selection is possible for best performance.

Thanks for commenting, congratulating or critisising!! All for my learning and improving my Maple understanding!!

Displacement and distance traveled with vectors

by: Lenin Araujo Castillo 1790 Product: Maple 18

August 28 2017

2 2

In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.

Displacement_and_distance_traveled_with_vectors.mw Updated

Displacement_and_distance_traveled_with_vectors_updated_2020.mw

Video

https://www.youtube.com/watch?v=jOcKYZ5EEM0

Lenin Araujo C

Ambassador of Maple

Shortcut in Vectors for Engineering

by: Lenin Araujo Castillo 1790 Product: Maple 18

August 25 2017

2 0

Here in this video you can observe the correct insertion of vectors; Making use of the keyboard, ascii code and tool palette of our Maple program. As our worksheet is very large, I made the explanation in two parts; I recommend that you observe this first part of performing any execution on your Maple worksheet. You can contrast your results with the apps also made in this software. In Spanish.

Shortcut_in_Vectors_for_Engineering.mw

Movie # 01

https://www.youtube.com/watch?v=EJtAli54q_A

Movie # 02

https://www.youtube.com/watch?v=m-JUmhkbWI8

Lenin Araujo Castillo

Ambassador of Maple

Kitonum's IntOverDomain Deconstructed

by: rlopez 3025 Product: Maple

August 24 2017

8 6

On 5/July/2017, Kitonum responded to the 3/July/2017 MaplePrimes question "How to perform double integration over subdomain" by providing code for a procedure IntOverDomain that implements Green's theorem applied to a planar region whose boundary is a simple, closed, rectifiable, oriented curve (SCROC by some authors).

I was intrigued. First, this is a significant extension of existing Maple functionalities. Second, the implementation admits boundaries defined piecewise with sections defined parametrically; or sections that are polygonal lines defined by a list of nodes.

But how was the line integral around such boundaries coded? In the worksheet "IntOverDomain_Deconstructed," I summarize the existing Maple functionality for implementing iterated double integrals over specified domains, then analyze how Kitonum coded Green's theorem as an extension of Maple's capabilities. After recognizing the great coding skills of Kitonum, I conclude with a short wishlist of related extensions that I would like to see added to Maple in the future.

Download the worksheet: IntOverDomain_Deconstructed.mw

A new and efficient code in Maple for Boundary...

by: Dr. Venkat Subramanian 431 Product: Maple

August 23 2017

5 10

A new code based on higher derivative method has been implemented in Maple. A sample code is given below and explained. Because of the symbolic nature of Maple, this method works very well for a wide range of BVP problems.

The code solves BVPs written in the first order form dy/dx = f (Maple’s dsolve numeric converts general BVPs to this form and solves).

The code can handle unknown parameters in the model if sufficient boundary conditions are provided.

This code has been tested from Maple 8 to Maple 2017. For Digits:=15 or less, this code works in all of the Maple versions tested.

Most problems can be solved with Digits:=15 with atol = 1e-10 or so. This code can be used to get a tolerance value of 1e-20 or any high precision as needed by changing the number of Digits accordingly. This may be needed if the original variables are not properly sacled. With arbitrarily high Digits, the code fails in Maple 18 or later version, etc because Maple does not support SparseDirect Solver at high precision in some of the versions (hopefuly this bug can be removed in the future versions).

For simple problems, Maple’s dsolve/numeric is superior to the code developed as it is implemented in hardware floats. For large scale problems and stiff problems, the method developed is much more superior to Maple and comparable to (and often times better than) state of the art codes for BVPs - bvp4c (MATLAB), COLSYS,TWPBVP, etc.

The code, as written, cannot be used for problems with a singularity at end points (doable in the future). In addition, mixed boundary conditions are not supported in this version of the code (for example, y1(1)=y2(0)). Future updates will include the application of this approach for DAE-BVPs, currently not supported by Maple’s dsolve/numeric command.

