Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello,

I have a quite big program designed with packages and subpackages.

I realized that i'm not to well understand the operation of local/ global/ export variables in this case.

Let's detail the issue.

I consider a package like this :

MAIN PACKAGE:=module()

local XM

global YM

export ZM

      SUBPACKAGE1:=module()

      local X1

      global Y1

      export Z1

      end module;

      SUBPACKAGE2:=module()

      local X2

      global Y2

      export Z2

      end module;

end module;

Question:

Can you describe in the simpliest way the rules for accessing to the variables in the case the variables are local/ global/ export and in the case you are writting procedures inside the MAINPACKAGE or the SUBPACKAGEs ?

In others words may you help me to answer to these questions  ?

Is the local variable XM accessible to the procedures used in SUBPACKAGE1? no
Is the local variable X1 accessible to the procedure used in MAINPACKAGE ? no

Is the global variable YM accessible to the procedures used in SUBPACKAGE1? yes
Is the global variable Y1 accessible to the procedure used in MAINPACKAGE ? yes

Is the export variable ZM accessible to the procedures used in SUBPACKAGE1? yes
Is the export variable Z1 accessible to the procedure used in MAINPACKAGE ? yes with the syntax SUBPACKAGE:-Z1

I let my opinion but i need certainty on these points...

I attach a first draft that i would like you help me.

AboutModuleLocalGlobalExport.mw

I thank you in advance for your help.

Requesting a code to compute (and graph) the following self referencing sequence:

a(1)=1. If a(n) is a novel term (seen for the first time) then a(n+1)= d(a(n)) where d(k) is the number of divisors of k. 
if a(n) has been seen before then a(n+1) = a(n)+m where m is the least prior term which has not already been used in this way (once m is used it cannot be used again).

Sequence starts:

1,1,2,2,3,2,4,3,5,2,4,6,4,7,2,5,7,11,2...,

note that there are often multiple copies of the least unused term, which might make accounting for them tricky. 

Thanks in advance 

 

 

help.mw

How to solve Linear first-order PDE by the Lagrange method?

dx/(x) =dy/0=dt/0=du/3=dv/v=dw/w, where x,y,t are independent variables and u,v,w are dependent variables.

Hello

I have used Maple almost daily for the last four years, but a few days ago two students approached me with an issue I had never encountered before. However, it had happened to both of them within a few weeks.

They described the issue as follows: When they opened a random Maple document and they tried to type in simple operators (like +, - or *), Maple would instead write an odd symbol, which none of them recognised as a mathematical symbol.

As they could not find a way to solve the problem within Maple, they tried restarting their computers. When they afterwards reopened Maple, the problem was gone and the operators worked as expected again. Neither of the students has experienced the issue since.

During the last few days, I have been trying to replicate the issue myself without success. Therefore, I also don't have any screenshots to share, so hopefully my simple explanation is enough.

My questions are: Has anyone heard about this issue before? Does anyone know what might have caused it? Is there a way to replicate it and/or prevent it from happening again in the future?

I hope someone is able to clarify it a bit for me! :)

Regards,

Frederik

How can I use symbols from the Emoji and Symbols collection on a Mac in a document or worksheet in Maple? I want to create documents but I find symbols not included in Maple that I require. I have found that some symbols will stay in the document if I insert them when in TEXT mode, but that does not work when entering a fraction for example and needing a symbol. When reloading a previously saved document, I find that the symbol has not saved.

 

A related question: how can I expand on the default symbols in the toolboxes?

 

Thanks.

 

Hello,

For debbugging big programs, i have been told that one good solution is to use the mint application.

I'm trying to do so that is to say to use the mint application with windows. But, i encounter some difficulties.

The program on which i would like to apply the mint is composed of several parts like in the package Shapes and the different parts of the module are called thanks to the $include syntax.

To test mint, i have launched a command window with the command cmd in windows.

After, i apply cd PathRepertoryContainingMint

On i am located in this repertory, i test the following syntax :
mint -I PathRepertoryContainingTheDifferentFiles PathRepertoryContainingTheMainProgram\program.mpl

In my case these two paths are the same.

