## Tough BesselJ Integral...

Hi,

I have a list of 603 integrals that I want to evaluate. Unfortunately, I can't get Maple to do most of them. Mathematica can do some that Maple can't, and returns an answer in terms of BesselJ functions. So my question is 2-fold

1) Is there a way to make Maple do this integral?
2) If not, is there a way to efficiently convert 603 expessions to Mathematica and back?

EXAMPLE INTEGRAL
restart;
assume(k1::real, k2::real, R::real, R>0);
a :=cos(x)*exp(I*(k1*R*sin(x)+k2*R*sin(x)-4*x))*sin(x):
int(a, x=-Pi/2..Pi/2) assuming real;

Thanks!

 > restart;
 > assume(k1::real, k2::real, R::real, R>0);
 > a :=cos(x)*exp(I*(k1*R*sin(x)+k2*R*sin(x)-4*x))*sin(x)
 (1)
 > int(a, x=-Pi/2..Pi/2) assuming real;
 (2)

 > ans := -(1/((k1 + k2)^6*R^6))*2*I*Pi* ( 10*(k1 + k2)^4*Pi*R^4*BesselJ(2, sqrt((k1 + k2)^2*R^2)) + 2*Pi ((k1 + k2)^2*R^2)^(3/2) (-30 + (k1 + k2)^2*R^2) *BesselJ(3, sqrt((k1 + k2)^2*R^2)) - (k1 + k2)^4*R^4*(-(k1 + k2)*R*cos((k1 + k2)*R) + sin((k1 + k2)*R)) + 8*(k1 + k2)^2*R^2*(-(k1 + k2)*R*(-6 + (k1 + k2)^2*R^2)*cos((k1 + k2)*R) + 3*(-2 + (k1 + k2)^2*R^2)*sin((k1 + k2)*R)) - 8*(-(k1 + k2)*R*( 120 - 20*k2^2*R^2 + k1^4*R^4 + 4*k1^3*k2*R^4 +
 > k2^4*R^4 + 4*k1*k2*R^2*(-10 + k2^2*R^2) +
 > k1^2*(-20*R^2 + 6*k2^2*R^4))*cos((k1 + k2)*R) +
 > 5*(24 - 12*k2^2*R^2 + k1^4*R^4 + 4*k1^3*k2*R^4 + k2^4*R^4 +
 > 4*k1*k2*R^2*(-6 + k2^2*R^2) +
 > 6*k1^2*R^2*(-2 + k2^2*R^2))*sin((k1 + k2)*R) ) );
 (3)
 >
 >

## How to find set of coordinates in Maple?...

Hello, forgive me if I used bad english, I am not a native speaker.

Anyhow: I have to decide the set of coordinates looking at the grafs intersections.  (I hope you understand that)

This is my function: f(x)=1/4*x3-x2-x+4

When you plot the function you see that the intersections is (-2,0) (2,0) and (4,0)

BUT I have to use a command to find these three intersections, plzz help me!

THANK YOU indeed.

[point of] intersection

## Mac OS X 10.11

For those who are running Maple and/or MapleSim on the Mac, and who may have missed an earlier question on this site, we wanted to let you know that there are some problems with running Maple and MapleSim on the new Mac OS, Mac OS X 10.11 (El Capitan). We’re working on a solution, which we expect will be ready in a few weeks. We’ll keep you posted, but in the meantime, please delay updating your Mac OS for now to avoid problems.

eithne

## Solve and plot differential equations...

I want to solve these two differential equations. I have the initial conditions:
x(0)=0
y(0)=0
x'(0)=5.7
t'(0)=8.1
What am I doing wrong?

## List of all the contents a MapleSim module GetMult...

Hello,

I would like to know : how I can get all the contents of the module GetMultibody of MapleSim?

Is there in classic maple a function enabling me to ask the content of a module ?

Thank a lot for your help.

## less than comparison...

Can Maple compare irrational numbers?

A simple command like   if(2<√5,0,1)   is not working for me.

## Simplificating in Vector Algebra...

I want to work (cross products, differentiating and simplificating) of three dimensional vector functions.

But I'd like to work with them as vector, not as components. Is it available in Maple?

## Working with Finitely Presented Groups in Maple

by:

The GroupTheory package in Maple includes facilities for working with finitely presented groups - groups defined by finitely many generators and defining relations.  We now have a video tutorial that covers the basics of this aspect of the package.  As always, we appreciate feedback and suggestions regarding this feature, or new features that you would like to see in the GroupTheory package.

