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Use of ATLAS in calculation of Riemannian metric i...

Asked by: Gideon Maschler 0
April 07 2018
0  2

I wish to calculate connection, curvature, Ricci curvature etc. for a

Riemannian metric given as follows: there is an orthogonal frame of vector

fields with stipulated Lie bracket relations between them. The frame is

orthogonal but not orthonormal, and the lengths of its vector fields are functions

of a single function on the manifold. Given these metric values on the frame and the

Lie bracket relations, the covariant derivatives are in principle computable from the

Koszul formula, hence connection and curvature are all determined.

When I try to define the metric using a dual coframe in ATLAS's Metric

routine, it allows me to define it but claims there is not actual curvature.

From the help it seems the coframes used in this routine are always given

as differentials of coordinates. Is there a way to get the metric via the data

given above without putting in by hand all the different Koszul formulas etc.?

bug or syntax error...

Asked by: awass 301
April 07 2018
0  6

Can anyone explain this?
> if  3 = 0 mod 3 then print(good) else print(bad) end if;
                        bad

> if  0 = 3 mod 3 then print(good) else print(bad) end if;
                       good
 

Tabulate and append text below...

Asked by: minhhieuh2003 140
format tabulate
April 07 2018
0  2

Help me about Tabulate and append text below.

file help: text_and_tabulate.mw

PDEsolve throws error with empty function...

Asked by: rahinui 110
April 07 2018
1  2

Hello,

     The following system of ODEs is handled correctly by dsolve, but PDEtools:-Solve raises an error:

ranking := [{A(), B(x)}]:
eqn_sys := {D(B)(x) = 0, A()* D(B)(x) = 0}:
dsolve(eqn_sys, ranking);
# {A() = A(), B(x) = _C1}
PDEtools:-Solve(eqn_sys, ranking);
#Error, (in dsolve) found many possible indications of the solving variables as [{B(x)}, [{A(), B(x)}]]

In particular, it seems the error is raised when 1) the ranking is a nested list and 2) at least one of the ranking elements is a function without any arguments.

Admittedly, this is a very strange case, but I did run into this earlier today. Of course, the example here is contrived (the nested-list ranking is completely unnecessary for this example), but it illustrates the error.

As a workaround, I found replacing the function A() with its name A in the ranking solves this problem (it can be left as a function in the system of equations). Nevertheless, I thought I would point this out as it seems dsolve handles this just fine even without the workaround, and presumably PDEtools/Solve should be able to as well.

This seems similar to a previous bug; this bug was fixed in Maple 2018. Unfortunately, I haven't updated yet, so I can't verify if the patch solves this problem as well.

How to get PDEtools/Solve to pass arguments...

Asked by: rahinui 110
April 06 2018
1  2

Hello,

     So, dsolve is able to pass arguments through to casesplit. Further, PDEtools/Solve is able to pass arguments through to dsolve. However, it appears PDEtools/Solve isn't able to pass arguments through dsolve to casesplit? For instance, consider the following differential equation:

eq := {diff(A(t),t) = A(t)*x}:
dsolve(eq, {A(t)}, ivars={x,t});
PDEtools:-Solve(eq, {A(t)}, ivars={x,t});

Here, I'm considering both x and t to be independent variables (hence, A(t) should not depend on x).

In that case, dsolve correctly gives the only solution as A(t) = 0. However, PDEtools/solve doesn't seem to pass-through the ivars option and incorrectly gives A(t) = _C1*exp(x*t) as a solution.

Is there another way to have PDEtools pass this option through to casesplit?

Thanks!

How to plot a 3D curve using implicit equations fo...

Asked by: rlewis 40
April 06 2018
1  24

For example, 

f(x,t) = t^2 x^2 + t x + 2x - 1, g(y,t) = t^2 y^3 + t y^2 + 2y - 1, h(z,t) = 2t^2 z^3 + t z + 3z - t^2, 0 < t < 4.

I have an initial point on the curve corresponding to t=0.  The answer is a curve in space, or maybe several curves.  The real example that I care about is much more complex than this and has trig functions of t.

Problem to simplify an expression ...

Asked by: Muhammad Usman 245
simplify simplification isolate
April 06 2018
0  6

Dear Users!

