## Error during integration...

I was computing an integral (Running Maple 18 on Windows 10):

The classic lenght of arc Integral of sqrt(1+(dy/dx)^2) dx

In this case, the function was a cartesian circle (x-R)^2+y^2=R^2 isolated as y=sqrt(R^2-(x-R)^2)

When I do the integration, the result of the integral is not correct.
But if I change R for a, the result is correct. Why? This does not make any sense.

R wasn't assigned to any variable. The code was:

Good Integral

[>y:=expand(sqrt(a^2-(x-a)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

Wrong Integral

[>y:=expand(sqrt(R^2-(x-R)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

In fact, any UPPERCASE letter used as the radius gives me the wrong answer whereas any LOWERCASE letter gives me the proper result. Why is this?

Thanks and have a nice day

## two vectors as output of proc ...

Dear all

I have a proc I would like to construct two vectors as output of  the proposed proc, the following code, contains  an example to illustrate this idea,

output_pro.mw

thanks for any help

## poinplot maple to plot many points same curve...

Dear all

I have many points, and I would like to use pointplot to hold all plots in the same curve.

plot_many_points.mw

thanks for any help

## plot table defined by elements inside loop ...

dear all

I have a three lines of codes, used to create vectors, I would like to put these vectors in two columns and each columns has a title.

simple_code_table.mw

thank you

## How to make the best use of known C libraries of g...

I am trying to calculate the number of  complete subgraphs K4 of a graph. Based on some similar discussions, like following links,

I wrote the following codes:

NumberOfK4:=proc(g::Graph)
local  n,N, i, j, k,l, g1,G1;
uses GraphTheory;
n:=NumberOfVertices(g);
g1 := RelabelVertices(g, [\$ i = 1..n]):
N:=0:
for i from 1 to n-3 do
for j from i+1 to n-2 do
for k from j+1 to n-1 do
for l from k+1 to n do
G1:=InducedSubgraph(g1,[i,j,k,l]);
if NumberOfEdges(G1)=6 then N:=N+1; fi;
od;
od;
od;
od;
N;
end proc:
with(GraphTheory): with(SpecialGraphs):
g:=CompleteGraph(5);
g1:=LineGraph(g);
NumberOfK4(g1)


5

I know the above codes are supposed to be inefficient in terms of speed. We want to improve this codes. One way I know  that is to take advantage of  the efficient graph theory programs such as igraph

Recently I learned how Maple calls external C programs.

The define_external command links in an externally defined function (for example, from a DLL under Windows, or from a shared library under UNIX), and produces a Maple procedure that acts as an interface to this external function.

From the help documentation, we need to compile the DLL files from the  source of C language. If it is a C program that does not need additional libraries, we can compile successfully, such as help documents

    void mat_mult( double *A, double *B, double *C, int I, int J, int K )
{
int i, j, k;
double t;
for( i = 0; i < I; ++i )
for( k = 0; k < K; ++k ) {
t = 0.0;
for( j = 0; j < J; ++j )
t += A[i*J+j] * B[j*K+k];
C[i*K+k] = t;
}
}


No offense, maple has relatively few functions on graph theory so far, while Sage has a strong advantage because of its ability to integrate open network resources. I think sage is considered better for graph theory researchers because of this.

I don't know if Maple has any guidance on integrating a publicly available  graph theory library ,such as igraph .

Where is the difficulty of using the written source code？ And my computer system is Windows 10 , are there any special requirements. If Maple does this better, it might be a wonderful thing for graph theorists.

## Convolution using FFT...

Hi

My integrals are convolutions.and I know I can evaluate this using numerical integration, but I am seeking a numerical solution of this problem using FFT. I have many many integrals of this type to evaluate and I need FFT for speed reasons.

fft.mw

This might inspire you.

## How to show equality of expressions with complex r...

I am searching for high level commands or techniques to show equality of expressions containing square roots that can be complex as here

In an ideal world is() with the right assumptions should show equality. However, in the attached example, I failed already with my manual skills.

What did I miss here?

Equality_of_exp_with_complex_roots.mw

## Stepwise regression using maple...

I have a data with one dependent variable Y say and 32 independent variables say X1,X2,X3,....

Now I need to find the best say, a linear fit with the role playing independent variables only choosen so that I get pvalue less and R^2 and adjusted R^2 more than 90%

Even if possible to write for a nonlinear fit too

How to do such a code

I have my data in Excel sheet which I need to import

## print result as matrix...

Dear all

I have the following code,

for i to 6 do
for j to i do
F[i, j] :=  g(i+1)/g(j);
end do;
end do;
How can display F as a full matrix

## How to extract values following solve() set...

Hi, I need a little help please.

I'm writing some code that involves using solve() to solve some simultaneous equations and the output set from solve() is as follows :

{c[1] = 8/3, c[2] = 10/3}

I would now like to used the values 8/3, -10/3 in another calulation. However, I don't know how to extract the values/loose the variable parts of the set (namely "c[1]=" and "c[2]="). Can anyone help please.

FYI - I can't use fsolve as my simultaneous equations contain an another unknown variable, which I need to preserve.

## missing plus and minus signs in output of Student:...

On my PC I can't see the plus and minus sign in the quotient expression when using Student:-Basics:-LongDivision.

Is this a know display issue and is there to correct it?

Windows 10, Maple 2021.2

 > interface(version);

 > restart;
 > A:=4*x^4; B:=3*x^2-60*x+36; Student:-Basics:-LongDivision(A,B,x); #NOTICE, no + sign shows in quotient

 > rem(A,B,x); quo(A,B,x); #signs shows up here OK

 >

## second question about a simple two column matrix...

Thank you very much, Maple Community !

I have another (hopefully) easy question about a data set

matrix_start_2_trim.pdf

I want to imitate Online Encyclopedia of Integer Sequences .b file

reference oeis.ort/A40

Cheers,

Matt

## How do I to find where .mla files are for packag...

I have two personal packages I wrote for Maple a few years age. I use them regurlary. They are stored in two differant locations.  Is there of interogerating Maple to find out where they are and some details obout them? What I load is

with(RationalTrigonometry) and with(RonanRoutines)

I finally found them again.

One in C\usersIRonan\Maple\persona\lib\RatTrig.mla

Other in (basically in) My documents\Maple\.A library\RonanRoutines1.mla

So the package load name and the .mla file name are different. I would like to know where the packages are being loaded from and under what name they are saved as.

## Avoiding Automatic Simplification in Typesetting...

The loglogplot procedure in the plots package labels the axes using "10 to the power notation" that looks like what you would see in LaTeX from the expresion "10^{-4}".

I"m at a loss about how to do the same.  If I try typesest(10^(-4)) the argument is converted to a rational before typeset gets the argument and the result is something equivlent to LaTeX's "\frac{1}{10000}".

Example:

loglogplot(x, x = 0.1*10^(-5) .. 10, title = typeset(10^(-4)));

produces:

## Custom Library not visible...

Hello,

I build a small simple custom library in MapleSim, for some reaon MapleSim is keep giving me that a variable can't be resolved and that there is no "LibraryName" visible.

The library loads successfully with no error though.

exact msg:

Cannot resolve type MyLibrary.Dh_Revolute of variable Main.DR1 in model Main; there is no MyLibrary visible