Hey,

i am trying to put u[0](zeta):=0 in maple but it gives an error, however it accepts u[0]:=0 but i have to involve zeta in it. help please.

here is my program

bc1 := u(x, y)-0;
dydxf := (1/2)*(-u[m+2](zeta)-3*u[m](zeta)+4*u[m+1](zeta))/h;
bc1 := subs(diff(u(x, y), x) = subs(m = 0, dydxf), u(x, y) = u[0](zeta), x = 0, bc1);
eq[0] := bc1;
u[0](zeta):=(solve(eq[0],u[0](zeta)));

on pressing enter a new window opens of title

clerify expression.

parts of expressions are ambigous. please select one of the suggested meanings.

function defination or remember table assignment.

then it gives the error below
Error, unable to parse

:=(Zeta)->(solve(eq[0],u[0](Zeta)));

## The dataplot command

by:

Maple 2015 has a new command, dataplot, for plotting datasets. It was designed to be easy to use and it offers several new features that are not available in Maple's other plotting commands. A few months ago, I recorded a video that gives an overview of the command. If you have any questions or comments about dataplot, feel free to post here. I'm also including the worksheet that is shown in the video: DataplotWebinar.mw

## Code Generation for R

by: Maple

Maple’s Code Generation makes it possible to translate your Maple code to various other programming languages including C, Python, and several others. In Maple 2015, we added a new Code Generation target to one of my other personal favourite languages, R. R is a programming language designed for statistical computing and graphics, so no code translation from Maple to R would be complete without attempting to translate as many commands as possible from Maple’s Statistics package.

Translating code from one language to another is tricky business. Maple 2015 represented the first time that any Code Generation target language added the ability to translate commands from the Statistics package. With R, we found that many common statistics commands had almost a one-to-one mapping, such as Statistics:-Mean = mean, but several others were much more complicated, including several commands for dealing with probability functions that did not have direct mappings due to differences in how the systems handle symbolic probability functions.

A list of statistics commands that can be translated from Maple to R can be found here.

In addition to assisting me recall the correct syntax in R, having worked with CodeGeneration[R] for several months now, I find that one of my most common uses for Maple’s code generation to R is simply to pass data between the systems. A simple example:

` CodeGeneration:-R( LinearAlgebra:-RandomMatrix( 5, 2 ) );`

translates to the following in R:

` cg <- matrix(c(-4,27,8,69,99,29,44,92,-31,67),nrow=5,ncol=2)`

To see a couple more short examples, here’s a short video that I recorded on Code Generation to R:

A little known fact about Code Generation is that the translation files can be viewed in from the “samples” directory in your Maple install directory. Similar to many of Maple’s packages, you can view all of the source code that Code Generation uses for its translations. For example, you can view the translations for the commands that I mentioned above from the “FunctionTable.mm” file inside of your “%MapleInstallDir%/ samples/CodeGeneration/R” directory.

Should you have any feedback on this translation, or any other, please feel free to contact us. We’re also on the hunt for our next code generation targets, so let us know what other languages you would like to see added as Code Generation targets.

## maple,matlab,latex,mathematica...

Hello people

i have a quetion

what is the perposes of these softwares,maple,matlab,mathmatica and latex.

for example i listened from somewhere that matlab is best for matrices, then what are the major task of these softwares which i listed above including matlab,

how we make comparison of these softwares.

thanks

## Why does (-8)^(1/3) become 1+Complex(1)* (3)^(1/2)...

Hello people in mapleprimes,

I have a question about why what is shown by maple by simplify(-8)^(1/3) is 1+ Complex(1)* (3)^(1/2)?

Solutions of x^3=-8 are -2, 1+Complex(1)*(3)^(1/2) and 1- Complex(1)*(3)^(1/2). And, as for the last one, 1- Complex(1)*(3)^(1/2), it is

the conjugate of the second, so it might not need to be written, because of it being easily seen so.

Is it the same reason why just -2 is not shown as the result of simplify((-8)^(1/3))?

PS. I know the instruction to use surd in such a case.

the reason I asked this question is this:

I am reading Essential Maple, where

ln(z) = ln(rho*exp(Complex(1)*theta));

ln(rho*exp(Complex(1)*theta))=ln(rho)+Complex(1)*theta;

ln(rho)+Complex(1)*theta;=ln(rho)+Complex(1)*arctan(y,x);

and

z^a=exp(a*ln(z));

and

"Because of

exp(w*Pi*Complex(1)*k)=cos(2*Pi*k) + Complex(1)*sin(2*Pi*k);

and

cos(2*Pi*k) + Complex(1)*sin(2*Pi*k)=1;

we could equally well have chosen

ln_k z = ln(z) + 2*Pi*Complex(1)*k"

are written.

Supposing these, there is a sentence that

"we choose k=0, and thus -Pi<=theta<=Pi to be the one (that for our canonical logarithm).

Every computer algebra language and numerical language follows this standard and takes the

complex logarithm to have its imaginary part in this range.

With this definition, (-8)^(1/3)=1 + Complex(1)*sqrt(3), and not -2. (the end of quotation)"

And, I can't understand the last sentence"With this definition", so I asked the above question.

I hope someone give an answer to the above question.

taro

## Comparisons

Maple

Hello all ,

Having read a recent post about comparing Maple and Mathematica I'd like to throw my 2 cents (FWIW).

It is *silly* (not to say stupid) to compare these two softwares.

Maple can do "things" that Mathematica can't. For examples Differential Geometry, Lie Algrebra, covariant derivative and the like.

And Mathematica Manipulate command is far better than Maple Explore (just another exemple).

I have being using Maple since Release V.2 (1992) and Mathematica since Release 1.1.a (1991).

I use both of them on a daily basis and I *LOVE* them both.

Inputs are welcome :-)

Kind regards to all,

Jean-Michel.