I test also the following syntax:

mint -o PathRepertoryContainingTheOuput\mintoutput.mpl PathRepertoryContainingTheMainProgram\program.mpl

It may run but i don't know where i can recover the output of mint

I have been told also to set the Windows PATH variable to include the Maple bin directory (thank you @Joe Riel for this tip). I think that it should be a good idea but I never do this type of manipulation.

On the net, I find that the process to do so is the following : setx path "%path%;c:\directoryPath"

Questions: 

1) If you have some experience in using mint with windows, may you give some tips (precise the right syntax) to use it ? 

2) In case the option -o is not used, where the output of mint is coming ?

I thank you in advance for your help.

Using a Cyrillic font in the Combo Box component gives an runtime error when saving workbook file (*.maple file extension).

cyr_wb_save_error.zip

Select the second item in Combo Box component and press save button.

 

Hi,

I am having trouble with a Lie algebra cohomology computation. Suppose I have a poset on {1,2,3,4} where 1 < 3, 1 < 4, 2 < 3, and 2 < 4. I can express this as a matrix:

* 0 * *
0 * * *
0 0 * 0
0 0 0 *

where *'s mean "any entry in my ground field," say R or C, and 0s are 0s. Basically, if there is a relation between row i and column j, there is a *. This is why there is a * in row-1 and column 3, as 1<3, but a 0 in row-1 and column 2. I can make the collection of all of these matrices into a Lie algebra using the commutator, as it is closed, and can further suppose it is of trace 0 - that is, it is Type A.

My question is this: I know this algebra has non-trivial cohology, and deforms. However, I want to make Maple do this for me, so I can try it on bigger algebras - however it always tells me that the cohomology is dead zero. What am I doing wrong? My approach is this:

Let P equal the following collection of matrices - these form my basis:

 [Matrix(4, 4, [[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]), Matrix(4, 4, [[0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]), Matrix(4, 4, [[0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]), Matrix(4, 4, [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0]]), Matrix(4, 4, [[0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0]]), Matrix(4, 4, [[0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]]), Matrix(4, 4, [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]])]

Now I can run the basic commands to get started:

L := LieAlgebraData(P, Ex1);
DGsetup(L);


I can now go straight to cohomology. If my algebra is named L, then I want to build my cochain complex C^*(L, L):

c := RelativeChains([e1,e2,e3,e4,e5,e6,e7]);

However, the answer is always that there are no non-trivial cochains: the answer is [[], []]. This will make it very difficult to have non-trivial cohomology.

I know this isn't true (see https://arxiv.org/pdf/1407.0428.pdf). I also tried the approach in the Maple documentation, where I work in the adjoint representation. This gave me non-trivial cochains, but the cohomolgy was 0.

Does anyone know what I'm doing wrong?

Thanks!

Hello,

I spent some hours to manipulate the Nabla operator as in textbook, but i have an issue.

Thank you for your help

First thing i did is :

with(Physics); with(Vectors);
 

I declare S0 and P0 as constant with

Parameters(S0,P0)

I have the expression

Exp := S0*(P(x, y, z, t) * - P0)

I apply the Nabla Operator and get

(%Nabla) S(x, y, z, t)) = S0*Nabla, P(x, y, z, t) * - S0*NablaP0

As S0 and P0 are constants, How to remove the S0*NablaP0 term  ?

I tried some combinations of expand and simplify.


