## How do you close all the paragraphs in a maple wor...

I use maple worksheet to organize a derivation, etc.

But most of the paragraphs and subparagraphs should normally be closed.

But after executing the file (using !!!) every paragraph is opened.

We need better ability to control the opening/closing of paragraphs.

How do I close ALL paragraphs.

Also, how do I close all TOP level paragraphs (but not subparagraphs).

Thanks, Chee

## Graph a displacement over a domain...

Where u and v are the displacement components in x and y directions respectively.

## Compiller Error...

Hi,

I used to use windows 32 bit, but I have 64 bit windows now. I installed the MapleSim 6.4 and Maple 18 and try to run the simulations that I created with the 32 bit windows. I have this error 'Unable to compile (rc=1), please try again, and if that fails verify your Windows compiller installation'. Could you please let me know what should I do to eliminate this problem?

Best

Onder

## Optimization problem about piecewise integration p...

Can maple solve maximization problem like

q := proc (a, b, c) options operator, arrow; .2*b+.1*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.2 b + 0.1 c
w := proc (a, b, c) options operator, arrow; .7*a+.1*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.7 ab + 0.1 c
e := proc (a, b, c) options operator, arrow; .7*a+.2*b*c end proc;
print(`output redirected...`); # input placeholder
(a, b, c) -> 0.7 a + 0.2 b c

with(Optimization)

Maxmize(int(min(100+(.7*a+q)*(1/2), a), q)+int(min(100+(.2*b+w)*(1/2), b), w)+int(min(100+(.1*c+e)*(1/2), c), e)-a-b-c-ab-ac-bc)

Error, (in Optimization:-NLPSolve) cannot convert procedures to piecewise

Thanks alot if you can help me.Urgent! Really appreciate.

## Export multiple worksheets to pdf ...

For different reasons I need to ocasionally export a number of Maple worksheet in a folder to pdf files. Is there a way to automate this? I would want that the worksheet is opened, output removed, then executed and eventually exported to pdf. It can take quite a while to do this manually for about 50 worksheets.

## Simple Physics Problem...

I have two Reissner Nordstrom black holes that are near extreme. How do I show they move?

## Plot command for solution to DE after the answer o...

y(t) = _C1*exp(-1.*t)*sin(.57736*t)+_C2*exp(-1.*t)*cos(.57736*t)

The answer i got for a DE raised in mapleprime is given above.

What command do i write now to get a plot of the same?

Ramakrishnan V

## Numerical intgration...

#DeHoog f4(t)

 >
 (1)
 >
 (2)
 >

How is it possible to numerically integrate the function containing Diract delta function.

The following code for example is failed to answer and makes computer memory full.

## Could Maplesoft support some investigations of po...

One of my post graduate students chose the theme "Discrete Wavelet analysis of medical signals with Maple" for her thesis. I test, is it possible to support such reearch be Maplesoft &  what may be the form of such support, if it is possible?

## How to define the derivative of a function as a fu...

Take a look at below. I was expecting maple to give me "g'(1)"! :)

## How to get derivation of (x derivation) in Maple...

the final result I want to get should be b*x

Thank you.

## Visualization of meme propagation on the internet

by:

Hi, we recently put together a web video on how memes spread on the internet using several visualizations generated from Maple 18:

http://youtu.be/vEhAkEPwESI

Found the new ability to specify a background image for plots to be very helpful.

## matrix solution...

the following program dont work

a := 1;
b := 2;
c := 3;
d := 4;
eq1 := a*x[1]-b*x[2] = 0;
eq2 := c*x[2]-d*x[1] = 3;
dd := fsolve({eq1, eq2}, {x[1], x[2]});
evalf(sin(dd[1]));

## Computer Algebra for Theoretical Physics

by:

Last week the Physics package was presented in a talk at the Perimeter Institute for Theoretical Physics and in a combined Applied Mathematics and Physics Seminar at the University of Waterloo. The presentation at the Perimeter Institute got recorded. It was a nice opportunity to surprise people with the recent advances in the package. It follows the presentation with sections closed, and at the end there is a link to a pdf with the sections open and to the related worksheet, used to run the computations in real time during the presentation.

