Glyph2.maple

The above link is a maple workbook containing the package Glyph2 together with the install script and two worksheets illustrating the difficulty I am having with the code in the procedure assignaltbasis (near the end of the code in Glyph2.mpl).

The problematic code is shown standalone is basisdemo worksheet, but reproduced below for reference. Interestingly, even though the table should be evaluated in a seq command, outside the module it works without eval. Inside the module evaluation does not make any difference.

indxs := [1, 2, 3, 4];
altbasis := [seq(seq(e[i[]], i = combinat:-choose(indxs, 2*k)), k = 1 .. 2)];
gen := table([seq(op(gen[i]) = bivec[i], i = 1 .. nops(gen))]);
exprs := [seq(exteriorp(seq(gen[op(2*i - 1 .. 2*i, b)], i = 1 .. nops(b)/2)), b = altbasis)];

The worksheet Basischangedemo shows how the exported procedure “assignaltbasis” is used in the module and the error that results if a bivector basis is used. From experimentation I have found that the error results because “assignaltbasis” passes the table name to the procedure “exteriorp” instead of the bivectors that should have resulted from evaluation of the table. Including the eval command within the seq procedure does not make any difference to the result. I am unclear whether this is a problem with evaluation of the table or a problem that results from namespace conflict.

I have a further namespace problem with the local variables, AltRoot, AltToStd, and StdToAlt which store the results from assignaltbasis.  If I declare these variables as exports, I get an error message “attempt to assign to a protected variable”. Therefore I added an exported procedure “ShowAltBasis” to display the results.  As you can see, this procedure produces the fully-qualified names of each blade making the result difficult to read. I would prefer to get rid of the “Glyph2:-” qualification.

The waters are muddied even further because the other worksheet, “basisdemo”, contains the core code extracted from assignaltbasis showing that the code using the table actually works (outside the module). From this I conclude that a namespace conflict exists within the module, preventing the table from fully evaluating.

My understanding is that within the module local and exported names are more or less equivalent, so I am puzzled why local and exported names in assignaltbasis are so problematic.

I would appreciate any advice about these issues. Clearly my understanding of maple’s namespaces is incomplete.

We often use the vector notation "< >" as in <x, y, z>.  However, when I use it with a function, it does not evaluate the same way as a simple list "[ , ]". 
 

The value of k is not applied in g2.  Can someone point me in the direction as to the difference between the two types of entities as interpreted by Maple?  

Download HowToDefineTensorRankZero.mw

Using the latest Physics package, I try define a tensor of rank zero, but an error accurs:

> Define(Theta = varepsilon[mu, ~mu](X));
Error, (in Physics:-Define) expected left-hand-side of tensor definition as a tensor with non-numerical indices, received: Theta

The same error occurs when I try:
> Define(Theta[] = varepsilon[mu, ~mu](X));
Error, (in Physics:-Define) expected left-hand-side of tensor definition as a tensor with non-numerical indices, received: Theta[]

So my question is: how can I define a tensor of rank zero? 
Hope someone can help me out. 

Regards, Wouter

Fyi, this solution to 1D wave pde is wrong. The solution does not even satisfy the PDE itself. Compared it to a numerical solution and they are not the same solution. Do not have time now to write the hand solution. But it is clear the solution is not valid.

I do not know now how to roll back to earlier version of the Physcis packages to see if this used to work OK before. Since when typing Physics:-Version(420) It gives error

Error, (in Physics:-Version) unable to determine the Physics Updates version, could you please report the problem to support@maplesoft.com

And Physics:-Version(425) seems to hang. I am not sure if these commands are supposed to automatically download the physics package from the cloud and install it on my PC or what.

Any way, could someone please verify the solution they get is the same as shown below? May be someone with earlier physics package could try to see if they get different solution?

Download sept_23_2019.mw

I'm trying to debug a problem with define_external, and I would love some help!

