## Maple17 performance on a simple integral of ration...

Dear all,

I've just discover something quite surprising for me... It turns out like if Maple didn't take in account the linearity of the integral.

In the middle of a calculation, I need to compute the following integral

int(3628800 / (y * (1 / 2 + y)^11) - 3628800 / (y * (39 / 2 + y)^11), y = 39 / 2..infinity);

Maple 17 is not able to instantly answer me, and I'm not so patient... (I've waited more than 30s)

Nevertheless, if I ask Maple 17 to compute

3628800 * int(1 / (y * (1 / 2 + y)^11) - 1 / (y * (39 / 2 + y)^11), y = 39 / 2..infinity);

as well as

int(3628800/(y*(1/2+y)^11), y = 39/2..infinity)-int(3628800/(y*(39/2+y)^11), y = 39/2..infinity);

Maple 17 answer me instantly... which turn out to be quite surprising!

Is there someone, here, who has some ideas of what is happening in this calculation? Why Maple17 has this strange behaviour?

Tolliob

## Simplification of Expression...

Why does

5103*`&Omega;`*(5*sqrt(7)+16)/((1+2*sqrt(7))^(3/2)*(7+2*sqrt(7))*(-2+sqrt(7))*(14+sqrt(7))*(2*sqrt(7)-1)*(4+sqrt(7)))

not simplify to

sqrt(1+2*sqrt(7))*`&Omega;`

???

## The integration of Jacobi elliptic functions...

Hello everybody.

I'd like to share an observation about the integration of the Jacobi elliptic functions, in particularly the elliptic sine sn(x,k).

It's correct answer. But when I make the integration of the expression

according to the Handbook of Elliptic Integrals for Engineers and Scientists we have slightly another result

What is the difference?

## how to calculate potential energy in terms of gaus...

how to calculate potential energy in terms of gauss curvature?

## Error, number of indices exceeds rank...

Hello.

I have been trying to create a code to solve a structure by using FEM, but I keep getting an error that stops me from moving on.

Everytime I run my code, Maple gives me the error in the Title of my question:
"Error, number of indices exceeds rank"

Unfortunately I can't find any help in Maplesoft support for such error, and I need immediate help for that.

Can someone help me with that? Should I post my entire code?

Thanks!

## solve trigonometric system of equation with condit...

I want to solve this equation with assumptions!!!

restart;
assume(d::real, d>0):
assume(a::real, -0.01 < a, a < 0):
sys:={-800*Pi*a*cos(6.557377048*Pi*(3.470797713+d))/(a+1)^3 = -.9396060697, 800*Pi*a*sin(6.557377048*Pi*(3.470797713+d))/(a+1)^3 = -.3238482794};
solve(sys, {a,d},useassumptions=true, AllSolutions=true);

one of the solutions has true "a" but "d" is wrong, I want one true solution!

## Eigenvalues. Mechanical problem...

I solve a mechanical exercise but i had a problem.

I know M (mass) and K (stifness) matrices (4x4).

I want to solve the (λ2M+K)v=0  eigenvalue problem, where λ are the eigenvalues and v eigenvectors.

How can i solve this problem.  I tried with the Eigenvectors() command but it didn't give the right solution.

The Eigenvalues are okay, but the eigenvectors not

K := Matrix([[4*10^7,-1.50*10^7,2*10^7,0],[-1.50*10^7,1.50*10^7,0,1.50*10^7],[2*10^7,0,8*10^7,2*10^7],[0,1.50*10^7,2*10^7,4*10^7]]);

M:=Matrix([[121.90,99.048,-91.429,0],[99.048,594.29,0,-99.048],[-91.429,0,243.81,-91.429],[0,-99.048,-91.429,121.90]]);

w1,w2:=Eigenvectors(K,M);

Acoording with the book the right eigenvectors(shape mode) are:

[0.013 991,  0.034 233,  0.073 683,  0.090 573]
[0.035 637, 0, -0.032 213, 0]
[0 ,-0.034 233, 0, 0.090 573]
[-0.013 991, 0.034 233, -0.073 683, 0.090 573]

