Thomas Richard

Mr. Thomas Richard

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11 years, 217 days
Maplesoft Europe GmbH
Technical professional in industry or government
Aachen, North Rhine-Westphalia, Germany

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These are answers submitted by Thomas Richard

We can help odetest in a trivial way:

simplify(eval(eval(the_diff_1,x=0),ic));

Likewise for the explicit solution.

Of course, odetest should do this automatically.

You can enter the fractional ODE as

fde := diff(g(t),t$alpha) = r*g(t)*t^(1-alpha)/GAMMA(2-alpha);

but dsolve does not handle ODEs of unspecified differential order.

For alpha=1, it's trivial, of course.

An easy workaround is

f := cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2));
f := radnormal(f);
F := int(f,x);
d := simplify(simplify(f-diff(F,x)));

That simplify is needed twice here is a weakness; it should be an idempotent operation.

P.S. I don't think the error message was a known problem, so I've submitted an SCR. Thank you for pointing it out!

I think the DataTable feature (suggested by @acer) solves your problem, but here's a complimentary remark: Maple 2021 introduced the PersistentTable package that you might want to take a look at. Let me quote the 1st paragraph of its description:

The PersistentTable package provides a connection object that behaves somewhat like a table, except it is (by default) backed by a file containing an SQLite table. As a consequence, any information stored in the table persists when Maple is shut down or restarted. Furthermore, there is some extra functionality for searching through the stored information.

 

You can set

infolevel[all]:=1:

to obtain diagnostic information. Caution - it's a lot of output, including the routines (methods) being applied.

Apparently, Solve is first trying to bring the system to RIF (Reduced Involutive Form) which seems to be inappropriate here...

There isn't really a setting, but you can give a hint so that int succeeds:

J := int(sin(x)^(2*n+1),x=0..Pi);
IntegrationTools:-Change(J,u=cos(x));

The assumption is not needed here - one of the benefits of the GAMMA function.

Maple can also take care of computing the Laplacian in polar coordinates:

lap := VectorCalculus:-Laplacian(w(r,theta),'polar'[r,theta]);
pde := lap = r^3*cos(3*theta);
sol := simplify(pdsolve(pde));
pdetest(sol,pde); # optional check

 

Please contact Customer Service at custservice@maplesoft.com and tell them about the problem (or link here). Make sure to include your school name and Purchase Code (do not post it here nor on other web sites).

See also https://www.maplesoft.com/support/index.aspx.

The D operator can be applied to procedures:

dg := D(g);

 

Maple has some packages that provide step-by-step solutions (see here for an overview), but inttrans is not one of them.

You can obtain some diagnostic output by setting

infolevel[invlaplace] := 5:

before, but that's more helpful for programmers than for users.

A core dump should never happen, of course. But I cannot reproduce it with Maple 2020 on our Linux box.

Could you cross-check with Maple 2021, where we updated the GMP library from 5.1.1 to 6.2.0, please?

By the way, the factors of RSA-100 have been published 30 years ago.

Finally, if you ever have any floating-point result whose exact representation cannot be obtained directly (say, from numerical integration), try to apply Maple's identify command, which is in some sense the inverse operation of evalf.

This is just a copy&paste error; it lost the powering (exponentiation). Correct code is as follows:

GlobalSolve(x^3-y^3-x+y, {x^2+2*y<=6}, x=0..5, y=0..5);

The online help pages are just static exports of Maple's built-in help pages, and mapping their format to HTML has limitations, of course. Better use Maple's help browser directly. With the click of a button, you can copy the Examples section, or open the entire help page as a worksheet.

I'm not really familiar with that topic, but Maple 2020 introduced the LieAlgebrasOfVectorFields package; please see here for the description. If that's what you need, consider upgrading from Maple 2019.

In Maple 2021, released two weeks ago, this package has been enhanced by the new MapDE command, by the way.

If we supply a hint, pdsolve succeeds:

infolevel[pdsolve] := 5: # optional
eq1 := 2*m*(E + 8*Pi*epsilon/r)*f(r, t)/h^2 + R*diff(f(r, t), r $ 2)/r - diff(f(r, t), t $ 2)/(a^2*c^2) = 0;
iv1 := f(r, 0) = 0, f(R, t) = 0, D[1](f)(0, 0) = R;
sys := [eq1, iv1]:
Sol := pdsolve(sys, HINT=`*`);
pt := pdetest(Sol, sys);

However, the solution is complicated, involving Airy wave functions and their derivatives. I've been unable to simplify some of the pdetest outputs to 0...

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