I have a Maple module that contains this line of Maple code:

EigValsVecsC := define_external('EigValsVecsC', LIB = cat(dll_home,"\\operators.dll"), 'm'::ARRAY(datatype=float[8]), 'n'::integer[4], 'eig_vals'::ARRAY(datatype=float[8]), 'eig_vecs'::ARRAY(datatype=float[8]), 'THREAD_SAFE');

Running the Maple code to create the module produces this error message:

"Error, (in ModuleLoad) external linking: error loading external library C:\Users\zander\maple\toolbox\EigLib\misc\operators.dll: The specified procedure could not be found."

I've discovered that there's a single line of C++ code (in the C++ function EigValsVecsC) that I can comment out to make the problem go away.  Here's the line of C++ code:

MKL_INT info = LAPACKE_dsyev(LAPACK_ROW_MAJOR, 'V', 'U', eig_vecs.rows(), eig_vecs.raw(), eig_vecs.rows(), eig_vals.raw());

To clarify:

• C++ compilation succeeds for operators.dll (which contains the function EigValsVecsC), with this one line either commented or uncommented.
• The C++ function EigValsVecsC works correctly when not called from Maple (i.e., called from Visual Studio or the command line), with this one line either commented or uncommented.  (Of course, it doesn't work fully correctly with this one line commented, since this one line is the whole point of the function.  But it runs successfully and does the correct massaging of inputs.)
• When this one line of C++ code is commented, the Maple module builds successfully, and I can call EigValsVecsC in Maple and get results back showing that, in the C++ code, the inputs to the commented line are being set up properly.

The relevant include statement in the C++ code is:

#include "mkl_lapacke.h"

I don't have to comment out the include statement (though the compiler may well be ignoring it if it's never used, when the call to LAPACKE_dsyev is commented out).

I have no good theories about what the problem may be.  I've been trolling the Web for any helpful information, and I've come up with nothing.

Can anyone help?  Thanks!

Download Transfer_function.mw

Hello

I have this problem:

in which I have to find the four transfer functions relating the outputs(y₁ and y₂) to the inputs (u₁,u₂).

The u and y are deviation variables. 

The objective is to find the four transfer functions:

So I have done it by hand but I was wondering if there are any maple commands, that could be used to solve such a question?

I found the transfer functions to be:

I have a vector calculus question. I was given three points, p,q, and r, and I got Maple to calculate vectors pq and pr. I also got Maple to calculate the cross product vector, pq x pr. The problem says to draw the triangle formed by p,q, and r, as well as the cross product vector. I tried to use the polygonplot tool to plot the triangle formed by the three points, but I am confused as to how to get the cross product vector to appear on the plot with the triangle. What tool do I use to plot the triangle with the cross product vector on it, so I can have a picture of the cross product vector starting at p, showing that it is orthogonal to vector pq and pr?

Thank you.

Hello MaplePrimes users

How do I find expressions of an integer as a sum of four squares in Maple?

I have some trouble solving the pde of:
ut + u^2*ux = u, u(x,0) = x, with x::real and t>0.

I think that I have 2 problems.

1.
The first part of the code I define u(x,t) with both the variable rp.
Then I define the variable q copying the definition of u(x,t).
When I try to insert q and u(x,t) in the initial equation - one is able to be reduced to one term while the other isn't.
So I'm not really sure what is happening here.

2.
When I use Maple's pdsolve() I get a result, but when I insert the answer in the initial equation - then it isn't correct.
I tried to show this in the last part of the code.

Download asol1-1.mw

I just  found what seems to be a serious problem and I am not able to figure if it is related to my own installation or not.

After I installed Physics 426 (Published on Sept 17, 2019) using the Maple GUI install button (which now works for my PC), I found I am not able to integrate basic things.

It seems to affect int when using some build in function with definite integration, but it could be others also. I need to test more. 

Could someone see if they get same problem as well?  

Could also someone please remind me of the library  commands to issue in order to remove current Physics version 426 and install earlier Physics version package, say 425, or any other version, so that  to see if this is related to version of a physics package or not?

