Also available:

## Expand (a+b)^n in binomial expansion form...

expand( (a+b)^n)

convert((a+b)^n,Sum)

none  expands in  binomial  form.  Is there any way for Maple to generate  binomial  expansion of (a+b)^n  without

entering  manually.

martin

## Vector math and conditional functions...

Level: Idiot (Me)

I have a matrix of 3 columns and lots of rows M

• First column is latitude in degrees
• Second column is longitude in degrees
• Third column is data

So I set lambda:=M(..,1) and phi_g:=M(..,2) giving me two column vectors.

I want to convert lambda and phi_g to polar coordinates theta and phi

theta:=90-lambda produces "Error, (in rtable/Sum) invalid arguments"

WHY?

I also want to convert phi_g to phi where phi=phi_g when phi_g is 0...180 and phi=phi_g +360 when phi_g <0

How do I create a conditional function like this?

## Vector Field to "normal" function...

Hello everyone.

I have a vector field in 2d-cartesian coordinates which I would like to convert to a "normal" function, that is f(x, y) where when you put x and y in, you get the magnitude of the vector at that point.

Example vector field:

This one is very hard to handle by hand which is why I want to use Maple for it.

I tried VectorCalculus[Norm] but it gave me this:

## convert data readed from text file to array ?...

i have read data from a text file. i want to convert this data to array,how should i do that ?

for example :
i have readed these files and i want convert them to array which for the first one,has 3 rows and 4 columns.
what should i do ?

 > restart:
 (1)
 (2)
 >

## Error, (in dsolve/numeric/bvp/convertsys) unable t...

hi.i encountered this erroe  [Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system] with solving set of differential equation.please help me.thanks a lot

dsys3 := {1*h1(theta)+1*(diff(h1(theta), theta, theta))+1*(diff(h2(theta), theta))+1*(diff(h2(theta), theta, theta, theta))+1*h3(theta)+1*(diff(h3(theta), theta, theta))+1*(diff(h1(theta), theta, theta, theta, theta)) = 0, 1*h2(theta)+1*(diff(h2(theta), theta, theta, theta, theta))+1*(diff(h2(theta), theta, theta))+1*(diff(h1(theta), theta))+1*(diff(h1(theta), theta, theta, theta))+1*(diff(h3(theta), theta))+1*(diff(h3(theta), theta, theta, theta)) = 0, h3(theta)^5*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+(diff(h3(theta), theta, theta))*h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+(diff(h3(theta), theta, theta, theta, theta))*h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+h1(theta)*h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+(diff(h1(theta), theta, theta))*h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+(diff(h2(theta), theta))*h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+(diff(h2(theta), theta, theta, theta))*h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+h3(theta)^4*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)+h3(theta)^4*(diff(h2(theta), theta, theta, theta, theta, theta, theta))*(1+ln(h3(theta))^2*1+2*ln(h3(theta))*1)-beta*h3(theta)^3*1-chi*ln(h3(theta))^2*1/kappa-chi*1/kappa-2*chi*ln(h3(theta))*1/kappa = 0, h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 1, h3(1) = 1, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h2))(0) = 0, ((D@@1)(h2))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0, ((D@@2)(h3))(0) = 0, ((D@@2)(h3))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 600, numeric, output = listprocedure);
%;
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

## convert help of older maple version to 18

by:

you can change help of older maple version to 18 by this command:

HelpTools:-Database:-ConvertAll():

for example if you download DirectSearch optimization package it's help don't open in maple 18 because in maple 18 .hdb converted to .help and you can do this convert by HelpTools:-Database:-ConvertAll():

DirectSearch version 2 created for maple 13 and i converted it's help to 18.

after i typed this command maple 18 wrote:

"Converting G:\\Program Files\\Maple 18\\lib\\DirectSearch.hdb to G:\\Program Files\\Maple 18\\lib\\DirectSearch.help"
Warning, .hdb help databases are deprecated, 'G:\Program Files\Maple 18\lib\DirectSearch.hdb' will not be used, see ?HelpTools,Migrate help page for more information.

and when try again it worked properly and DirectSearch help opened.

## Units conversion problem...

This is an addition to the following post:

http://www.mapleprimes.com/questions/141795-Unit-Conversion-Problem

But I use the clickable facilities of Maple.  Here is the problem:

>32[[degC]];

32[[degC]]
right-click -> Units -> Replace units -> degF

288
--- [[degF]]
5

>evalf[5]( (2) );
57.600[[degF]]

but if I do that:

>convert(32, 'temperature', 'degC', 'degF');

448
---
5

>evalf[5]( (4) );
89.600

Why the conversion is bad when you try to do it by the clickable way????????????