A paper has been submitted to JCAM. I welcome feedback on the code and solicit input from Mapleprimes members if they are able to test (and break this code) for any BVP.

PDF of the paper submitted, example maple code and the solver as a text file needed are uploaded here. Additional examples are hosted on my website at http://depts.washington.edu/maple/HDM.html

>

##################################################################################

Troesch's problem
This is an inherently unstable, difficult, nonlinear, two-point BVP formulated by Weibel and Troesch that describes the confinement of a place column by radiation pressure. Increasing epsilon increases the stiffness of the ODE.
1. E.S. Weibel, On the confinement of a plasma by magnetostatic fields, Phys. Fluids. 2 (1959) 52-56.
2. B. Troesch, A simple approach to a sensitive two-point boundary value problem, J. Comput. Phys. 21 (1976) 279-290.

Introduction
The package HDM solves boundary value problems (BVPs) using higher derivative methods (HDM) in Maple®. We explain how to solve BVPs using this package. HDM can numerically solve BVPs of ordinary differential equations (ODEs) of the form shown is the fowllowing example.

###################################################################################

>

Reset the program to clear the memory from previous execution command.

>

restart:

>

Read the txt file which contains the HDM solver for BVPs.

>	read("HDM.txt");

>

Declare the precision for the entire Maple® sheet.

>	Digits:=15;

(1)

>

Enter the first-order ODEs into EqODEs list.

>	EqODEs:=[diff(y1(x),x)=y2(x),diff(y2(x),x)=epsilonsinh(epsilony1(x))];

(2)

>

Define the left boundary condition (bc1), and the right boundary condition (bc2). One should collect all the terms in one side.

>	bc1:=evalf([y1(x)]);

(3)

>	bc2:=evalf([y1(x)-1]);

(4)

>

Define the range (bc1 to bc2) of this BVP.

>	Range:=[0.,1.];

(5)

>

List any known parameters in the list.

>	pars:=[epsilon=2];

(6)

>

List any unknown parameters in the list. When there is no unknown parameter, use [ ].

>	unknownpars:=[];

(7)

>

Define the initial derivative in nder (default is 5 for 10th order) and the number of the nodes in nele (default is 10 and distributed evenly across the range provided by the user). The code adapts to increase the order. For many problems, 10th order method with 10 elements are sufficient.

>	nder:=5;nele:=10;

(8)

>

Define the absolute and relative tolerance for the local error. The error calculation is done based on the norm of both the 9th and 10th order simulation results.

>	atol:=1e-6;rtol:=atol/100;

(9)

>

Call HDMadapt procedure, input all the information entered above and save the solution in sol. HDMadapt procedure does not need the initial guess for the mesh.

>	sol:= HDMadapt(EqODEs,bc1,bc2,pars,unknownpars,nder,nele,Range,atol,rtol):

>

Present some details of the solution.

>	sol[4]; # final derivative

(10)

>	sol[5]; # Maximum local RMSE

(11)

>

Store the dimension of the solution (after adjusting the mesh) to NN.

>	NN:=nops(sol[3])+1;

(12)

>

Plot the interested variable (the ath ODE variable will be sol[1][i+NN*(a-1)] )

>	node:=nops(EqODEs); odevars:=select(type,map(op,map(lhs,EqODEs)),'function');

(13)

>	xx:=Vector(NN):

>	xx[1]:=Range[1]:

>	for i from 1 to nops(sol[3]) do xx[i+1]:=xx[i]+sol[3][i]: od:

>	for j from 1 to node do plot([seq([xx[i],rhs(sol[1][i+NN*(j-1)])],i=1..NN)],axes=boxed,labels=[x,odevars[j]],style=point); end do;

>

Download Example_3_Troesch.mws

The patch package project

by: Christopher2222 6035 Product: Maple

August 19 2017

0 4

Was just pondering this idea and posted this in the post topic for discussion.