COMPUTER ALGEBRA FOR THEORETICAL PHYSICS

 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 implemented most of the mathematical objects and mathematics used in theoretical physics computations, and dramatically approximated the notation used in the computer to the one used in paper and pencil, diminishing the learning gap and computer-syntax distraction to a strict minimum. In connection, in this talk the Physics project at Maplesoft is presented and the resulting Physics package illustrated tackling problems in classical and quantum mechanics, general relativity and field theory. In addition to the 10 a.m lecture, there will be a hands-on workshop at 1pm in the Alice Room.

 ... Why computers? 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

Notation and related mathematical methods that were missing:

coordinate free representations for vectors and vectorial differential operators,

covariant tensors distinguished from contravariant tensors,

functional differentiation, relativity differential operators and sum rule for tensor contracted (repeated) indices

Bras, Kets, projectors and all related to Dirac's notation in Quantum Mechanics

Inert representations of operations, mathematical functions, and related typesetting were missing:

inert versus active representations for mathematical operations

ability to move from inert to active representations of computations and viceversa as necessary

hand-like style for entering computations and texbook-like notation for displaying results

Key elements of the computational domain of theoretical physics were missing:

ability to handle products and derivatives involving commutative, anticommutative and noncommutative variables and functions

ability to perform computations taking into account custom-defined algebra rules of different kinds

(problem related commutator, anticommutator, bracket, etc. rules)

 Vector and tensor notation in mechanics, electrodynamics and relativity
 Dirac's notation in quantum mechanics

 • Computer algebra systems were not originally designed to work with this compact notation, having attached so dense mathematical contents, active and inert representations of operations, not commutative and customizable algebraic computational domain, and the related mathematical methods, all this typically present in computations in theoretical physics.
 • This situation has changed. The notation and related mathematical methods are now implemented.

Tackling examples with the Physics package

Classical Mechanics

Inertia tensor for a triatomic molecule

Problem: Determine the Inertia tensor of a triatomic molecule that has the form of an isosceles triangle with two masses  in the extremes of the base and mass  in the third vertex. The distance between the two masses  is equal to a, and the height of the triangle is equal to h.

 Solution

Quantum mechanics

Quantization of the energy of a particle in a magnetic field

Show that the energy of a particle in a constant magnetic field oriented along the z axis can be written as

where and  are creation and anihilation operators.

 Solution
 The quantum operator components of  satisfy

Unitary Operators in Quantum Mechanics

(with Pascal Szriftgiser, from Laboratoire PhLAM, Université Lille 1, France)

A linear operator U is unitary if , in which case, Unitary operators are used to change the basis inside an Hilbert space, which physically means changing the point of view of the considered problem, but not the underlying physics. Examples: translations, rotations and the parity operator.

 1) Eigenvalues of an unitary operator and exponential of Hermitian operators
 2) Properties of unitary operators
 3) Schrödinger equation and unitary transform
 4) Translation operators

Classical Field Theory

The field equations for a quantum system of identical particles

Problem: derive the field equation describing the ground state of a quantum system of identical particles (bosons), that is, the Gross-Pitaevskii equation (GPE). This equation is particularly useful to describe Bose-Einstein condensates (BEC).

 Solution
 The field equations for the  model
 Maxwell equations departing from the 4-dimensional Action for Electrodynamics

General Relativity

Given the spacetime metric,

a) Compute the trace of

where  is some function of the radial coordinate,  is the Ricci tensor,  is the covariant derivative operator and  is the stress-energy tensor

b) Compute the components of the traceless part of   of item a)

c) Compute an exact solution to the nonlinear system of differential equations conformed by the components of   obtained in b)

Background: paper from February/2013, "Withholding Potentials, Absence of Ghosts and Relationship between Minimal Dilatonic Gravity and f(R) Theories", by P. Fiziev.

 a) The trace of
 b) The components of the traceless part of
 c) An exact solution for the nonlinear system of differential equations conformed by the components of
 The Physics Project "Physics" is a software project at Maplesoft that started in 2006. The idea is to develop a computational symbolic/numeric environment specifically for Physics, targeting educational and research needs in equal footing, and resembling as much as possible the flexible style of computations used with paper and pencil. The main reference for the project is the Landau and Lifshitz Course of Theoretical Physics.   A first version of "Physics" with basic functionality appeared in 2007. Since then the package has been growing every year, including now, among other things, a searcheable database of solutions to Einstein equations and a new dedicated programming language for Physics.   Since August/2013, weekly updates of the Physics package are distributed on the web, including the new developments related to our plan as well as related to people's feedback.

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

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