Hope everyone is fine. I am want use the command of isolate only red color term. Then I need help to simplify the expression term by term like simplify the rational expressions, combine powers, simplify radicals etc..

x*c*(diff(f(eta), eta))*epsilon/(-epsilon*t+1)^2+(1/2)*x*c^2*(diff(f(eta), eta, eta))*y*epsilon/((-epsilon*t+1)^3*sqrt(c/(nu*(-epsilon*t+1)))*nu)+x*c^2*(diff(f(eta), eta))^2/(-epsilon*t+1)^2-sqrt(c*nu/(-epsilon*t+1))*f(eta)*x*c*(diff(f(eta), eta, eta))*sqrt(c/(nu*(-epsilon*t+1)))/(-epsilon*t+1) = a*x*epsilon/(-epsilon*t+1)^2+a^2*x/(-epsilon*t+1)^2+x*c^2*(diff(f(eta), eta, eta, eta))/(-epsilon*t+1)^2+sqrt(2)*GAMMA*x^2*c^3*(diff(f(eta), eta, eta))*sqrt(c/(nu*(-epsilon*t+1)))*(diff(f(eta), eta, eta, eta))/(-epsilon*t+1)^3+A*g*beta[T]*theta(eta)*T[w]-A*g*beta[T]*theta(eta)*T[infinity]+A*g*beta[C]*phi(eta)*C[w]-A*g*beta[C]*phi(eta)*C[infinity]-sigma*B^2*x*c*(diff(f(eta), eta))/(rho*(-epsilon*t+1))+sigma*B^2*a*x/(rho*(-epsilon*t+1))

I am waiting your postive answer on it.

 

How do I solve for the real part of a variable?...

Asked by: SimonFriborg 10
complex solve inequality
April 06 2018
1  3

Hi

I am trying to solve an inequality for the real parts of the solution to be less than 0. How do I do that? When trying to use solve, and specifying Re() Maple warns about lost solutions. I can see there are complex solutions to the equation, but i cannot make Maple calculate them. Maple gives me a range for the real solutions (6.1.11) and (6.1.12), but if I use a number out of the range the inequality is still met, the solutions is just complex, which does not matter. The variable a seems to be able to be between -8 and 3 for the real part of the solution to be less than 0.

Kind regards

Simon

How to Quantify the Difference between Representat...

Asked by: Jjjones98 45
series fourier approximation
April 06 2018
0  4

I am considering a Fourier series

$cos (\alpha x) = \frac{1}{2}a_0 + \sum_{k=1}^{\infty}a_k cos(kx)$ for x between -pi and pi.

I have also shown using a different Fourier series that cos (\alpha x) has an alternative representation:

\frac{cos(\alpha x)}{\sin \alpha \pi} = \frac{1}{\pi \alpha} (1 + \frac{(\alpha \ pi)^2}{6} - \frac{\alpha x^2}{2 \pi} + \frac{2*\alpha^3}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{k^2(k^2 - \alpha^2}*cos(kx)$.

To show that the second representation is a better approximation, I need to find the number of terms for this series and the original Fourier series needed for there to be a difference of 10^{-3} from the exact value of cos(\alpha \pi), assuming that \alpha = 0.75.  Could someone advise how I might do this?


 

Problem with large document block (large expressio...

Asked by: ebrahimina 40
2dmath large-expressions
April 06 2018
0  3

Hello, when I write a large document block in maple and want to do some operations, maple shows wait cursor (hourglass) for 2-3 minutes again and again. I attached a sample file below. 

I found out when maple is installed , javaw.exe also instal and when I open bellow file, the javaw use 15% of cpu and this cause maple works slowly. 

the attached file is just an example for large document block and I undrestand that it can be simplified. I want to know how to handle large expressions generally?

K-Euler_Lagrange.mw

 

dividing the function on its maximum...

Asked by: adel-00 135
maximum
April 05 2018
0  3

Dear all,

Trying to divide the function (f1) at its maximum and normalized it.. there is error on. the (proc)

could anyone help me on that PLEASE.

 

restart:
assume(Delta,real):assume(c,real):xr:=1:ao:=sqrt(1+c^2):theta:=arctan(c):a:=ao*exp(I*theta):b:=I*0.5*Delta-a*(k-1)*xr*0.5:no:=1:AA:=5:theta1:=0:Omega:=10:
f:=sqrt(Pi/ao)*exp(-I*0.5*theta)*sum(exp(b^2/a)*exp(-a*(k-1)^2*xr^2),k=1..1):alpha:=AA*exp(I*theta1):
f1:= AA^2+((Re(f))^2+(Im(f))^2)*Omega^2+2*Omega*Im(conjugate(alpha)*f):
P1:=plot3d((f1),Delta=-5..5,c=-5..5,axes=boxed,font=[1,1,18]):
Normalize:= proc(P::specfunc(anything, PLOT))
local A,Smax1;
A:= op([1,1], P);
Smax1:= max(A[..,2]);
if A::list then A:= Matrix(A) end if;
A[..,2]:= A[..,2]/Smax1;
subsop([1,1]= A, P)
end proc:
P1:= Normalize(P1):
display([P||(1..1)]);

 

Maple won't open...

Asked by: Chrras 20
launch
April 05 2018
2  2

Hi

 

Maple 2017.3 wont open, when I launch it. I've tried updating Maple, updating Java, updating my graphic driver and of course restarting my computer. It just keeps on the loading launcher at a completely empty loading bar.