Each Maple finished version of Maple may still have certain bugs that will not be updated for that version, so I am suggesting (I think anyone could implement it) that if there is a workaround, one could wrap it up in something I would call a patch package updateable by us users we could update here on mapleprimes. It would be good for people who haven't upgraded or can't upgrade due to costs etc...

For example, there was recent issue with pdsolve that was fixed quite quickly in the seperate updateable Physics package. Things could be done similarily that might work with other workarounds using this patch package idea.

If anyone thinks this is good or even viable idea then lets implement it. I envisioned it with just this one rule to follow - the name of the patch package would reflect the version we are patching (ie. with(patch12) or with(patch2016) for Maple 12 and Maple 2016 respectively etc...) We could make these patch packages available in this post or start another.

As I said, I'm just throwing the idea out there. Thoughts?

Issues with integrating exp and trigs

by: Bart 117 Product: Maple 2017

August 17 2017

1 1

There seems to be a bug with improper integration:

integrate(cos(t)*exp(-x*t),t=-infinity..infinity)

gives

0

Substituting any number for x, or assuming x >= 0 (or x<=0) does give the correct result,

The problem also persists when assuming x>-1 (or x>-Maple_floats(MIN_FLOAT))

a look at recursive functions

by: Matt C Anderson 190 Product: Maple 13

August 14 2017

1 0

Hi MaplePrimes,

another_recursive_sequence.mw

another_recursive_sequence.pdf

These two files have the same content. One is a .pdf and the other is a Maple Worksheet. I explore integer sequences of the form -

a(r) = c*a(r-1)+d*a(r-2) with a(1) and a(2) given.

Some of these sequences are in (the Online Encyclopedia of Integer Sequences) OEIS.org and some are not. If we restrict c to 1 and assume that a(1)=1 and a(2) = 2 we have the parameter d remaining. See additional webpage -

https://sites.google.com/site/recrusivefunction/

Let me know if you like the code.

Regards,

Matt

Books free of maple

by: Lenin Araujo Castillo 1790 Product: Maple 2017

August 11 2017

2 4

Books free. Like!!!

Lenin Araujo Castillo

Plot of Position Vector in Maple

by: Lenin Araujo Castillo 1790 Product: Maple 18

August 07 2017

2 0

As you can see this app performs the trace of a given path r (t), then locate the position vector in a specific time. It also graphs the velocity vector, acceleration, Tangential and Normal unit vectors, along with the Binormal. Very good app developed entirely in Maple for our engineering students.

Plot_of_Position_Vector_UPDATED.mw

https://youtu.be/OzAwShHHXq8

Lenin Araujo Castillo

Ambassador of Maple

Option in Maple to treat numbers within sin,...

by: Christopher2222 6035 Product: Maple

August 04 2017

0 6

It seems a large number of people, when initially using maple, wrongly deduce that for example sin(60) is the sin of 60 degrees and not the sin of 1/3 Pi radians. I believe mathematica's default is degrees. When a student compares an expression to another but forgets to realize a value is read as radians and not degrees they are perplexed when Maple returns false and Mathematica returns true.

As a suggestion, under tools->options allow a user to be able to change how maple reads values within trigonometric funtions as either radians or degrees.

Most times when someone computes the sin(60) what they really mean in Maple..
is sin(convert(60 degrees, radians))

ACA 2017 - The Appell doubly hypegeometric Functio...

by: ecterrab 14540 Product: Maple

August 02 2017

3 0

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra -2017" . It was a very interesting event. This fifth presentation, about "The Appell doubly hypergeometric functions", describes a very recent project I've been working at Maple, i.e. the very first complete computational implementation of the Appell doubly hypergeometric functions. This work appeared in Maple 2017. These functions have a tremendous potential in that, at the same time, they have a myriad of properties, and include as particular cases most of the existing mathematical language, and so they have obvious applications in integration, differential equations, and applied mathematics all around. I think these will be the functions of this XXI century, analogously to what happened with hypergeometric functions in the previous century.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.

