## Do I misunderstand this Mobius transformation?...

The worksheet below includes a sample use of the Mobius transformation which produces a hyperbolic reflection of a point in the Poincare disk, followed by my attempt to produce the same result from first principles in a procedure.

Do I misunderstand the Mobius transformation and its use and/or is my procedure incorrect?

InversePoint.mw

## Comment compléter ce tableau et ainsi que les autr...

Soit h : [1 ; + ∞[ℝ

1.a°) Complète le tableau ci-dessus et trace la courbe ( Ch) de h dans un repére orthonormé ( O,I,j )

𝑥 1 2 3 4 5

h(𝑥 )

b°) Montre que h est une bijection

c°) Détermine la bijection réciproque h-¹ de h

d°) Calcule hoh-¹ et h-¹oh ( 𝑥 )

2.) Trace la courbe ( Ch-¹) dans le même repére que ( Ch)

## How to create orthonormal triads with "Physics:-Ve...

Hello,
I recently discovered the "Physics" package wich provides tools for manipulating abstract vectors (non-component).
In the "Physics:-Vectors", an orthonormal basis (i,j,k) is available and my main concern is how to generate arbitrary other 3D orthonormal bases to be able to calculate results in "vectorial form" without manipulating vectors' components.

To better explain my needs I have setup a kind of minimal example in the attached file where some questions are asked.

Thanks in advance for any feedback.

Creation of 2 rotation matrices

 (1)

Creation of  orthogonal unit "Physics:-Vectors" from previous matrices

Q1: Is there a more elegant way of creating "Physics:-Vectors" from matrices ?

Now, suppose that we want to compute  : since  we have

The cross product operator   yields

 (2)

(which is a correct answer) instead of  because vector  has is not known as a unit basis vector.

Similarly,  yields  instead of   as it would be the case when computing  ?

Q2: Is there a way to declare new triads of "Physics:-Vectors" with properties similar to the provided triad  ?

Q3: Is the code defining the canonical basis available for inspection and inspiration to setup orthonormal triads ?

Q4: Is it possible to get a (column) matrix of the vector components ? The function  can only get 1 component at a time and only in the canonical basis .

After a proper definition of 2 new vector bases  and , the position vector

 (3)

projected on  would yield directly  instead of

 (4)

because of the unit vectors.

## Bug in simplify piecewise...

This used to work in Maple 2022.  Something is broken in 2023.

 > restart;
 > kernelopts(version);

 > Physics:-Version();

 > U := Int(exp(-1/4*t - 1/4*x)*piecewise(x < -2, 1, x < -1, -x - 1, 0), x = -t .. 0);

 > Uval := simplify(value(U));

 > eval(Uval, {x=5, t=6});

 >

## .L Test.cpp+ fails , why?...

The following test program (Test.cpp) fails with.L + Test.cpp+, but not with plain .L, nor with gcc. It also does not tell me anything about why where it fails!

#include <string>
int Test(std::string x) {
cout << x << "\n";
return 1;
};

Error in <ACLiC>: Executing 'C:\root_v6.28.06\bin\rootcling -v0 "--lib-list-prefix=C:\Users\snyde\BFROOT\ROOT\Test_cpp_ACLiC_map" -f "C:\Users\snyde\BFROOT\ROOT\Test_cpp_ACLiC_dict.cxx"  -rml Test_cpp -rmf "C:\Users\snyde\BFROOT\ROOT\Test_cpp.rootmap" -DR__ACLIC_ROOTMAP -I%ROOTSYS%\include -D__ACLIC__  "C:/Users/snyde/BFROOT/ROOT/Test.cpp" "C:\Users\snyde\BFROOT\ROOT\Test_cpp_ACLiC_linkdef.h"' failed!

Huh? Why?

I can't learn what's wrong using 'g++  -c Test.cpp' (outside ROOT)  as it compiles w/o complaint in that case.

Is there a way to get ROOT to tell us what it objects to?

## How I can solve the error in maple ...

How I can solve the error in maple which is ( (in PDEtools:-DeterminingPDE) expected the number of infinitesimals (4) to be equal to the sum of the number of independent (2) and dependent (1) variables; received: 4 <> 2 + 1)

## Suggestion for storing data...

I would like to create a database of component information. I have previously done this using a table which is indexed by the part number. Each element is a DataFrame, which includes several items with values and at least 2 DataFrames. The 2 DataFrames are extracted from a Spreadsheet with 2 tabs, that is stored in a Maple Workbook. Each DataFrame has an name for the row and 2 columns; Description and Value. The Description is text and the value is a single value or 3-element list with unit. Such at [9, 10, 11]*~Unit('ohm')

Anyway, I'm wondering if this is the most efficient way. I'm also wondering if there is a way to create such a database so it can be used with other software tools, primarily Mathcad and Excel.

