Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

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

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)

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.

orthonormal-triads.mw

NULL

restart

with(Physics)

with(Physics[Vectors])

Creation of 2 rotation matrices

dir1 := `<,>`(0, 0, 1)

dir2 := `<,>`(0, 1, 0)

seq(assign(cat(R, i), Student:-LinearAlgebra:-RotationMatrix(theta[i], eval(cat(dir, i)))), i = 1 .. 2)

print(R1, R2)

Matrix(%id = 36893490614987576012), Matrix(%id = 36893490614987577572)

(1)

whattype(R1)

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

x1_ := _i*R1[1, 1]+_j*R1[2, 1]+_k*R1[3, 1]``

y1_ := _i*R1[1, 2]+_j*R1[2, 2]+_k*R1[3, 2]

z1_ := _i*R1[1, 3]+_j*R1[2, 3]+_k*R1[3, 3]NULL

NULL

x2_ := _i*R2[1, 1]+_j*R2[2, 1]+_k*R2[3, 1]NULL

y2_ := _i*R2[1, 2]+_j*R2[2, 2]+_k*R2[3, 2]

z2_ := _i*R2[1, 3]+_j*R2[2, 3]+_k*R2[3, 3]

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

Now, suppose that we want to compute `&x`(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`) : since `#mover(mi("y2"),mo("&rarr;"))` = `#mover(mi("j"),mo("&and;"))` we have `&x`(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`) = sin(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("j"),mo("&and;"))`)*`#mover(mi("z1"),mo("&rarr;"))` and sin(`#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("j"),mo("&and;"))`)*`#mover(mi("z1"),mo("&rarr;"))` = sin((1/2)*Pi-`&theta;__1`)*`#mover(mi("z1"),mo("&rarr;"))` and sin((1/2)*Pi-`&theta;__1`)*`#mover(mi("z1"),mo("&rarr;"))` = cos(theta[1])*`#mover(mi("z1"),mo("&rarr;"))`

The cross product operator  `&x`(x1_, y2_) yields

cos(theta[1])*_k

(2)

(which is a correct answer) instead of cos(theta[1])*`#mover(mi("z1"),mo("&rarr;"))` because vector `#mover(mi("z1"),mo("&rarr;"))` has is not known as a unit basis vector.

Similarly, `&x`(z1_, x1_) yields -sin(theta[1])*`#mover(mi("i"),mo("&and;"))`+cos(theta[1])*`#mover(mi("j"),mo("&and;"))` instead of  `#mover(mi("y1"),mo("&rarr;"))` as it would be the case when computing `&x`(_k, _i) ?

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

Q3: Is the code defining the canonical basis i, _j, _kavailable for inspection and inspiration to setup orthonormal triads ?

Q4: Is it possible to get a (column) matrix of the vector components ? The function Physics:-Vectors:-Component(y1_, n) can only get 1 component at a time and only in the canonical basis i, _j, _k.

NULL

restart

with(Physics)

with(Physics[Vectors])NULL

After a proper definition of 2 new vector bases `#mover(mi("x1"),mo("&rarr;"))`, `#mover(mi("y1"),mo("&rarr;"))`, `#mover(mi("z1"),mo("&rarr;"))` and `#mover(mi("x2"),mo("&rarr;"))`, `#mover(mi("y2"),mo("&rarr;"))`, `#mover(mi("z2"),mo("&rarr;"))`, the position vector OM_ := l__1*x1_+l__2*x2_NULLNULL

l__1*x1_+l__2*x2_

(3)

NULL

projected on `#mover(mi("x2"),mo("&rarr;"))` would yield directly Typesetting[delayDotProduct](l__1, `#mover(mi("x2"),mo("&rarr;"))`.`#mover(mi("x1"),mo("&rarr;"))`, true)+l__2 instead of expand(OM_.x2_)

l__1*Physics:-Vectors:-`.`(x1_, x2_)+l__2*Physics:-Vectors:-Norm(x2_)^2

(4)

because of the unit vectors.

Download orthonormal-triads.mw

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

 

restart;

kernelopts(version);

`Maple 2023.1, X86 64 LINUX, Jul 07 2023, Build ID 1723669`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1561 and is the same as the version installed in this computer, created 2023, October 20, 22:58 hours Pacific Time.`

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

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

Uval := simplify(value(U));

Uval := `simplify/piecewise/unfactor`(4*piecewise(t < 1, 0, t < 2, t-5+4*exp(`&ndash;`((1/4)*t)+1/4), 2 <= t, 1+4*exp(`&ndash;`((1/4)*t)+1/4)-4*exp(`&ndash;`((1/4)*t)+1/2)))

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

`simplify/piecewise/unfactor`(4+16*exp(-5/4)-16*exp(-1))

 
 

Download simplify-piecewise-bug.mw

 

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 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)

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

I found this option in an API command ?MapleSim,LinkModel,Simulate:

    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?

 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?

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 ?

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?

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.

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

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

Dear all 

I have a function defined on many sub-intervals, how can I simplify this the funciton obtained at each iteration. I hope obatin B_{i,1}, B_{i,2}, and B_{i,3} 

B_Spline.mw

Thank you 

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