Posts - MaplePrimes

correct the API for dsolve with series option

by: nm 10219

January 17 2015

1 6

I do not think the current API for dsolve when asking for series solution is done right. If one wants to obtain a series solution for an ODE, but wants different order than the default 6, now one must set this value using a global setting before making the call, like this:

eq:=diff(y(x),x$2)+y(x)=0;
Order:=10;
dsolve({eq,y(0)=1,D(y)(0)=0},y(x),type='series');

It would be better if options to calls are passed along with the other parameters in the call itself. Something like

dsolve({eq,y(0)=1,D(y)(0)=0},y(x),type='series',order=10);

This should also apply to any command that takes Order, such as series(cos(x),x=0,order=10);

Passing options and values to functions using global and environment variables is not safe and not a good way to go about it as it can cause programming errors.

Hello Everyone, I am new one in the community..

by: kakballi 10

January 11 2015

1 1

Hello Everyone, I am new one in the community..

Programming Embedded Components for Graphics in...

by: Lenin Araujo Castillo 1790 Product: Maple 18

January 08 2015

2 0

In this work we show you what to do with the programming of Embedded Components applied to graphics in the Cartesian plane; from the visualization of a point up to three-dimensional objects and also using the Maple language generare own interactive applications for touch screen technology in mobile devices techniques. Given that computers use multicore and designed algorithms that solve calculus problems with very good performance in time; this brings programming to more complex mathematical structures such as in the linear algebra, analytic geometry and advanced methods in numerical analysis. The graphics will show real-time results for the correct use of the parallel programming undertook to bear the procedural technique is well suited to the data structure, curves and surfaces. Interaction in a single graphical container allowing the teaching and / or research the rapid change of parameters; giving a quick interpretation of the results.

FAST_UNT_2015.pdf

Programming_Embedded_Components_for_Graphics_in_Maple.mw

Atte.

L.Araujo C.

Physics Pure

Computer Science

Top 10 Webinars of 2014

by: kkoserski 230 Products: Maple , MapleSim

January 06 2015

2 1

Happy New Year! Now that 2014 is behind us, I thought it would be interesting to look back on the year and recap our most popular webinars. I’ve gathered together a list of the top 10 academic webinars from 2014 below. All these webinars are available on-demand, and you can watch the recording by clicking on the webinar titles below.

-----------------------------------------------

See What’s New in Maple 18 for Educators

In this webinar, an expert from Maplesoft will explore new features in Maple 18, including improved tools for developing quizzes, enhanced tools for visualizations, updated user interface, and more.

Introduction to Teaching Calculus with Maple: A Complete Kit

During this webinar you will learn how to boost student engagement with highly interactive lectures, reinforce concepts with built-in “what-if” explorations, consolidate learning with carefully-constructed homework questions, and more.

Maplesoft Solutions for Math Education

In this webinar, you will learn how Maple, The Möbius Project, and Maplesoft’s testing and assessment solutions are redefining mathematics education.

Teaching Concepts with Maple

This webinar will demonstrate the Teaching Concepts with Maple section of our website, including why it exists and how to use it to help students learn concepts more quickly and with greater insight and understanding.

Revised Calculus Study Guide - A Clickable-Calculus Manual

This webinar will provide an overview of the Revised Calculus Study Guide, the most complete guide to how Maple can be used in teaching and learning calculus without first having to learn any commands.

Clickable Engineering Math: Interactive Engineering Problem Solving

In this webinar, general engineering problem-solving methods are presented using clickable techniques in the application areas of mechanics, circuits, control, and more.

Hollywood Math 2

In this second installment of the Hollywood Math webinar series, we will present some more examples of mathematics being used in Hollywood films and popular hit TV series.

Robotics Design in Maple and MapleSim

In this webinar, learn how to quickly create multi-link robots by simply defining DH parameters in MapleSim. After a model is created, learn to extract the kinematic and dynamic equations symbolically in Maple.

Introduction to Maple T.A. 10

This webinar will demonstrate the key features of Maple T.A. from both the instructor and student viewpoint, including new features in Maple T.A. 10.

The Möbius Project: Bringing STEM Courses Online

View this presentation to better understand the challenges that exist today when moving a STEM course online and to find out how the Maplesoft Teaching Solutions Group can help you realize your online course vision.

-----------------------------------------------

Are there any topics you’d like to see us present in 2015? Make sure to leave us a comment with your ideas!

Kim

January’s Featured Live Webinars

by: kkoserski 230

January 05 2015

0 0

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinars we think may be of interest to the MaplePrimes community. For the complete list of upcoming webinars, visit our website.