The four double-hypergeometric Appell functions,

a complete implementation in a computer algebra system

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

Abstract:
The four multi-parameter Appell functions, AppellF1 , AppellF2 , AppellF3 and AppellF4 are doubly hypergeometric functions that include as particular cases the 2F1 hypergeometric and some cases of the MeijerG function, and with them most of the known functions of mathematical physics. Appell functions have been popping up with increasing frequency in applications in quantum mechanics, molecular physics, and general relativity. In this talk, a full implementation of these functions in the Maple computer algebra system, including, for the first time, their numerical evaluation over the whole complex plane, is presented, with details about the symbolic and numerical strategies used.

Appell Functions (symbolic)

The main references:

•	P. Appel, J.Kamke de Feriet, "Fonctions hypergeometriques et Hyperspheriques", 1926

•	H. Srivastava, P.W. Karlsson, "Multiple Gaussian Hypergeometric Series", 1985

•	24 papers in the literature, ranging from 1882 to 2015

	Definition and Symmetries

	Polynomial and Singular Cases

	Single Power Series with Hypergeometric Coefficients

	Analytic Extension from the Appell Series to the Appell Functions

	Euler-Type and Contiguity Identities

	Appell Differential Equations

	Putting all together

	Problem: some formulas in the literature are wrong or miss the conditions indicating when are they valid (exchange with the Mathematics director of the DLMF - NIST)

Appell Functions (numeric)

Goals

•	Compute these Appell functions over the whole complex plane

•	Considering that this is a research problem, implement different methods and flexible optional arguments to allow for: a) comparison between methods (both performance and correctness), b) investigation of a single method in different circumstances.

•	Develop a computational structure that can be reused with other special functions (abstract code and provide the main options), and that could also be translated to C (so: only one numerical implementation, not 100 special function numerical implementations)

Limitation: the Maple original evalf command does not accept optional arguments

The cost of numerically evaluating an Appell function

•	If it is a special hypergeometric case, then between 1 to 2 hypergeometric functions

•	Next simplest case (series/recurrence below) 3 to 4 hypergeometric functions plus adding somewhat large formulas that involve only arithmetic operations up to 20,000 times (frequently less than 100 times)

•	Next simplest case: the formulas themselves are power series with hypergeometric function coefficients; these cases frequently converge rapidly but may involve the numerical evaluation of up to hundreds of hypergeometric functions to get the value of a single Appell function.

Strategy for the numerical evaluation of Appell functions (or other functions ...)

The numerical evaluation flows orderly according to:

1) check whether it is a singular case

2) check whether it is a special value

3) compute the value using a series derived from a recurrence related to the underlying ODE

4) perform an sum using an infinite sum formula, checking for convergence

5) perform the numerical integration of the ODE underlying the given Appell function

6) perform a sequence of concatenated Taylor series expansions

	Examples

	Series/recurrence

	Numerical integration of an underlying differential equation (ODEs and dsolve/numeric)

	Concatenated Taylor series expansions covering the whole complex plane

Subproducts

	Improvements in the numerical evaluation of hypergeometric functions

	Evalf: an organized structure to implement the numerical evaluation of special functions in general

	To be done

Download Appell_Functions.mw
Download Appell_Functions.pdf

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

ACA 2017 - The FunctionAdvisor, beyond a database...

by: ecterrab 14540 Product: Maple

August 02 2017

2 1

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra -2017" . It was a very interesting event. This fourth presentation, about "The FunctionAdvisor: extending information on mathematical functions with computer algebra algorithms", describes the FunctionAdvisor project at Maple, a project I started working during 1998, where the key idea I am trying to explore is that we do not need to collect a gazillion of formulas but just core blocks of mathematical information surrounded by clouds of algorithms able to derive extended information from them. In this sense this is also unique piece of software: it can derive properties for rather general algebraic expressions, not just well known tabulated functions. The examples illustrate the idea.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.