 

NULL

restart

with(LinearAlgebra):

alpha := .985

.985

(1)

for i to 7 do for j from -1 by .1 to 1 do Exact[j] := ((1-j)*(1/2))*exp((1+j)*(1/2)); Y[0] := proc (x) options operator, arrow; -(1/8)*exp(1)+1/2+(-(1/8)*exp(1)-3/4)*x+(1/8)*exp(1)*x^2+((1/8)*exp(1)+1/4)*x^3 end proc; Ics := Z(-1) = 1, Z(1) = 0, (D(Z))(-1) = 0, (D(Z))(1) = -(1/2)*exp(1); exp(x) := convert(taylor(exp(x), x = 0, 25), polynom); f := proc (x) options operator, arrow; ((1/32)*x-5/32)*exp((1/2)*x+1/2) end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; -1/4 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; -1/16 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(f(x)-p(x)*(diff(Y[i-1](x), `$`(x, 3)))-q(x)*(diff(Y[i-1](x), `$`(x, 2)))-r(x)*(diff(Y[i-1](x), x))-u(x)*Y[i-1](x)); s[i] := evalf(dsolve({Ics, eq[i]}, Z(x))); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do

[1.00000001, 1, 0.1e-7]

 

[.99889373, .9987075410, 0.1861890e-3]

 

[.99542387, .9946538260, 0.7700440e-3]

 

[.98930908, .9875591065, 0.17499735e-2]

 

[.98020108, .9771222065, 0.30788735e-2]

 

[.96769238, .9630190630, 0.46733170e-2]

 

[.95132386, .9449011655, 0.64226945e-2]

 

[.93059225, .9223939070, 0.81983430e-2]

 

[.90495743, .8950948190, 0.98626110e-2]

 

[.87384983, .8625717020, 0.112781280e-1]

 

[.83667770, .8243606355, 0.123170645e-1]

 

[.79283435, .7799638580, 0.128704920e-1]

 

[.74170543, .7288475200, 0.128579100e-1]

 

[.68267630, .6704392900, 0.122370100e-1]

 

[.61513924, .6041258120, 0.110134280e-1]

 

[.53850104, .5292500040, 0.92510360e-2]

 

[.45219044, .4451081856, 0.70822544e-2]

 

[.35566578, .3509470278, 0.47187522e-2]

 

[.24842284, .2459603111, 0.24625289e-2]

 

[.13000273, .1292854830, 0.7172470e-3]

 

[0., 0., 0.]

 

[1.00000001, 1, 0.1e-7]

 

[.99870526, .9987075410, 0.22810e-5]

 

[.99464487, .9946538260, 0.89560e-5]

 

[.98753974, .9875591065, 0.193665e-4]

 

[.97708963, .9771222065, 0.325765e-4]

 

[.96297160, .9630190630, 0.474630e-4]

 

[.94483868, .9449011655, 0.624855e-4]

 

[.92231783, .9223939070, 0.760770e-4]

 

[.89500815, .8950948190, 0.866690e-4]

 

[.86247884, .8625717020, 0.928620e-4]

 

[.82426685, .8243606355, 0.937855e-4]

 

[.77987484, .7799638580, 0.890180e-4]

 

[.72876867, .7288475200, 0.788500e-4]

 

[.67037492, .6704392900, 0.643700e-4]

 

[.60407851, .6041258120, 0.473020e-4]

 

[.52922004, .5292500040, 0.299640e-4]

 

[.44509347, .4451081856, 0.147156e-4]

 

[.35094315, .3509470278, 0.38778e-5]

 

[.24596164, .2459603111, 0.13289e-5]

 

[.12928690, .1292854830, 0.14170e-5]

 

 

[-0.2e-7, 0., 0.2e-7]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

 

[1.00000000, 1, 0.]

 

[.99902820, .9987075410, 0.3206590e-3]

 

[.99581870, .9946538260, 0.11648740e-2]

 

[.98992527, .9875591065, 0.23661635e-2]

 

[.98089421, .9771222065, 0.37720035e-2]

 

[.96826375, .9630190630, 0.52446870e-2]

 

[.95156339, .9449011655, 0.66622245e-2]

 

[.93031319, .9223939070, 0.79192830e-2]

 

[.90402310, .8950948190, 0.89282810e-2]

 

[.87219221, .8625717020, 0.96205080e-2]

 

[.83430805, .8243606355, 0.99474145e-2]

 

[.78984585, .7799638580, 0.98819920e-2]

 

[.73826774, .7288475200, 0.94202200e-2]

 

[.67902206, .6704392900, 0.85827700e-2]

