## Problem in execution of summation symbol ...

Dear Users!

Hope you would be fine. I have some problem in execution the last loops (highlighted as red) where sumation is present. When NN>3 it takes alot of time more than 12 hours. Is there any alternative command to reduce the query. I am waiting for your response. Thanks in advance.

restart; with(LinearAlgebra); Digits := 30; NN := 2; nu := 1; M1 := NN; M2 := NN; M3 := NN;

for k1 from 0 while k1 <= M1-1 do for k2 from 0 while k2 <= M2-1 do for k3 from 0 while k3 <= M3-1 do

SGP[M3*(M2*k1+k2)+k3+1] := simplify(sum((-1)^(k1-i1)*GAMMA(k1+i1+2*nu)*x^i1*(sum((-1)^(k2-i2)*GAMMA(k2+i2+2*nu)*y^i2*(sum((-1)^(k3-i3)*GAMMA(k3+i3+2*nu)*z^i3/(GAMMA(i3+nu+1/2)*factorial(k3-i3)*factorial(i3)), i3 = 0 .. k3))/(GAMMA(i2+nu+1/2)*factorial(k2-i2)*factorial(i2)), i2 = 0 .. k2))/(GAMMA(i1+nu+1/2)*factorial(k1-i1)*factorial(i1)), i1 = 0 .. k1)) end do end do end do;

SGPxyz := `<,>`(seq(seq(seq(SGP[M3*(M2*(i-1)+j-1)+k], k = 1 .. M3), j = 1 .. M2), i = 1 .. M1));

Lambda := `<,>`(seq(seq(seq(chi[M3*(M2*(i-1)+j-1)+k], k = 1 .. M3), j = 1 .. M2), i = 1 .. M1));

for i while i <= NN^3 do for j while j <= NN^3 do for k while k <= NN^3 do

q[i, j, k] := int(int(int(SGP[i]*SGP[j]*SGP[k]*(-x^2+x)^(nu-1/2)*(-y^2+y)^(nu-1/2)*(-z^2+z)^(nu-1/2), z = 0 .. 1), y = 0 .. 1), x = 0 .. 1) end do end do end do;

U := Matrix(NN^3, NN^3, 0);

for j while j <= NN^3 do for k while k <= NN^3 do U[j, k] := simplify(sum(chi[i1]*q[i1, j, k], i1 = 1 .. NN^3)) end do end do;

F := simplify(evalm(U));

Special request to @acer @Carl Love @Kitonum @Preben Alsholm

## A very strange result...

Hi,

I do not understand why this simple procedure evaluates so differently depending on the type of its second parameter?

A typo somewhere or a bug?

 > restart:
 > interface(version)
 (1)
 > KL := (a, b) -> (1/4)*(2*ln(a+b)*a^2+4*ln(a+b)*b*a+2*ln(a+b)*b^2-2*ln(b)*b^2-a^2-2*a*b)/a
 (2)
 > evalf(KL(1e-10, 1/2))
 (3)
 > evalf(KL(1e-10, 0.5))
 (4)
 > evalf(KL(1e-10, convert(0.5, rational)))
 (5)
 > limit(KL(a, 1/2), a=0, left); limit(KL(a, 1/2), a=0, right)
 (6)
 > limit(KL(a, 0.5), a=0, left); limit(KL(a, 0.5), a=0, right)
 (7)
 >

## Integral of a sum...

I have an integral of a sum

`Int(Sum(-(Nb*t-n*t__rev)*exp((1/2)*(L+sqrt(-4*C*L*R^2+L^2))*t/(L*R*C)-(1/2)*(Nb*t-n*t__rev)^2/(Nb^2*sigma__b^2)), n = 0 .. Nb-1), t);`

that I want to convert into a sum of integrals since Maple will not integrate the sum but it will integrate the summands. I tried IntegrationTools, but none of these tools seem to do it. It is a part of a larger expression so doing this by hand is not a real option.

Mac Dude.

## From Fortran to Maple...

Hi!