The FunctionAdvisor: extending information on mathematical functions

with computer algebra algorithms

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

Abstract:

A shift in paradigm is happening, from: encoding information into a database, to: encoding essential blocks of information together with algorithms within a computer algebra system. Then, the information is not only searchable but can also be recreated in many different ways and actually used to compute. This talk focuses on this shift in paradigm over a real case example: the digitizing of information regarding mathematical functions as the FunctionAdvisor project of the Maple computer algebra system.

	The FunctionAdvisor (basic)

Beyond the concept of a database

" Mathematical functions, are defined by algebraic expressions. So consider algebraic expressions in general ..."

	Formal power series for algebraic expressions

	Differential polynomial forms for algebraic expressions

	Branch cuts for algebraic expressions

	The n^th derivative problem for algebraic expressions

	Conversion network for mathematical and algebraic expressions

	References

Download FunctionAdvisor.mw

Download FunctionAdvisor.pdf

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

ACA 2017 - Computer Algebra in Theoretical Physics...

by: ecterrab 14540 Product: Maple

August 02 2017

5 1

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra -2017" . It was a very interesting event. This third presentation, about "Computer Algebra in Theoretical Physics", describes the Physics project at Maplesoft, also my first research project at University, that evolved into the now well-known Maple Physics package. This is a unique piece of software and perhaps the project I most enjoy working.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.

Computer Algebra in Theoretical Physics

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

Abstract:

Generally speaking, physicists still experience that computing with paper and pencil is in most cases simpler than computing on a Computer Algebra worksheet. On the other hand, recent developments in the Maple system have implemented most of the mathematical objects and mathematics used in theoretical physics computations, and have dramatically approximated the notation used in the computer to the one used with paper and pencil, diminishing the learning gap and computer-syntax distraction to a strict minimum.

In this talk, the Physics project at Maplesoft is presented and the resulting Physics package is illustrated by tackling problems in classical and quantum mechanics, using tensor and Dirac's Bra-Ket notation, general relativity, including the equivalence problem, and classical field theory, deriving field equations using variational principles.

... and why computer algebra?

We can concentrate more on the ideas instead of on the algebraic manipulations

We can extend results with ease

We can explore the mathematics surrounding a problem

We can share results in a reproducible way

	Representation issues that were preventing the use of computer algebra in Physics

Classical Mechanics

	*Inertia tensor for a triatomic molecule

Quantum mechanics

	*The quantum operator components of satisfy

*Unitary Operators in Quantum Mechanics

	*Eigenvalues of an unitary operator and exponential of Hermitian operators

*Properties of unitary operators

Consider two set of kets and , each of them constituting a complete orthonormal basis of the same space.

	*Verify that , maps one basis to the other, i.e.:

	*Show that is unitary

	*Show that the matrix elements of in the and basis are equal

	Show that and have the same spectrum (eigenvalues)

	Schrödinger equation and unitary transform

	Translation operators using Dirac notation

	*Quantization of the energy of a particle in a magnetic field

Classical Field Theory

	The field equations for the model

	*Maxwell equations departing from the 4-dimensional Action for Electrodynamics

	*The Gross-Pitaevskii field equations for a quantum system of identical particles

General Relativity

	Exact Solutions to Einstein's Equations

	*"Physical Review D" 87, 044053 (2013)

	The Equivalence problem between two metrics

	*On the 3+1 split of the 4D Einstein equations

	Tetrads and Weyl scalars in canonical form

Download Physics.mw

Download Physics.pdf

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

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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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Choose Your Own Adventure, for Students New to...

Report Generation with Experimental Data Received...

Displacement and distance traveled with vectors

Shortcut in Vectors for Engineering

Kitonum's IntOverDomain Deconstructed

A new and efficient code in Maple for Boundary...

The patch package project

Issues with integrating exp and trigs

a look at recursive functions

Books free of maple

Plot of Position Vector in Maple

Option in Maple to treat numbers within sin,...

ACA 2017 - The Appell doubly hypegeometric Functio...

ACA 2017 - The FunctionAdvisor, beyond a database...

ACA 2017 - Computer Algebra in Theoretical Physics...

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