 

I've also tried downloading Maple 2018.0, and the same problem appears. This is how it looks:

Do anyone know how to fix this?

factor of a polynomial ...

Asked by: gaurav_rs 65
polynomial factor
April 05 2018
0  8


 

> 

restart;
> 

Digits:=50;
> 

A11:= 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> 

 

> 

factor(A11);

Warning,  computation interrupted

  
> 

 

50

 (1)
> 

 

> 

 

> 

``


 

Download factor_puz.mw

Dear Maple users,

I am struck with a polynomial. Is there a way to factor it ?

work sheet is attached.

 

regards,

 

solve the equation......

Asked by: mehran rajabi 120
solve
April 05 2018
0  8

Hi every body: 

How can I solve this equation with maple? assuming x>0

eq:=-44.51913564*sinh(sqrt(x))*x^5*sin(sqrt(x))*cos(0.6232678986e-1*x)+5.872275982*x^(11/2)*cosh(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)+5.872295982*x^(11/2)*sinh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)-0.1e-5*x^6*sinh(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)+11465.08352*x^6*cosh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)-0.10000e-4*x^(11/2)*sin(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)+.1246535797*cosh(sqrt(x))*x^4*cos(sqrt(x))*cos(0.6232678986e-1*x)+158.9969129*x^(9/2)*sinh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)-94.84329962*cosh(sqrt(x))*x^5*cos(sqrt(x))*sin(0.6232678986e-1*x)-0.2e-2*x^7*sinh(sqrt(x))*sin(sqrt(x))*sin(0.6232678986e-1*x)+0.4000e-2*x^(13/2)*cosh(sqrt(x))*sin(0.6232678986e-1*x)*sinh(sqrt(x))+0.10000e-4*x^(11/2)*cosh(sqrt(x))*sinh(sqrt(x))*cos(0.6232678986e-1*x)-158.9969129*cosh(sqrt(x))*x^(9/2)*sin(sqrt(x))*cos(0.6232678986e-1*x)+38209.64552*sinh(sqrt(x))*x^6*sin(sqrt(x))*sin(0.6232678986e-1*x)-3761.932636*x^(13/2)*cosh(sqrt(x))*sin(sqrt(x))*sin(0.6232678986e-1*x)-3761.924636*x^(13/2)*sinh(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)-0.4000e-2*x^(13/2)*sin(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)-2.*10^(-7)*x^(13/2)*cosh(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)-11465.08352*x^6*cos(0.6232678986e-1*x)+.1246535797*x^4*cos(0.6232678986e-1*x)-94.84329962*x^5*sin(0.6232678986e-1*x)+0.1e-5*x^6*cosh(sqrt(x))^2*cos(0.6232678986e-1*x)-0.1e-5*x^6*cos(sqrt(x))^2*cos(0.6232678986e-1*x)+0.3e-5*cosh(sqrt(x))^2*x^6*sin(0.6232678986e-1*x)-0.2e-2*x^7*cos(sqrt(x))^2*sin(0.6232678986e-1*x)+0.2e-2*x^7*cosh(sqrt(x))^2*sin(0.6232678986e-1*x)+2.*10^(-7)*x^(13/2)*sinh(sqrt(x))*cosh(sqrt(x))*cos(0.6232678986e-1*x)+2.*10^(-7)*x^(13/2)*cos(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)-2.*10^(-7)*x^(13/2)*sinh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)+1.159305284*10^5*cosh(sqrt(x))*x^(11/2)*sin(sqrt(x))*sin(0.6232678986e-1*x)-1.159305284*10^5*x^(11/2)*sinh(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)-8.359616334*10^6*x^7*cosh(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)+8.359616334*10^6*x^7*sin(0.6232678986e-1*x) = 0

tnx ... 

batch file and directory...

Asked by: taro 505
terminal
April 05 2018
1  2

Hello people in mapleprimes,
I have two files: a batchfile named test.command, and a mpl file,
both in <<my home directory>>.

And, the codes written there are, for the test.command,

/Library/Frameworks/Maple.framework/Versions/2017/bin/maple test.mpl > output.txt

And, for the mpl file,

1+1;
diff(x^2,x);
int(x^3,x);

The test.command was made executable with chmod u+x  test.command, in advance.

From my home directory, I can run the test.command, and obtain output.txt with the result of the calculation of 
the mpl file. The above things have no problem. 

My question is a following.

When I moved the two files, the batch file and the mpl file, to /Users/myname/Desktop/maple_test, 
I cannot get maple to exhaust the appropriate output.txt but an error message, saying it could not read the mpl file.
What should be done to the contents of two files?

I hope you will teach me about this.

Thanks in advance.

taro

 

 

 

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