 

[.61154254, .6041258120, 0.74167280e-2]

 

[.53524746, .5292500040, 0.59974560e-2]

 

[.44953895, .4451081856, 0.44307644e-2]

 

[.35380210, .3509470278, 0.28550722e-2]

 

[.24740416, .2459603111, 0.14438489e-2]

 

[.12969376, .1292854830, 0.4082770e-3]

 

[0.1e-7, 0., 0.1e-7]

 

[1.00000002, 1, 0.2e-7]

 

[.99870689, .9987075410, 0.6510e-6]

 

[.99464990, .9946538260, 0.39260e-5]

 

[.98754844, .9875591065, 0.106665e-4]

 

[.97710162, .9771222065, 0.205865e-4]

 

[.96298633, .9630190630, 0.327330e-4]

 

[.94485556, .9449011655, 0.456055e-4]

 

[.92233620, .9223939070, 0.577070e-4]

 

[.89502732, .8950948190, 0.674990e-4]

 

[.86249795, .8625717020, 0.737520e-4]

 

[.82428488, .8243606355, 0.757555e-4]

 

[.77989071, .7799638580, 0.731480e-4]

 

[.72878132, .7288475200, 0.662000e-4]

 

[.67038351, .6704392900, 0.557800e-4]

 

[.60408269, .6041258120, 0.431220e-4]

 

[.52922015, .5292500040, 0.298540e-4]

 

[.44509054, .4451081856, 0.176456e-4]

 

[.35093889, .3509470278, 0.81378e-5]

 

[.24595805, .2459603111, 0.22611e-5]

 

[.12928542, .1292854830, 0.630e-7]

 

[-0.1e-7, 0., 0.1e-7]

 

[1.0000000, 1, 0.]

 

[.9987075, .9987075410, 0.410e-7]

 

[.9946539, .9946538260, 0.740e-7]

 

[.9875592, .9875591065, 0.935e-7]

 

[.9771225, .9771222065, 0.2935e-6]

 

[.9630194, .9630190630, 0.3370e-6]

 

[.9449015, .9449011655, 0.3345e-6]

 

[.9223945, .9223939070, 0.5930e-6]

 

[.8950954, .8950948190, 0.5810e-6]

 

[.8625722, .8625717020, 0.4980e-6]

 

[.8243613, .8243606355, 0.6645e-6]

 

[.7799644, .7799638580, 0.5420e-6]

 

[.7288483, .7288475200, 0.7800e-6]

 

[.6704399, .6704392900, 0.6100e-6]

 

[.6041262, .6041258120, 0.3880e-6]

 

[.5292503, .5292500040, 0.2960e-6]

 

[.4451084, .4451081856, 0.2144e-6]

 

[.3509472, .3509470278, 0.1722e-6]

 

[.2459606, .2459603111, 0.2889e-6]

 

[.1292855, .1292854830, 0.170e-7]

 

[0.1e-6, 0., 0.1e-6]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

(2)

``


 

Download fourthLINEARBOUD042021.mw
 

NULL

restart

with(LinearAlgebra):

alpha := .985

.985

(1)

for i to 7 do for j from -1 by .1 to 1 do Exact[j] := ((1-j)*(1/2))*exp((1+j)*(1/2)); Y[0] := proc (x) options operator, arrow; -(1/8)*exp(1)+1/2+(-(1/8)*exp(1)-3/4)*x+(1/8)*exp(1)*x^2+((1/8)*exp(1)+1/4)*x^3 end proc; Ics := Z(-1) = 1, Z(1) = 0, (D(Z))(-1) = 0, (D(Z))(1) = -(1/2)*exp(1); exp(x) := convert(taylor(exp(x), x = 0, 25), polynom); f := proc (x) options operator, arrow; ((1/32)*x-5/32)*exp((1/2)*x+1/2) end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; -1/4 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; -1/16 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(f(x)-p(x)*(diff(Y[i-1](x), `$`(x, 3)))-q(x)*(diff(Y[i-1](x), `$`(x, 2)))-r(x)*(diff(Y[i-1](x), x))-u(x)*Y[i-1](x)); s[i] := evalf(dsolve({Ics, eq[i]}, Z(x))); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do

