Greetings to all. I am writing to present a Maple computation that is somewhat of a programming challenge. A recent Post at Math.Stackexchange.Com asked to compute the number of inequivalent colorings of the vertices and edges of a regular hexagon with two colors available for the vertices and three colors for the edges (vertex colors different from edge colors) under the simultaneous action of the dihedral group D₆ on the vertices and edges. This is a standard application of Burnside's Lemma and can be computed very straightforwardly using a negligible amount of computing resources. Important: this is the accepted method, it is documented at the MSE link and it works quite well. The answer is that there are 4183 unique configurations.

My purpose in this message is to propose the following task: write a program in your favorite programming language to verify this number by enumerating all possible configurations, computing the orbits of each, and tracking the orbits to eventually arrive at, we hope, the answer, 4183 as stated. This being MaplePrimes the programming language in question is Maple, of course. I implemented the enumeration method and it can be found in the attachments to this message. The algorithm takes about two minutes on the machine that I used and peak memory allocation is about 70 MB. This made for a frustrating debug cycle as it needed a two minute wait to see the result of the changes made to the source code. I therefore decided to use Perl instead of Maple. Imagine my surprise when the very same algorithm (consult attachment) implemented in Perl had a running time on the same machine of about three seconds, used a hash table of about 1.6MB and had resident memory footprint of 6MB. (In fact the hash table can be reduced to half size by simplifying the keys which makes them a bit more difficult to read during debugging.) Let me state it like this: Perl vs. Maple resulted in a speed gain of a factor of forty and a memory savings of 90 percent.

Now how to profit from this experience. A question naturally appears at this point: can we optimize the Maple code so as to bring it into the range of the parameters of the Perl? Here we permit all sorts of optimizations that may occur to the Maple coder other than using Burnside where the motivation is that for many of us including myself there always remain additional Maple programming techniques to learn and acquire. I hope this makes for an enjoyable exercise and I am looking forward to seeing a Maple implementation that can compete with the Perl. This is not code golf but conciseness is a plus.

hex-maple.txt

hex-pl.txt

Happy computing!

Best regards, Marko Riedel

PS: I suspect working with hash tables rather than sets may be a start.

MAPLE 15 on Windows 10

I have a file on which I can no longer open. This happened after my computer made me long on again after being gone for a little while. Maple was not running when I got back on. This is not unusal and I just clinck on the file and restart.

This time this did not work.

It comes up with a message asking me to select an input mode. Whatever I select even 'Plain text' it just hangs.

I'd send you an image, but I don't see how to do it. The button provide only allows for something with  url and the snip I made is on my desktop.

I need to get thiis worksheet back. I've put a lot of effort into it.

-Traruh

Here is my code in Maple.

#Solve the initial-value problem using the technique of question 2. Find the implicit solution.
eqn3:=(exp(x)+y)*dx+(2+x+y*exp(y))*dy=0;
(exp(x) + y) dx + (2 + x + y exp(y)) dy = 0
#subject to y(0)=1.
M:=exp(x)+y; N:=2+x+y*exp(y);
exp(x) + y
2 + x + y exp(y)
int(M, x); int(N,y);
exp(x) + y x
y x + 2 y + y exp(y) - exp(y)
implicitsoln1 := exp(x)+y*x+2*y+y*exp(y)-exp(y)=C;
exp(x) + y x + 2 y + y exp(y) - exp(y) = C
y1 := solve(implicitsoln1,y);
RootOf(-exp(_Z) _Z - _Z x + C + exp(_Z) - 2 _Z - exp(x))
C:=subs({x=0,y=1},lhs(implicitsoln1));
exp(0) + 2
y1;

How do I get it to to not have "root of" and give me a more specific solution.