The algorithm in this PDF is written in Fortran, but unfortunately I do not known this programming languaje (actually, I am not an "expert" in progamation).

Algoritmo_Fortram.pdf  [removed by moderator. © Institute of Mathematics AS CR, 1980]

https://dml.cz/handle/10338.dmlcz/103855

Could someone please write this algorithm in Maple? Or, at least, indicate me how to do.

## Evaluation of Double Integral...

Hello Everyone
My maple is evaluating the following provided in figure. I have  attached MAPLE file. Kindly help me to solve this. Thanks in advance.

question.mw

## Is "numpoints" an effective option of SurfaceOfRe...

Hi,

While "numpoints=..." is said to be an admissible option of SurfaceOfRevolution (or VolumeOfRevolution, default value set to 50), the graphical results doesn't account for the value of numpoints.

Is this a known issue?

TIA

Surface0fRevolution.mw

## Realistic 3D rendering of a complex system

by: Maple 2015

Hi,

No big math here, just a demonstrator of Maple's capabilities in 3D visualization.

All the plots in the file have been discarded to reduce the size of this post. Here is a screen capture to give you an idea of what is inside the file.

## How to get the name a colour in this case?...

Hi,

I ran this command
and I wonder how I could get the  NearestNameColor of all elements in list  c ?

## How to pick certain part of a formula with interac...

Hello

I wanted to create a group of interactive components that, when given an eqaution in a math container of an ellepses (in the form of ((x/A)^2)+((y/B)^2)=1) would pick A and B and give back two formulas of the type

x(t)=A*cos(t)

y(t)=b*sin(t)

So, is there a way to extract A and B from the initial formula?

## How to draw a circle point by point in a plot?...

Hello everyone! I was trying to draw a circle point by point using animate, but there's a catch: I'd like it to be created in front of the user, that is seeing every point being drawn in sequence.

Like this, but with the point leaving a trail behind him.

Can anyone help?

## How do I draw a petersen graph?...

Hello everyone, we are doing some excercises on graphs. The commands PetersenGraph and GeneralisedPetersenGraph only draw an indirected one, and i was wondering, is there a way to draw a directed Petersen graph?

## Foreground and background do not change when the f...

Hi,

I represent 3 thin parallel slices of colors red, green and blue; all have the same transparency equal to 0.5
For the default orientation of the display, the blue slice is on the forefront, the red one in the background and the green one in beween. Then the blue slice is "bluer" than green and  the green one "greener" than red (FIG 1)
If you rotate manually the figure in order to place the red slice in the forefront and the blue one in the background, you expect to have the red slice "redder" than the green one and the green one "greener" than the blue one (FIG 2)
This is not the case.

The order in which the slices appear in the PLOT3D command defines the foreground and the background, but these latter are not dynamically recalculated when the figure is rotated.
To recover the correct colors one must revert the order of the slices in PLOT3D (FIG 3)

Are we comdamned to change to change manually the order of the slices in PLOT3D or does it exist an option whixh avoids doing so?

Don't pay too much attention to the plots above for the foreground is strangely correct on figure 2 ???

 > restart
 > with(plottools):
 > alpha := Pi/18.: a := 2*cos(alpha): b := 2*sin(alpha): e := 0.02: p := [[0,0,0],[a,b,0],[a,b,1],[0,0,1]],      [[0,e,0],[a,b+e,0],[a,b+e,1],[0,e,1]],      [[0,0,0],[0,e,0],[0,e,1],[0,0,1]],      [[a,b,0],[a,b+e,0],[a,b+e,1],[a,b,1]],      [[0,0,0],[a,b,0],[a,b+e,0],[0,e,0]],      [[0,0,1],[a,b,1],[a,b+e,1],[0,e,1]]
 (1)
 > f   := k -> transform((x, y, z) -> [x, y+k, z]): col := k-> COLOR(RGB, op(ListTools:-Rotate([1, 0, 0], -k))): t   := TRANSPARENCY(0.5): PLOT3D(POLYGONS(p, t, col(0)), f(1)(POLYGONS(p, t, col(1))), f(2)(POLYGONS(p, t, col(2))), AXESLABELS(2, 3, 1))
 > PLOT3D(POLYGONS(p, t, col(0)), f(1)(POLYGONS(p, t, col(1))), f(2)(POLYGONS(p, t, col(2))), AXESLABELS(2, 3, 1))
 > PLOT3D(f(2)(POLYGONS(p, t, col(2))), f(1)(POLYGONS(p, t, col(1))), POLYGONS(p, t, col(0)), AXESLABELS(2, 3, 1))
 >