[1.00000001, 1, 0.1e-7]

 

[.99889373, .9987075410, 0.1861890e-3]

 

[.99542387, .9946538260, 0.7700440e-3]

 

[.98930908, .9875591065, 0.17499735e-2]

 

[.98020108, .9771222065, 0.30788735e-2]

 

[.96769238, .9630190630, 0.46733170e-2]

 

[.95132386, .9449011655, 0.64226945e-2]

 

[.93059225, .9223939070, 0.81983430e-2]

 

[.90495743, .8950948190, 0.98626110e-2]

 

[.87384983, .8625717020, 0.112781280e-1]

 

[.83667770, .8243606355, 0.123170645e-1]

 

[.79283435, .7799638580, 0.128704920e-1]

 

[.74170543, .7288475200, 0.128579100e-1]

 

[.68267630, .6704392900, 0.122370100e-1]

 

[.61513924, .6041258120, 0.110134280e-1]

 

[.53850104, .5292500040, 0.92510360e-2]

 

[.45219044, .4451081856, 0.70822544e-2]

 

[.35566578, .3509470278, 0.47187522e-2]

 

[.24842284, .2459603111, 0.24625289e-2]

 

[.13000273, .1292854830, 0.7172470e-3]

 

[0., 0., 0.]

 

[1.00000001, 1, 0.1e-7]

 

[.99870526, .9987075410, 0.22810e-5]

 

[.99464487, .9946538260, 0.89560e-5]

 

[.98753974, .9875591065, 0.193665e-4]

 

[.97708963, .9771222065, 0.325765e-4]

 

[.96297160, .9630190630, 0.474630e-4]

 

[.94483868, .9449011655, 0.624855e-4]

 

[.92231783, .9223939070, 0.760770e-4]

 

[.89500815, .8950948190, 0.866690e-4]

 

[.86247884, .8625717020, 0.928620e-4]

 

[.82426685, .8243606355, 0.937855e-4]

 

[.77987484, .7799638580, 0.890180e-4]

 

[.72876867, .7288475200, 0.788500e-4]

 

[.67037492, .6704392900, 0.643700e-4]

 

[.60407851, .6041258120, 0.473020e-4]

 

[.52922004, .5292500040, 0.299640e-4]

 

[.44509347, .4451081856, 0.147156e-4]

 

[.35094315, .3509470278, 0.38778e-5]

 

[.24596164, .2459603111, 0.13289e-5]

 

[.12928690, .1292854830, 0.14170e-5]

 

[-0.2e-7, 0., 0.2e-7]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

 

[1.00000000, 1, 0.]

 

[.99902820, .9987075410, 0.3206590e-3]

 

[.99581870, .9946538260, 0.11648740e-2]

 

[.98992527, .9875591065, 0.23661635e-2]

 

[.98089421, .9771222065, 0.37720035e-2]

 

[.96826375, .9630190630, 0.52446870e-2]

 

[.95156339, .9449011655, 0.66622245e-2]

 

[.93031319, .9223939070, 0.79192830e-2]

 

[.90402310, .8950948190, 0.89282810e-2]

 

[.87219221, .8625717020, 0.96205080e-2]

 

[.83430805, .8243606355, 0.99474145e-2]

 

[.78984585, .7799638580, 0.98819920e-2]

 

[.73826774, .7288475200, 0.94202200e-2]

 

[.67902206, .6704392900, 0.85827700e-2]

 

[.61154254, .6041258120, 0.74167280e-2]

 

[.53524746, .5292500040, 0.59974560e-2]

 

[.44953895, .4451081856, 0.44307644e-2]

 

[.35380210, .3509470278, 0.28550722e-2]

 

[.24740416, .2459603111, 0.14438489e-2]

 

[.12969376, .1292854830, 0.4082770e-3]

 

[0.1e-7, 0., 0.1e-7]

 