Download int_not_working.mw

Why Maple 2019.1 gives an error when no initial conditions are given for the following heat PDE with periodic BC?

I am using Physics 426 (current version). On windows 10.

When adding ic as some arbitrary function f(x), then the error goes away. But no ic needs to be given to solve this PDE. The answer can be left using arbitrary constants in this case.

I also found that this seems to happen when the BC are periodic. When using the normal Dirichlet B.C. and omitting the initial conditions, the error went away.

Am I doing something wrong or is this a bug?

Download problem_09_20_2019.mw

Hi,

I have this code to calculate taylor method but I do not know how to write the part about derivative of a function f  inside the loop for ??

restart;
f:=(t,y)->y-t^2+1:
eqn:=diff(y(t),t)=y(t)-t^2+1:
ex:=dsolve({eqn,y(0)=0.5},y(t)):
t[0]:=0:w[0]:=0.5:h:=0.2:ex[0]:=0.5:e[0]:=0:
for n from 1 to 10 do
t[n]:=n*h;ex[n]:=t[n]^2 + 2*t[n] + 1 - exp(t[n])/2;
w[n]:=w[n-1]+h*f(t[n-1],w[n-1])+((h^2/factorial(2))*(f(t[n-1],w[n-1])-2*t[n-1]));
e[n]:=abs(ex[n]-w[n]);
od:

printf(" i | t[i] |(Taylor)w[i] |(exact)y[i] |Error | \n ");for i from 0 to n-1 do
printf("%2.2f| %5.2f  | %5.6f| %5.6f  |  %5.6f | \n", i, t[i], w[i] ,ex[i],e[i]) ;
od;

Hi there! 

One of my favorite videogames is pokémon as you can probably guess from the title. As a player I always wanted to optimize my chances of obtaining the rarest and best pokémon in the game. I have been working on an application that aims to use graph theory to analyze the game Pokémon Blue. The application explores the following questions:

Which is the rarest pokémon in the game?
Where can I find an specific pokémon and with what probabilities?
What is the place with most different species of wild pokémon?

I also included algorithms for the following: Given a certain desired team

• Find the minimum amount of places to visit to catch them and return the list of the places the player will need to visit.
• What are the routes with best probabilities to catch each pokémon from my desired team?

Check out my application at: https://www.maplesoft.com/applications/view.aspx?SID=154565.

The following are some of the results obtained in the app:

What is the most common pokémon?

I did not only considered the amount of places a pokémon can appear in but also the probabilities of it appearing in each place.

What are the connections between pokémon and places?

In my graph, I connected a pokémon and a place if such pokémon could be caught in that place. The following is an example for the pokémon Pidgey. The weights of the edges are the probabilities of finding Pidgey in each route.

Viceversa, I did the same for how a route is connected to the pokémons in it:

 

Map of the Game
I also generated a colour coded version for the map of the game: where blue means that the place is a water route, brown means it's a cave and green means it's a tall-grass route.
It's amazing what Maple's graph theory toolbox can do.

My problem is as following:
Our school has a requirement that we have to show the numeric values, when we calculate. And i was wondering if there's an easy way to do it?

Example of how i would normally do it:
A:=5
B:=5

C:=A+B = 10. 

What they want:
A:=5
B:=5

C:=A+B = 5+5=10

Does anyone have an easy way of doing this? Because in an exam I wont have the time to plug in the values myself.

Hey, I have been using maple for a whole 30 minutes, and have no idea what I am doing! I have some code set up to run the Eulers approximation to solve an ODE.

The code seems to run fine, but in the final output where it should give a number value, I am getting 6+0.10f (where f is a variable define beforehand). My friend who has run the same code does not run into this problem.

The Maple software is a on a public school computer, so maybe the specific one I am using has some setting set up that are not default?

Does anyone know what is going on? In the end I would like the output to be a decimal number. 

Reference image: https://imgur.com/a/A4DZuik