## Help file .maple...

Hello everyone.

I've took part in a math competition and we use Maple 15 as software to solve the various problems. We, apart from solving the problems, to correct and give a score to 4 other participants per problems. We have to download their solution and read it and then valuate it. However one of the files is .maple and not .mw. How can I open it? The tutors said to us that we just have to change extension and copy-paste the content into another document, but the the program doesn't let me copy the text (it's a mess) because "it's too big to be copied". I have obviously asked them how to solve this since what they said isn't working, but they didn't answer...

So, does anyone know how I could convert a file from .maple to .mw and still see the document as it was intended?

## Can anyone tell me what is causing this error and ...

Hi everyone! I was writing this code for an interactive component, when I stumbled into a problem that I couldn't solve...

Here is the code.

use DocumentTools in
if type(Do(%NIniziale), posint) then
if Do(%NIterazioni)<=100 then
if type(Do(%NIterazioni), posint) then
Do(%E="Valid Values!");
Even:=Do(%Pari);
Odd:=Do(%Dispari);
Iterazioni:=proc (N, i)
local m, n;
n:=N;
for m from 1 to i do
if type(n, even) = true then
n := Even;
else
n := Odd;
end if;
end do;
return (SetCellFormula("Risultati", i, 1, eval(n)));
end proc;
ix:=Do(eval(%NIterazioni));
Nx:=Do(eval(%NIniziale));
seq(Iterazioni(Nx,y),y=1..eval(ix));
if Do(%NIterazioni)<100 then
seq(SetCellFormula("Risultati", x, 1, "//"), x=1+ix..100);
end if;
else
Do(%E="Inavalid Values");
seq(SetCellFormula("Risultati", x, 1, "ERROR"), x=1..100);
end if;
else
Do(%E="Invalid Values");
seq(SetCellFormula("Risultati", x, 1, "ERROR"), x=1..100);
end if;
else
Do(%E="Invalid Values");
seq(SetCellFormula("Risultati", x, 1, "ERROR"), x=1..100);
end if;
end use;

Now this are what the names stands for:

%Pari is a math conainer in which there is a function of n that is to be used when n is even;

%Dispari is a math conainer in which there is a function of n that is to be used when n is odd;

"Risultati" is the name of a spreadsheet on which the results will be displayed;

%NIterazioni is a math conainer in which there is a posint that indicates how many times the procedure is to be iterated;

%NIniziale is a math conainer in which there is the starting number (another posint) to which on which the procedure will operate;

%E is a text area that will signal the validity of the input.

What I wanted to do was a procedure that reiterated two function on a given number a given amount of times and returned the result of every passage, however, when computing, it returns the function in n and not the final numbers.

I have opened the Spread package in the startup-code, and I really want to use the spreadsheet even though it is deprecated in newer versions. When you'll open, the function will be the ones of the Collatz Conjecture, however I want it to be able to iterate any function of n, which will be acquired via input, and will be to the user's choice.

I tried everything that came to my mind: using text area, assigning n outside of the preocedure, using evalf, eval, putting the return inside the if system, opening and closing a do inside "then" and one isndide "else" , changing names and everything... But I couldn't solve it. on the internet and on the MapleHelp I didn't find anything.

So can anyone tell me ( most importantly) why it doens't compute the formulas and just leaves them as input and (less important then the why, but still important and would appreciate) how can it be solved? Thanks to everyone even if you just read this, I know it is amybe a little too much.