[1.00000002, 1, 0.2e-7]

 

[.99870689, .9987075410, 0.6510e-6]

 

[.99464990, .9946538260, 0.39260e-5]

 

[.98754844, .9875591065, 0.106665e-4]

 

[.97710162, .9771222065, 0.205865e-4]

 

[.96298633, .9630190630, 0.327330e-4]

 

[.94485556, .9449011655, 0.456055e-4]

 

[.92233620, .9223939070, 0.577070e-4]

 

[.89502732, .8950948190, 0.674990e-4]

 

[.86249795, .8625717020, 0.737520e-4]

 

[.82428488, .8243606355, 0.757555e-4]

 

[.77989071, .7799638580, 0.731480e-4]

 

[.72878132, .7288475200, 0.662000e-4]

 

[.67038351, .6704392900, 0.557800e-4]

 

[.60408269, .6041258120, 0.431220e-4]

 

[.52922015, .5292500040, 0.298540e-4]

 

[.44509054, .4451081856, 0.176456e-4]

 

[.35093889, .3509470278, 0.81378e-5]

 

[.24595805, .2459603111, 0.22611e-5]

 

[.12928542, .1292854830, 0.630e-7]

 

[-0.1e-7, 0., 0.1e-7]

 

[1.0000000, 1, 0.]

 

[.9987075, .9987075410, 0.410e-7]

 

[.9946539, .9946538260, 0.740e-7]

 

[.9875592, .9875591065, 0.935e-7]

 

[.9771225, .9771222065, 0.2935e-6]

 

[.9630194, .9630190630, 0.3370e-6]

 

[.9449015, .9449011655, 0.3345e-6]

 

[.9223945, .9223939070, 0.5930e-6]

 

[.8950954, .8950948190, 0.5810e-6]

 

[.8625722, .8625717020, 0.4980e-6]

 

[.8243613, .8243606355, 0.6645e-6]

 

[.7799644, .7799638580, 0.5420e-6]

 

[.7288483, .7288475200, 0.7800e-6]

 

[.6704399, .6704392900, 0.6100e-6]

 

[.6041262, .6041258120, 0.3880e-6]

 

[.5292503, .5292500040, 0.2960e-6]

 

[.4451084, .4451081856, 0.2144e-6]

 

[.3509472, .3509470278, 0.1722e-6]

 

[.2459606, .2459603111, 0.2889e-6]

 

[.1292855, .1292854830, 0.170e-7]

 

[0.1e-6, 0., 0.1e-6]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

(2)

``


 

Download fourthLINEARBOUD042021.mw
 

NULL

restart

with(LinearAlgebra):

alpha := .985

.985

(1)

for i to 7 do for j from -1 by .1 to 1 do Exact[j] := ((1-j)*(1/2))*exp((1+j)*(1/2)); Y[0] := proc (x) options operator, arrow; -(1/8)*exp(1)+1/2+(-(1/8)*exp(1)-3/4)*x+(1/8)*exp(1)*x^2+((1/8)*exp(1)+1/4)*x^3 end proc; Ics := Z(-1) = 1, Z(1) = 0, (D(Z))(-1) = 0, (D(Z))(1) = -(1/2)*exp(1); exp(x) := convert(taylor(exp(x), x = 0, 25), polynom); f := proc (x) options operator, arrow; ((1/32)*x-5/32)*exp((1/2)*x+1/2) end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; -1/4 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; -1/16 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(f(x)-p(x)*(diff(Y[i-1](x), `$`(x, 3)))-q(x)*(diff(Y[i-1](x), `$`(x, 2)))-r(x)*(diff(Y[i-1](x), x))-u(x)*Y[i-1](x)); s[i] := evalf(dsolve({Ics, eq[i]}, Z(x))); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do

[1.00000001, 1, 0.1e-7]

 

[.99889373, .9987075410, 0.1861890e-3]

 

[.99542387, .9946538260, 0.7700440e-3]

 

[.98930908, .9875591065, 0.17499735e-2]

 