Creating Questions in Maple T.A. – Part #2

This presentation is part of a series of webinars on creating questions in Maple T.A., Maplesoft’s testing and assessment system designed especially for courses involving mathematics. This webinar, which expands on the material offered in Part 1, focuses on using the Question Designer to create many standard types of questions. It will also introduce more advanced question types, such as sketch, free body diagrams, and mathematical formula.

The third and final webinar will wrap up the series with a demonstration of math apps and Maple-graded questions.

To join us for the live presentation, please click here to register.

Clickable Calculus Series – Part #1: Differential Calculus

In this webinar, Dr. Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Differential Calculus.

Clickable Calculus™, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

To join us for the live presentation, please click here to register.

Draghilev’s method, F(x)=0. Animation.

by: one man 1330 Product: Maple 15

January 02 2015

0 13

D_Method.mw

The classical Draghilev’s method. Example of solving the system of two transcendental equations. For a single the initial approximation are searched 9 approximate solutions of the system.
(4*(x1^2+x2-11))*x1+2*x1+2*x2^2-14+cos(x1)=0;
2*x1^2+2*x2-22+(4*(x1+x2^2-7))*x2-sin(x2)=0;
x01 := -1.; x02 := 1.;

3d model of a cam mechanism. Animation.

by: one man 1330

December 28 2014

0 3

Equation: ((x1+.25)^2+(x2-.2)^2-1)^2+(x3-.1)^2-.999=0;

a_cam_3D.mw

Cam mechanism. Animation.

by: one man 1330

December 27 2014

2 0

Cam mechanism animation. Equation: (xx2-1.24)^10+5*(xx1-.66)^10-9.=0
a_cam.mw

Transformation with animation

by: one man 1330

December 26 2014

4 0

Transformation and rotation.

transformation.mw

Putnam done with Maple

by: Markiyan Hirnyk 7799 Product: Maple

December 26 2014

2 35

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the world (regardless of the students' nationalities). One can see some problems and answers here. I find it remarkable that a lot of these problems can be done with Maple. Here is a sample (The DirectSearch package should be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=101333 and installed in your Maple.).

rsolve({a(k)=a(k-1)^2-2,a(0)=5/2},a)#2014,A-3

$rs := unapply(rsolve({a(0) = 5/2, a(k) = a(k-1)^2-2}, a), k)$

(1)

(2)

(3)

(4)

$sol := solve({1/x-1/(2*y) = 2*(-x^4+y^4), 1/x+1/(2*y) = (x^2+3*y^2)*(3*x^2+y^2)}, explicit)$

(5)

plots:-implicitplot([1/x+1/(2*y) = (x^2+3*y^2)*(3*x^2+y^2), 1/x-1/(2*y) = 2*(-x^4+y^4)], x = 0 .. 2, y = 0 .. 1, color = [red, blue], gridrefine = 4)

Re(convert(int(ln(x+1)/(x^2+1), x = 0 .. 1), polylog))

(6)

Im(convert(int(ln(x+1)/(x^2+1), x = 0 .. 1), polylog))

(7)

$DirectSearch:-GlobalOptima(int(sqrt(x^4+(-y^2+y)^2), x = 0 .. y), {y = 0 .. 1}, maximize)$

(8)

(9)

floor(10^20000/(10^100+3))

(10)

(11)

l := [seq(LinearAlgebra:-Determinant(Matrix(n, proc (i, j) options operator, arrow; 1/min(i, j) end proc)), n = 1 .. 10)]

(12)

$[{u(n+1)+(n^2+5*n+6)*u(n+2), u(0) = 1, u(1) = -1/2}, ogf]$

(13)

(-1)^n*(n+1)/GAMMA(n+2)^2

(14)

Hope the reader will try to continue the above.

Download Putnam_done_with_Maple.mw

when Maple meets a major holiday

by: eithne 2022

December 15 2014

3 1

Ever year about this time, somewhat geeky holiday-themed content makes the rounds on the internet. And I realized that even though I have seen much of this content already, I still enjoy seeing it again. (Why wouldn’t I want to see a Dalek Christmas tree every year?)

So in the spirit of internet recycling, here are a couple of older-but-still-fun Maple applications with a Christmas/holiday theme for your enjoyment.

Talkin’ Turkey

The Physics of Santa Claus

Other examples (old or new) are most welcome, if anyone wants to share.

eithne

Automatic simplification and a new Assume (as...

by: ecterrab 14135

December 09 2014

8 6

Hi
Two new things recently added to the latest version of Physics available on Maplesoft's R&D Physics webpage are worth mentioning outside the framework of Physics.

automaticsimplification. This means that after "Physics:-Setup(automaticsimplification=true)", the output corresponding to every single input (literally) gets automatically simplified in size before being returned to the screen. This is fantastically convenient for interactive work in most situations.
Add Physics:-Library:-Assume, to perform the same operations one typically performs with the assume command, but without the side effect that the variables get redefined. So the variables do not get redefined, they only receive assumptions.

