Making Matrix nice and neat in observation...

I need my results are nice and neat in final presentation so how can I change the way it present matrix in maple, its so messy in hear like picture . It happend resulted in Maple can reduce the same ratio such as As^2+Bs^2=(A+B)s^2, I tried all my best to find way to simply it but its so hard due to my noob in maple. Please help me make it nice and neat in array of matrix [    ].

Problem when substituting terms in an equation...

I have the following equation:

eqn := m*`&ell;`^2*(diff(q[1](t), t, t))+k[t]*`&ell;`^2*q[1]+5*k[r]*q[1]-4*k[r]*q[2]+k[r]*q[3]-5*P*`&ell;`*q[1]+2*`&ell;`*P*q[2]+2*`&ell;`*T*q[1]-`&ell;`*T*q[2] = 0;

And I want to execute the following substitutions:

k[r]/(k[t]*`&ell;`^2) = alpha;
P/(k[t]*`&ell;`) = sigma
T/(k[t]*`&ell;`) = theta

For that, I have tried:

expand(eqn/(k[t]*`&ell;`^2));
eqn1:= algsubs({k[r]/(k[t]*`&ell;`^2) = alpha, P/(k[t]*`&ell;`) = sigma, T/(k[t]*`&ell;`) = theta}, %);

And:

eqn1:= algsubs(k[r]/(k[t]*`&ell;`^2) = alpha, %);
eqn2:= algsubs(P/(k[t]*`&ell;`) = sigma, %);
eqn3:= algsubs(T/(k[t]*`&ell;`) = theta, %);

But none of these have worked. Does anyone know how to solve this?

How to use convert/Diff with eval...

Hi all,

I have an differential equation in terms of the D-operator and am trying to convert it to diff form. Using convert/Diff works fine as long as partially evaluated functions don't appear in the equation. However, I can't figure out how to get the two to cooperate.

For instance, running

D[2](eta)(t,x)+D[2](phi)(t,x,0)+D[2](phi)(t,x,0):
convert(%, Diff);

returns

D[2](eta)(t,x) + Diff(phi(t,x,0),x)

Why is the eta term not converted to diff(eta(t,x),x)?

Thanks a lot!

Differentiation and Integration with Interpolation...

In Maple 2018 help written:

The interpolation methods available in the Interpolation package all work as follows. First, the user calls one of the commands in the package, submitting the input points and the values at these points. This returns an object encapsulating all the data and options submitted. This object can then be used like a normal mathematical function, e.g. for plotting, integration, or just to evaluate at a given point.

The Interpolation[Interpolate] command was introduced in Maple 2018

My test example:

with(Interpolation):

points := [seq(x, x = 0 .. 10, 1)]; data := [seq(sqrt(1.+x^2), x = 0 .. 10, 1)];

f := Interpolate(points, data);

f(1); # OK works :).

int(f(x), x = 0 .. 1); # Not working ?

int(f(x), x = 0 .. 1,numeric); # Not working ?

eval(diff(f(x), x), x = 2);# Not working ?

plot(f(x), x = 0 .. 10);#  OK works :)

plot([f(x), diff(f(x), x)], x = 0 .. 10);# Not working ?

plot([f, diff(f, x)], 0 .. 10);# Only a half  working ?

Thanks.

How do I replace this variable with a number?...

I want ot replace the free variable introduced by the BackwardsSubstitution procedure with a number. But though the variable looks like x1 I think it must be something else.

problem.maple

Bug in Physics metric?...

Hi all,

I found some strange behavior while usings tensors from Physics; I wanted to make sure I wasn't missing something here.

It seems that changing the metric (for instance, to +++-) causes raising and lowering problems. As an example:

with(Physics):
Setup(metric=`+++-`):

# Define our system of equations
Coordinates(X):

# Define tensors
{U[~mu] = [u(X),0,0,1],
A[~mu]=[0,0,0,n(X)]}:
Define(op(%)):

F[mu,nu]=d_[mu](A[nu]) - d_[nu](A[mu]):
Define(%):

# Multiply tensors
TensorArray(F[~0,~mu].U[mu]);

This produces

-diff(n(X),x1)*u(X)-2*diff(n(X),x4)

However, only the first term should be present. It seems that changing the mulitplication to F[0,~mu].U[mu] produces the correct output, as does removing the Setup call. Also, manually defining F produces the expected output; only defining it via A seems to generate the discrepancy.

Any idea if this is a bug or a feature?

Thanks!

write finite  boundary conditions in dsolve?? ...

how i can write these boundary conditions for dsolve?

(diff(u(r), r))^(n-1)*(diff(r*(diff(u(r), r)), r))/r    be [finite] at r =0

and  u(0) = finite?

Thanks..

Using Physics inside a procedure...

Hello!

I can't seem to figure out how to use the Physics package within a procedure. In particular, I can't get tensors to be recognized within the body of the proc.

As an example, here's a short program that works correctly when not in a procedure:

with(Physics):
Coordinates(X,quiet):
d_[mu](X[~mu]);
# Returns 4; Correct

However, placing this code inside a proc causes the tensor X to not be recognized as a tensor:

Test := proc()
uses Physics:

Coordinates(X,quiet):
d_[mu](X[~mu]);
end proc:
Test();
# Returns 0; Wrong

Apparently, Physics:-Coordinates still defines the tensor X (as can be checked by calling Physics:-Define()). However, the derivative d_[mu] (X[~mu]) seems to be treating X as a standard symbol. Any idea how I would go about correcting this?

Thanks!

Odditity in CircleSum Procedure...

I have a procedure which works. &oplus;(a,b) gives annwer.   a &oplus; b also gives answer. That was a surprise, discovered from a typing mistake. If b is negative is needs to be enclosed in delay evulation quotes.

2  questions

Can anyoone expllain this useful property? Any way around having to use delay evaluation quotes for negative numbers?

 (1)

 (2)

 (3)

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How to obtain the Version number of the Physics pa...

On the maple cloud, I see that current version is 38 for Physics

After I installed, I typed

Physics:-Version();

It gives

I was expecting to see "38".  Why does Physics:-Version(); does not give the version number as shown on Maple cloud? Using only a date for a version number is not a good idea. There should be a number there. (date can also be included, but a number should be the official version number).

Is there another command to use to obtain Version number "38"?

Does each package shown on cloud support packageName:-Version()? I tried this command on another package I have, but I got an error saying it does not Version()

OrthogonalExpansions:-Version();
Error, Version is not a command in the OrthogonalExpansions package

Yet, on cloud, it says the version number is "1" for the above package. What does the version number shown on the cloud then really mean?

pdsolve: PDE by series?...

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

It's a bug, design or  something else ?

Error, (in dsolve/numeric/process_input) system mu...

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

solve does not show result!!

dtm.mw