Thanks

## Does dsolve offer options to scale systems of DAEs...

scalemethod : one of the following: "none", "minimum", "maximum", "geometric"
Method of variable scaling applied to the system.

I did not find anything about scaling in Maples help system.

What exactly does the scaling do?

## Memory Leak Problem, continued...

In the memory leak problem with my DStarLepNu simulation program, I did find one cause in that due to normalization errors the accept/reject algorithm in ‘PickAngles’ was executed too many times. This should have just made angle generation inefficient but occasionally, but not always produced very big memory bumps when a large number of trials were needed to pick angles. It’s not clear why these bumps occurred as the code being executed is always the same and is simple.

Fixing this did however not prevent memory crashes or even reduce them much.

I have since turned off accept/rej and calls to ‘arccos’ and more modest spikes remain and crashes still occur!

I don’t understand how Maple memory management works. My B-meson decay prov ‘bDecay’ usually gives  still shows occasional spikes and and there’s a weird correlation between the first (B1) and second (B2) call:

DStar3DKinRecoLoopDebugCombo200EventsExportRun2.mw

çMemory added by ‘bDecay’ proc on 1st call vs 2nd call in the B1-B2 event loop..

èWhat with the slope and difference in width?

## preview print function not working correct after ...

When printing a Maple Worksheet  often I go in the PrintPrewiev of the Mac and then select some sides to print.

This is not working anymore since I have updated from Maple 2021 to Maple 2023.

Is this known ?

Any help for his ?

## Constrained Dynamics: How can the AugType option b...

I found this option mentioned in help(MapleSim,Multibody,Dynamic_Exports).

For the example of the help page I tried

SliderCrank:-GetDynEQs(AugType = Reaction);
SliderCrank:-GetDynEQs(AugType = Lagrange);

but the output is the same (which I would expect since GetDynEQs is not defined with parameters).

In the help system I only find deprecated commands that use this option

How can this option be set in newer versions of MapleSim without using deprecated commands?

## Integro-Diff-Eq steps to solution...

For the following Equation:

Equation := int(diff(u(x), x)*v(x), x) = int(u(x)^(1/2)*v(x), x)^(-2/3);
Maplesoft finds the following solution:

Solution1:=3/4*u(x)^(4/3) + 2/3*u(x)^(5/6)*Intat(1/(sqrt(u(x))*Int(v(_b), _b))^(5/3), _b = x) + _C1 = 0

or , which I believe as an alternative, can be written as

Solution2:=3/4*u(x)^(4/3) + 2/3*u(x)^(5/6)*Int(1/(sqrt(u(x))*Int(v(x),x))^(5/3) +_C1=0

My question is how did Maple arrive at 'Solution1' from 'Equation'? In other words, can someone fill

in the steps between 'Equation'  and 'Solution1'? Or even, prove that Solution 1 is a valid solution to Equation.

Plugging the Solution1 into Equation, did not clearly demonstate the validity of the solution (to me at least)

Unfortunately, I am still unable to post the corresponding Maplesoft worksheet onto this post.

## Gfun's listtoalgeq erroneous output?...

Invoked by the OEIS superseeker, Maple "gfun" package "listtoalgeq" identified possible lgdegf for https://oeis.org/A035001

1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232, 256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048, 2329, 3104, 3328, 4096, 4864, 6266, 6802, 7168, 8192, 11952, 15360, 16384, 16428, 19149, 28928, 32768, 37120, 42168

as follows:

1024-5120*a(n)+11520*a(n)^2-15360*a(n)^3+13440*a(n)^4-8064*a(n)^5+3360*a(n)^6-960*a(n)^7+180*a(n)^8-20*a(n)^9+a(n)^{10}

The coefficients of above polynomial are:

{1, -20, 180, -960, 3360, -8064,13440, -15360, 11520, -5120, 1024,...}

It is interesting that the absolute values of above polynomial coefficients satisfy a(n) of

https://oeis.org/A013609

for n=55...65,

which is the 11th row in the triangle presentation of A013609, so in other words the absolute values of above polynomial coefficients are T={11, k} for k=1...11

## System of equation into matrix for each "n"...

Dear Users!

I hope you are doing well. I have the following discretized form

for n>=1 and j=0..M. We obtained the following matrix equation for any "n" and j=0..M as:

I want matrix proc of any useful way to define A^n, u^n, and b^n. I am waiting for your positive response. Thanks in advancs