This new Assume implements the concept of an "extended assuming". It permits re-using expressions involving the variables being assumed, expressions that were entered before the assumptions were placed, as well as reusing all the expressions computed while the variables had assumptions, even after removing the variable's assumptions. None of this is possible when placing assumptions using the standard assume. The new routine also permits placing assumptions on global variables that have special meaning, that cannot be redefined, e.g. the cartesian, cylindrical or spherical coordinates sets, or the coordinates of a coordinate spacetime system within the Physics package, etc.

Examples:

>

This is Physics from today:

>

(1.1)

•	Automatic simplification is here. At this point automaticsimplification is OFF by default.

>

(1.2)

Hence, for instance, if you input the following expression, the computer just echoes your input:

>

(1.3)

There is however some structure behind (1.3) and, in most situations, it is convenient to have these structures
apparent, in part because they frequently provide hints on how to proceed ahead, but also because a more
compact expression is, roughly speaking, simpler to understand. To see this automaticsimplification in action,
turn it ON:

>

(1.4)

Recall this same expression (you could input it with the equation label (1.3) as well)

>

(1.5)

What happened: this output, as everything else after you set and with no
exceptions, is now further processed with simplify/size before being returned. And enjoy computing with frankly
shorter expressions all around! And no need anymore for "simplify(%, size)" every three or four input lines.

Another example, typical in computer algebra where expressions become uncomfortably large and difficult to
read: convert the following input to 2D math input mode first, in order to compare what is being entered with the
automatically simplified output on the screen

>

-Physics:-`*`(Physics:-`*`(Physics:-`*`(3, sin(x)^(1/2)), cos(x)^2), sin(x)^m)+Physics:-`*`(Physics:-`*`(Physics:-`*`(3, sin(x)^(1/2)), cos(x)^2), cos(x)^n)+Physics:-`*`(Physics:-`*`(Physics:-`*`(4, sin(x)^(1/2)), cos(x)^4), sin(x)^m)-Physics:-`*`(Physics:-`*`(Physics:-`*`(4, sin(x)^(1/2)), cos(x)^4), cos(x)^n)

(1.6)

You can turn automaticsimplification OFF the same way

>

(1.7)

•	New facility; welcome to the world of "extended assuming" :)

Consider a generic variable, x. Nothing is known about it

>

x:

nothing known about this object

Each variable has associated a number that depends on the session, and the computer (internally) uses this
number to refer to the variable.

>

(1.8)

When using the assume command to place assumptions on a variable, this number, associated to it, changes,
for example:

>

(1.9)

Indeed, the variable x got redefined and renamed, it is not anymore the variable x referenced in (1.8).

>

Originally x, renamed x~:

is assumed to be: RealRange(Open(0),Open(1/2*Pi))

The semantics may seem confusing but that is what happened, you enter x and the computer thinks x~, not x
anymore.This means two things:

1) all the equations/expressions, entered before placing the assumptions on x using assume, involve a variable x
that is different than the one that exists after placing the assumptions, and so these previous expressions cannot
be reused. They involve a different variable.

2) Also, because, after placing the assumptions using assume, x refers to a different object, programs that depend
on the x that existed before placing the assumptions will not recognize the new x redefined by assume .

For example, if x was part of a coordinate system and the spacetime metric depends on it, the new variable x
redefined within assume, being a different symbol, will not be recognized as part of the dependency of This
posed constant obstacles to working with curved spacetimes that depend on parameters or on coordinates that
have a restricted range. These problems are resolved entirely with this new Library:-Assume, because it does not
redefine the variables. It only places assumptions on them, and in this sense it works like assuming , not assume .
As another example, all the Physics:-Vectors commands look for the cartesian, cylindrical or spherical coordinates
sets in order to determine how to proceed, but these variables disappear if you use
assume to place assumptions on them. For that reason, only assuming was fully compatible with Physics, not assume.

To undo assumptions placed using the assume command one reassigns the variable x to itself:

>

(1.10)

Check the numerical address: it is again equal to (1.8)

>

(1.11)

·All these issues get resolved with the new Library:-Assume, that uses all the implementation of the existing
assume command but with a different approach: the variables being assumed do not get redefined, and hence:
a) you can reuse expressions/equations entered before placing the assumptions, you can also undo the
assumptions and reuse results obtained with assumptions. This is the concept of an extended assuming. Also,
commands that depend on these assumed variables will all continue to work normally, before, during or after
placing the assumption, because the variables do not get redefined.