--------------------------------------
Mario Lemelin
Maple 18 Ubuntu 13.10 - 64 bitsMaple 18 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

## Error, (in dsolve/numeric/bvp/convertsys) unable t...

i am trying to solve 6 ODE with boundary condition

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)

 (20)

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)

 (20)

then i get this error

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

i dont know where i need to change after view it one by one..

## Maple LaTeX font consistency...

Dear Mapleprimes,

I have been struggling with a problem in the last couple of days. I wish to export a Maple plot to LaTeX while ensuring font consistency. While searching for solutions online, I found the psfrag package in LaTeX. So far, however, I have been unsuccesful in making this work. As as test, I attempted to export plot(x^2) to LaTeX. I used the following code to convert to .eps which worked fine:

plotsetup(ps, plotoutput = plot1.eps, plotoptions = portrait, noborder,height=5in,width=5in);plot(x^2);

Then in LaTeX, I have:

\documentclass{article}

\usepackage{graphicx}

\usepackage{psfrag}

\begin{document}

\begin{figure}[!h]
\centering
\psfrag{x}{$\alpha$}
\includegraphics[scale=0.5]{plot1.eps}
\end{figure}
\end{document}

However, no replacements are made. After intense Google searching I found the following post http://www.mapleprimes.com/posts/43255-Trouble-Replacing-Maple-Axes-Labels which to sum up argues that this was only possible with earlier versions of Maple.

Does anyone know if the problem has been resolved?

Does anyone know any other ways to ensure font consistency for plots imported from Maple to LaTeX?

Thank you very much in advance!

C

## printf for list 0 format conversion help...

Hi all,

Say I have some list like this,

tmp:=[[0, 0, 1], [0, 1, 0], [0, 1, 1], [0, 1, 2], [1, 0, 0], [1, 0, 1], [1, 0, 2], [1, 1, 0], [1, 1, 1], [1, 1, 2], [1, 2, 0]];

And I have worked out some probabilities for each of them, a,b,c,d, ect.

I want to print them like this

Pr( 001 ) = 1

Pr( 010 ) = 1-phi[2]+phi[2]*(1-p[3])*(1-phi[3])

Pr( 011 ) = phi[2]*p[3]*(1-phi[3])

and so on.

I there a way to do that?

The probabilities can be extracted from a Vector. I have no problem to print them.

I dont know how to convert the 0,1,2 into the desired format as shown above.

This is the best I can do.

Also, is it possible to convert all the subscripte [] to _ when printing the output?

and get ride of all * as well.

Thanks,

casperyc

## convert 2nd order ODE to system of First ODE ...

Dear all;

Please Have some one an idea to transform or convert 2nd order ODE to system of First ODE ( of course using maple).

Thanks

## A problem with dsolve...

Hi,

I have a problem with dsolve in the following code

restart;
>
n:=20;
m:=1;
cc:=-200;
zzeta:=0.1;
sefr1:=0.3;
sefr:=0.2;
MM:=0;
lambda:=0.1;
Br:=1;
nn:=3;
>
>
#u(tau):=tau;
u(tau):=421.7129935*tau-2217.587728*tau^2+8897.376593*tau^3-27612.59182*tau^4+64248.00336*tau^5-1.083977605*10^5*tau^6-10.57029600-1.080951714*10^6*tau^13+7.999517316*10^5*tau^14-4.788741005*10^5*tau^15+2.309563748*10^5*tau^16+26511.11102*tau^18-5959.001794*tau^19+1.148523882*10^5*tau^7-95.23809524*tau^21+4.545454545*tau^22-9435.563781*tau^8-2.587683745*10^5*tau^9+6.473880128*10^5*tau^10+948.0272727*tau^20-88660.41892*tau^17-1.008692404*10^6*tau^11+1.175504242*10^6*tau^12;
>
>
B := 1+(2*(1-zzeta))*Br*(int(tau*(diff(u(tau), tau))^2, tau = (1/2)*zzeta*(1-zzeta) .. 1/2*(1-zzeta)));
eq4 := 4*B*u(tau)-(1+zzeta)*(diff(tau*(diff(theta(tau), tau)), tau))/tau-(1+zzeta)*Br*(diff(u(tau), tau))^2;

theta(tau):=sum(p^ii*theta[ii](tau),ii=0..nn);
HH:= p*((4*(1+(2*(1-zzeta))*Br*(int(tau*(diff(u(tau), tau))^2, tau = (1/2)*zzeta*(1-zzeta) .. 1/2-(1/2)*zzeta))))*u(tau)-(1+zzeta)*(diff(theta(tau), tau)+tau*(diff(theta(tau), tau, tau)))/tau-(1+zzeta)*Br*(diff(u(tau), tau))^2)+(1-p)*(diff(theta(tau),tau\$2)):
eq5:=simplify(HH):
eq6:=collect(expand(eq5),p);

eq7:=
convert(series(collect(expand(eq5), p), p, nn+1), 'polynom');