After running Maple in a shell file, I come up with this error that I do not understand on my Mac,

gap_long := 0.117647058823529 Pi

gap_lat := 0.0588235294117647 Pi

lat_begin := 0.441176470588235 Pi

long_begin := -Pi

lat_begin_0 := 0.441176470588235 Pi

long_begin_0 := -Pi

long_max := 0.882352941176471 Pi

lat_max := -0.441176470588235 Pi

33

Warning, `parameter` is implicitly declared local to procedure `set_par_eff`

distance eff distance_eff
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
im in has not
Im in has par
Im in has par
Error, invalid input: eval expects its 2nd argument, eqns, to be of type
{integer, equation, set(equation)}, but received par_eff_post
13

32

31

17

hou := 0

mini := 0

seci := 0

memory used=4.0MB, alloc=32.3MB, time=0.23



If needed, I can attach more files if my question is still a bit too cryptic. Please let me know asap as this is urgent. Thank you so much,
-Z

Hi all,

Please help me with this question. I want to solve a PDE by Maple.

Download SolvePDE.mwSolvePDE.mw

Dear All

Say I have created a Maple module called MYMODULE. This means that I have a .mpl file called

mymodule.mpl, with inside

   MYMODULE := module()

   export myfunction;

   ****

   ****

   end module:

   savelib(MYMODULE, "MYMODULE.mla"):

Hence I use it in such a way:

> with(MYMODULE);

                                                              [myfunction]

I want to associate a help to the function myfunction. I know that with Maple18 things have changed

but I am not able to find enough information online. Say I have a .txt file called help_myfunction.txt.

How can I enable this help for my function, so that at the command

> ?myfunction;

the content of help_myfunction.txt shows up?

Many thanks,Simone

I have two sets 

f:={1,2,3,4};

h:={1,2,4,5}

L=seq(i,i=1..4):

I want to program , if it is true that f[i] = h[i], then it prints f[i]. So the output should be {1,2}.

for i in L do
if evalb(f[i]=h[i]) then
print(f[i]);
end if;
end do;

I get no output. https://i.imgur.com/qA5hU3i.png

I tried changing the set f to list, f:= [1,2,3,4], still no output.

Hi...

I want to solve  this ODEs using Maple...

f’’’ + f f’’ – f’² + λ θ = 0

(1/Pr) θ’’ + f θ’ – f’ θ = 0

and boundary conditions

f(0) = s,  f’(0) = σ + a f’’(0) + b f’’’(0),  θ(0) = 1,

f’(η) = 0, θ(η) = 0  as  η → ∞.

Can anyone help me to solve this problem? Thank you... =)

hi 

how i can apply this differential in maple?

thabks...

hi .please help me for solve this equations.

bbb2.mw

if former equations are not solvable , please help me for another way, in which at first two equation solve..in this way in equation [J and B] assume that q[311]=e[311]=0 and dsolve perform to find Φ and  ψ

after by finding Φ and  ψ is use for detemine w and u0

please see attached file below[bbb2_2.mw]

bbb2_2.mw

Download bbb2.mw

I have the following PDE system steaming from Flash Photolysis:

when I use pdsolve(pdesys,[J,C]) I get:

The solution appears to be either C(x,t) = 0 or J(x,t) = 0. This are the obvious solutions (0 = 0). I have the analytical solution to this PDE system where neither C(x,t) nor J(x,t) are 0.

How to solve this system in maple? Thanks.

Hi

In attached mw file I have a equation that "a" is in unknown parameter. X and Y are matrixes of data. How can I calculate the "a" parameter?

Best regard

question.mw

Example 6 from Maple Help.

restart:

with(Optimization):

LPSolve(2*x+5*y, {3*x-y = 1, x-y <= 5}, assume = {integer, nonnegative})

Kernel crash the same with Maple 2015.

Does anyone can confirm?

Mariusz Iwaniuk

Geometry Presentation

в_Простран.ppt

Images :      Вращения_picks.mws     Сечения.mws     Цилидр_поверхн_РИС.mws      Цилиндр_кругов_РИС.mws      Цилиндр_наклонн_РИС.mws

Programs :      Вращения_прогр.mws      Цилидр_поверхн_прогр.mws      Цилиндр_кругов+СЕч_прогр.mws      Цилиндр_наклонн_прогр.mws

hi.please help me for solve this equation

i encounter with error''

Error, (in StringTools:-IsPrefix) second argument must be a string''

equations which be solved attached as pdf file

thanks

Kernel4.mw

root.pdf

Download Kernel4.mw