Hello people in mapleprimes,

This time question is a sequel of the previous one:
https://www.mapleprimes.com/questions/224346-Batch-File-And-Directory
, where I could obtain the file with the output.
Maple has been terminated after exhausting the output file.

But, I want  to do the next calculation while using the result in the output file.
For that, I think it might be a good way to have maple calculate a mpl file again, after having added 
new expressions to the original mpl file. But, copying and pasting expressions seen in the output file to the original mpl file with my hand, seems a little messy.

So, what I want to know is whether there isn't a good way for continuing calculations one after another,
while having maple termination after each calculation.

I will be very glad if you will give me an answer to this question.

 Thanks in advance.

Hello i ve tried getting a decimal answer from this subs(x=7,diff(y,x$8)); where y:=sin((x^2)/((x^10)+4))*e^(3*x);
but its not working what should i do?

after the substituion i used evalf(%) but it still had an answer like this 

How do i get the decimal answer???

Thank you,

Hello,

     I've been trying to figure out how to partially expand a trig function using the sum-rule but not the multiple-angle rule. For instance, I would like to expand

sin(2*x+3*y)

to

sin(2*x)*cos(3*y) + cos(2*x)*sin(3*y)

Unfortunately, expand also uses the multiple-angle rules, which is unwanted. The trigsubs command looked promising, but I don't know the names of the variables (x and y here) a priori, so I believe I need something with type matching (like applyrule with x::monomial + y::monomial).

Thanks for your help!

In x axis (0..0.5,0.05) and y axis (0..1)

then how to plot this values 

[.486935382154125, .485087274176440, .483255914856304, .481441076124814, .479642533998987, .477860068520125, .476093463645627, .474342507167362, .472606990609939, .470886709216958, .469181461771770]

I originally posted this question @ Reconciling roots of a series  However, I got no responses.  I have done further work on the problem & attempted to delete my original posting to initiate this one.    I did not see the option to delete Reconciling roots of a series.  So if any website moderator can delete the original & leave this one stand that would be helpful.  The results in this posting are more illuminating.

I have an infinite series that is function of

                                   /2 Pi k x\
                               sin|--------|
                                     \   T    / where k is the frequency parameter that is an integer value from 1 to m.  The series is also linearly dependent on the coefficient, Ck.  However, Ck is nonlinear with respect to k.  3 other parameters are undefined, a0, N, & tau.  Taking the derivative of the series removes the constant a0 & the factor (2 Pi k)/T comes out of the sin term & the sin term bcomes a cos term.  N is a positive integer & tau is a real #, generally between 0 & 1.

The derivative of the series can be evaluated since Ck falls of by 1/k^2 which renders the factor (2 Pi k)/T to (2 Pi)/T.  All is well & MAPLE seems to confirm that by the result (5).  I then attempt to find the roots of the derivative after defining the values for m, a0, N, & tau with both the solve & RootFinding:-Analytic commands.  The results from the 2 do not seem to coincide.

I then repeat the process with chek2.  Now there seems to be some overlap in the results.  But as I pointed out in Reconciling roots of a series in the case of chek the series parameters m, a0, N, & tau have not been assigned values.  In the case of chek2 those parameters do have assigned values; hence, the solution characteristics are different for the solve command, but not for RootFinding:-Analytic.

In a different problem, but somewhat related someone pointed out the superior computational performance of the RootFinding:-Analytic as opposed to the solve command.  The results here if I interpret them correctly suggest that the solve command can be WRONG altogether.  Can this be explained in a concise & coherent manner that most users can follow?  Also, solve can produce an analytic expression as opposed the RootFinding:-Analytic command.  Is there a way to use the RootFinding package to produce an analytical result?  In the case presented below I suppose the analytic result for solutions to chek would be JUNK?

reconcile_solns.mw

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.?

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
 

Help me about Tabulate and append text below.

file help: text_and_tabulate.mw

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.

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!

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.

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.

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

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?

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