Example:

>

x:

nothing known about this object

So this simplification attempt accomplishes nothing

>

(1.12)

Let's assume now that

>

(1.13)

The new command echoes the internal format representing the assumption placed.

a) The address is still the same as (1.8)

>

(1.14)

So the variable did not get redefined. The system however knows about the assumption - all the machinery of the
assume command is being used

>

Originally x, renamed x:

is assumed to be: RealRange(Open(0),Open(1/2*Pi))

Note that the renaming is to the variable itself - i.e. no renaming.

Hence, expressions entered before placing assumptions can be reused. For example, for (1.12), we now have

>

(1.15)

To clear the assumptions on x, you can use either of Library:-Assume(x=x) or Library:-Assume(clear = {x, ...}) in
the case of many variables being cleared in one go, or in the case of a single variable being cleared:

>

x:

nothing known about this object

The implementation includes the additionally functionality, for that purpose add the keyword additionally
anywhere in the calling sequence. For example:

>

(1.16)

>

Originally x, renamed x:

is assumed to be: RealRange(Open(0),infinity)

>

(1.17)

>

In summary, the new Library:-Assume command implements the concept of an extended assuming, that can be
turned ON and OFF at will at any moment without changing the variables involved.

Download AutomaticSimplificationAndAssume.mw

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

Branch Cuts for a Product of Two Square Roots

by: Stephen Forrest 481

December 08 2014

2 5

Naive simplification of $f(z)=sqrt(z-1)*sqrt(-1*(-z-1))$ to $F(z)=sqrt(z^2-1)$ results in a pair of functions that agree on only part of the complex plane. In this application, the enhanced ability of Maple 18 to find and display branch cuts of composite functions is used to explore the branch cuts and regions of agreement/disagreement of f and F.

The algorithm by which Maple calculates branch cuts for square-root functions involves squaring, to remove the square root, and solving appropriate equations and inequalities. Unfortunately, this process is inherently prone to introducing spurious solutions, in which case the returned branch cut is not correct. One such instance in which a spurious solution arises is in the calculation of the branch cut for f; a best suggestion for dealing with such errors is found in the application.

Application: Branch Cuts for a Product of Two Square Roots

For those interested in learning more, the design for the new branch-cut facility in Maple 18 is inspired by the following paper:

England, M., Bradford, R., Davenport, J. H., and Wilson, D. 2013. Understanding branch cuts of expressions. In: Carette, J., Aspinall, D., Lange, C., Sojka, P. and Windsteiger, W., eds. Intelligent Computer Mathematics. Berlin: Springer, pp. 136-151. (Lecture Notes in Computer Science; 7961)

Exploration Mathematics with Maple through Embedded...

by: Lenin Araujo Castillo 1790 Product: Maple 18

December 03 2014

2 0

Today science professionals in engineering software used to only work on the desktop and even just looking to download and use mobile apps math; but they are not able to design their own applications.Maplesoft to set the solution to it through its Maple package; software supports desktop and mobile; solves problems of analysis and calculation with Embedded Components. To show this we have taken the area of different mathematical topics; fixed horizontally to a certain range of parameters and not just a constant as it is customary to develop. This paper shows how the Embedded Components allow us to develop mathematics in all areas. Achieving build applications that are interactive in mobile devices such as tablets; which are used at any time. Maple gives us design according to our university or research need, based on contemporary and modern mathematics.With this method we encourage students, teachers and researchers to use graphics algorithms.

CSMP_PUCP_2014.pdf

Coloquio_PUCP.mw

Lenin Araujo Castillo

Physics Pure

Computer Science

Add to the Physics:-Simplify and Physics:-Library:...

by: Andriy 270 Product: Maple

December 03 2014

2 0

Partial rectification for the Physics:-Simplify and Physics:-Library:-SortProducts procedures dealing with Fermi annihilation/creation operators

This post will be useful for physicists dealing with Fermi annihilation/creation operators. Physics Package provides plenty of powerful tools for quantum operators handling, however some of them often fail to render correct result. In particular incorrect behaviour with respect to Fermi annihilation/creation operators is observed for routines Simplify and SortProducts. In this post I present my procedures and which partially solve these issues.

	Problems with Physics Package routines

	Short explanation of custom routines and

	Weak points

	Final notes

Download FermiCreationAnnihilation.mw

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correct the API for dsolve with series option

Hello Everyone, I am new one in the community..

Programming Embedded Components for Graphics in...

Top 10 Webinars of 2014

January’s Featured Live Webinars

Draghilev’s method, F(x)=0. Animation.

3d model of a cam mechanism. Animation.

Cam mechanism. Animation.

Transformation with animation

Putnam done with Maple

when Maple meets a major holiday

Automatic simplification and a new Assume (as...

Branch Cuts for a Product of Two Square Roots

Exploration Mathematics with Maple through Embedded...

Add to the Physics:-Simplify and Physics:-Library:...

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