Thank you

## Kernel connection lost...

Regarding my recent question http://www.mapleprimes.com/questions/221909-How-To-Extract-Data-From-Implicit-Function I would like to share an interesting observation. Here the code of the program:

```restart;
R0 := ln(y)+Re(Psi(1/2+(2*(p^2+(1/2)*sqrt(2*I+4*ksi_fs^2*p^2)*tanh(sqrt(2*I+4*ksi_fs^2*p^2)*x)/(tau+0.5e-2*a)))/y))+gamma+2*ln(2)
tau:= 10.000:ksi_fs:=10:p:=0.037:
R0p:= unapply(R0, [a,x]):
R0f:= proc(a,x)
local r:= fsolve(R0p(a,x), y= 0..1);
`if`(r::float, r, Float(undefined))
end proc:
M:= Matrix(
(100,100),
(i,j)-> R0f(i, 1 + (j-1)*(0.5-0)/(100-1)),
datatype= float[8]
);```

After approximately 2 hours of calculations I get a message window

But I repeat this calculations on another computer with the same Windows 7 64 bit and Maple 17 I don't get such error and I obtain desired data.

So can Maple be sensitive to the hardware?

## How to numerically solve differential equation?...

I'm trying to numerically solve the differential equation: y' = -2xy + 1. Naturally, I come across the non-elementary integral of e^(x^2). By hand, I used a 2nd degree MacLaurin polynomial to get y = xe^(-x^2) + x^3/3e^(-x^2)+x^3/6e(-x^2).

How do I use Maple to numerically solve this, with step sizes of h=0.1 and h=0.05 and plot them?

## How do i write a "if...then" function in Maple?...

Hi all, I'm using text box and push button to create my user interface for my system. I  wish to use a if..then function to check some condition, if the condition is true then do statement and print out in the text box. When is key coding in the push button and click the push button, then if ...then function not working and the result that not suitable for the condition also have been printed out in text box.So,can someone help my to solve the problem?

Here in the coding i did

use DocumentTools in

Do (C = %txtC);
Do (p = %txtpk1);
Do (q = %txtpk2);
Do (d = %txtpk3);
Do (A1 = %txtA1);
Do (A2 = %txtA2);
Do (w = `mod`((C*d), A2));
Do (mp = `mod`(w^((p+1)*(1/4)), p));
Do (mq = `mod`(w^((q+1)*(1/4)), q));
Do (hl = `mod`((mp-mq)/p, q));
Do (h2 = `mod`((-mp-mq)/p, q));
Do (m1 = mp+(hl*p));
Do (m2 = mp+(h2*p));
Do (m3 = (p*q)-m1);
Do (m4 = (p*q)-m2);
if m1 <= 2^(2*k-1) then t1 := (C+(-A1*(m1^2)))/A2 end if;
Do (t1);
if m2 <= 2^(2*k-1) then t2 := (C+(-A1*(m2^2)))/A2 end if;
Do (t2);
if m3 <= 2^(2*k-1) then t3 := (C+(-A1*(m3^2)))/A2 end if;
Do (t3);
if m4 <= 2^(2*k-1) then t4 := (C+(-A1*(m4^2)))/A2 end if;
Do (t4);

Do (%txtw = w);
Do (%txtm1 = m1);
Do (%txtm2 = m2);
Do (%txtm3 = m3);
Do (%txtm4 = m4);
Do (%txtt1 = t1);
Do (%txtt2 = t2);
Do (%txtt3 = t3);
Do (%txtt4 = t4);
end use;

Thabk you.

## Creating a list of Matrices...

I need to create a list of matrices.

with(LinearAlgebra):
interface(rtablesize=50);
E:=[E1,E2,E3]:
P:=[0,1,2]:
N:=3:
B:=[1,2,3]:
for b from 1 to 12 by 5 do
B:=(i,j)->
if i=b+P[a] and j=b+P[a] then E[a]
elif i=b+P[a] and j=b+N+2+P[a] then -E[a]
elif i=b+P[a]+N+2 and j=b+P[a] then -E[a]
elif i=b+P[a]+N+2 and j=b+P[a]+N+2 then E[a]
else 0:
end if:
end do;
H:=[seq(B[b],b=1..12,5)];

It isn't indexing the first and second variable, only the last one was indexed.

## Error, (in plot3d) bad range arguments:...

Can't understand what's wrond. This text from my academic books but it doesn't work on practice. Help please

plot3d(polygons([[0, 0, 0], [1, 0, 0], [1, 0, 0], [0, 1, 0]], [[0, 0, 0], [0, 1, 0], [0, 1, 1], [0, 0, 1]], [[1, 0, 0], [1, 1, 0], [1, 1, 1], [1, 0, 1]], [[0, 0, 0], [1, 0, 0], [1, 0, 1], [0, 0, 1]], [[0, 1, 0], [1, 1, 0], [1, 1, 1], [0, 1, 1]], [[0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1]]), light(0, 0, 0.0, 0.7, 0.0), light(100, 45, 0.7, 0.0, 0.0), light(100, -45, 0.0, 0.0, 0.7), ambientlight(.4, .4, .4), title(cube), style(patch), color(zhue));

Error, (in plot3d) bad range arguments: light(0, 0, 0., .7, 0.), light(100, 45, .7, 0., 0.)

## Display Expression...

I have a expression p:=C*A+A, when i type this to maple, maple display into p:=A*C+A because commutative property of multiplication

but I dont want to do like that. How can I display into p:=C*A+A?

## How can I get an Exact solution for system of ODE ...

I have a system of ODE that I need to get an exact solution to. How can I do this using Maple? I tried doing it but error pops out.

Thanks

## How to extract data from implicit function with a ...

I plotted number of functions y=y(x) with different parameter aa for given value of tau (see the code below)

``````restart;
R0:=gamma+2*ln(2)+Re(Psi(1/2+(1+I)*tanh((1+I)*x)/((tau+0.25e-1*a)*y)))+ln(y);
tau := 9.975;
with(plots);
implicitplot({seq(R0, a = 1 .. 50)}, x = 0 .. 5, y = 0 .. 1, numpoints = 1000);
``````