for ii to nn do
ss[ii] := (coeff(eq7, p^ii)) ;
print (ii);
end do;

ss[0]:=diff(theta[0](tau), tau, tau);

icss[0]:=theta[0](zzeta/(2*(1-zzeta)))=0, D(theta[0])(1/(2*(1-zzeta)))=1;

dsolve({ss[0], icss[0]});
theta[0](tau):= rhs(%);

for ii to nn do
ss[ii]:=evalf[5](ss[ii]);
icss[ii]:=theta[ii](zzeta/(2*(1-zzeta)))=0, D(theta[ii])(1/(2*(1-zzeta)))=0;
dsolve({ss[ii], icss[ii]});
theta[ii](tau):=rhs(%);
end do;

I would be most grateful if you help me to find this problem.

## convert Matlab code to Maple...

Dear all

I would like to convert Matlab code to Maple, is there anu idea, this is the code.

% Usage: [y t] = abm4(f,a,b,ya,n) or y = abm4(f,a,b,ya,n)
% Adams-Bashforth-Moulton 4-th order predictor-corrector method for initial value problems
% It uses
% Adams-Bashforth 4-step method as a precdictor,
% Adams-Moulton 3-step method as a corrector, and
% Runge-Kutta method of order 4 as a starter
%
% Input:
% f - Matlab inline function f(t,y)
% a,b - interval
% ya - initial condition
% n - number of subintervals (panels)
%
% Output:
% y - computed solution
% t - time steps
%
% Examples:
% [y t]=abm4(@myfunc,0,1,1,10);          here 'myfunc' is a user-defined function in M-file
% y=abm4(inline('sin(y*t)','t','y'),0,1,1,10);
% f=inline('sin(y(1))-cos(y(2))','t','y');
% y=abm4(f,0,1,1,10);

function [y t] = abm4(f,a,b,ya,n)
h = (b - a) / n;
h24 = h / 24;

y(1,:) = ya;
t(1) = a;

m = min(3,n);

for i = 1 : m % start-up phase, using Runge-Kutta of order 4
t(i+1) = t(i) + h;
s(i,:) = f(t(i), y(i,:));
s2 = f(t(i) + h / 2, y(i,:) + s(i,:) * h /2);
s3 = f(t(i) + h / 2, y(i,:) + s2 * h /2);
s4 = f(t(i+1), y(i,:) + s3 * h);
y(i+1,:) = y(i,:) + (s(i,:) + s2+s2 + s3+s3 + s4) * h / 6;
end;

for i = m + 1 : n % main phase
s(i,:) = f(t(i), y(i,:));
y(i+1,:) = y(i,:) + (55 * s(i,:) - 59 * s(i-1,:) + 37 * s(i-2,:) - 9 * s(i-3,:)) * h24; % predictor
t(i+1) = t(i) + h;
y(i+1,:) = y(i,:) + (9 * f(t(i+1), y(i+1,:)) + 19 * s(i,:) - 5 * s(i-1,:) + s(i-2,:)) * h24; % corrector
end;

## How to Xor two hex strings...

number10:=466d06ece998b7a2fb1d464fed2ced7641ddaa3cc31c9941cf110abbf409ed39598005b3399ccfafb61d0315fca0a314be138a9f32503bedac8067f03adbf3575c3b8edc9ba7f537530541ab0f9f3cd04ff50d66f1d559ba520e89a2cb2a83:

number8:=315c4eeaa8b5f8bffd11155ea506b56041c6a00c8a08854dd21a4bbde54ce56801d943ba708b8a3574f40c00fff9e00fa1439fd0654327a3bfc860b92f89ee04132ecb9298f5fd2d5e4b45e40ecc3b9d59e9417df7c

I first define

f:=x->convert(x, decimal, hex):

with(Bits):
str1:=convert( Xor(f(number8), f(number10)), bytes);

now how can I get back the alphabets, since again use of convert with bytes return the inital argument.

Moreover, I would really appreciate if someone could explain the difference between

convert(expr, bytes)

convert( [expr], bytes)

Many regards!!

## convert(...., sincos) ...

> assume(a < 0);
> convert(cosh(sqrt(a)), sincos);
print(output redirected...); # input placeholder
/ (1/2)\
cos\(-a) /

This is what I expected.

Now

> assume(L > 0);
> assume(K > 0);
> assume(mu > 0);
> assume(mu^2 < 4*L*k);
> assume(t > 0);
> convert(cosh((1/2)*t*sqrt(mu^2-4*L*k)/L), sincos);
print(output redirected...`); # input placeholder
/ (1/2)\
| / 2 \ |
|t \mu - 4 L k/ |
cosh|--------------------|
\ 2 L /

I wanted to obtain again the cos function. Could someone help me?
(What is the reason that convert does not work "well" in later case?)

Thanks,  Sandor

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