[.98020108, .9771222065, 0.30788735e-2]

 

[.96769238, .9630190630, 0.46733170e-2]

 

[.95132386, .9449011655, 0.64226945e-2]

 

[.93059225, .9223939070, 0.81983430e-2]

 

[.90495743, .8950948190, 0.98626110e-2]

 

[.87384983, .8625717020, 0.112781280e-1]

 

[.83667770, .8243606355, 0.123170645e-1]

 

[.79283435, .7799638580, 0.128704920e-1]

 

[.74170543, .7288475200, 0.128579100e-1]

 

[.68267630, .6704392900, 0.122370100e-1]

 

[.61513924, .6041258120, 0.110134280e-1]

 

[.53850104, .5292500040, 0.92510360e-2]

 

[.45219044, .4451081856, 0.70822544e-2]

 

[.35566578, .3509470278, 0.47187522e-2]

 

[.24842284, .2459603111, 0.24625289e-2]

 

[.13000273, .1292854830, 0.7172470e-3]

 

[0., 0., 0.]

 

[1.00000001, 1, 0.1e-7]

 

[.99870526, .9987075410, 0.22810e-5]

 

[.99464487, .9946538260, 0.89560e-5]

 

[.98753974, .9875591065, 0.193665e-4]

 

[.97708963, .9771222065, 0.325765e-4]

 

[.96297160, .9630190630, 0.474630e-4]

 

[.94483868, .9449011655, 0.624855e-4]

 

[.92231783, .9223939070, 0.760770e-4]

 

[.89500815, .8950948190, 0.866690e-4]

 

[.86247884, .8625717020, 0.928620e-4]

 

[.82426685, .8243606355, 0.937855e-4]

 

[.77987484, .7799638580, 0.890180e-4]

 

[.72876867, .7288475200, 0.788500e-4]

 

[.67037492, .6704392900, 0.643700e-4]

 

[.60407851, .6041258120, 0.473020e-4]

 

[.52922004, .5292500040, 0.299640e-4]

 

[.44509347, .4451081856, 0.147156e-4]

 

[.35094315, .3509470278, 0.38778e-5]

 

[.24596164, .2459603111, 0.13289e-5]

 

[.12928690, .1292854830, 0.14170e-5]

 

[-0.2e-7, 0., 0.2e-7]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

 

[1.00000000, 1, 0.]

 

[.99902820, .9987075410, 0.3206590e-3]

 

[.99581870, .9946538260, 0.11648740e-2]

 

[.98992527, .9875591065, 0.23661635e-2]

 

[.98089421, .9771222065, 0.37720035e-2]

 

[.96826375, .9630190630, 0.52446870e-2]

 

[.95156339, .9449011655, 0.66622245e-2]

 

[.93031319, .9223939070, 0.79192830e-2]

 

[.90402310, .8950948190, 0.89282810e-2]

 

[.87219221, .8625717020, 0.96205080e-2]

 

[.83430805, .8243606355, 0.99474145e-2]

 

[.78984585, .7799638580, 0.98819920e-2]

 

[.73826774, .7288475200, 0.94202200e-2]

 

[.67902206, .6704392900, 0.85827700e-2]

 

[.61154254, .6041258120, 0.74167280e-2]

 

[.53524746, .5292500040, 0.59974560e-2]

 

[.44953895, .4451081856, 0.44307644e-2]

 

[.35380210, .3509470278, 0.28550722e-2]

 

[.24740416, .2459603111, 0.14438489e-2]

 

[.12969376, .1292854830, 0.4082770e-3]

 

[0.1e-7, 0., 0.1e-7]

 

[1.00000002, 1, 0.2e-7]

 

[.99870689, .9987075410, 0.6510e-6]

 

[.99464990, .9946538260, 0.39260e-5]

 

[.98754844, .9875591065, 0.106665e-4]

 

[.97710162, .9771222065, 0.205865e-4]

 

[.96298633, .9630190630, 0.327330e-4]

 

[.94485556, .9449011655, 0.456055e-4]

 

[.92233620, .9223939070, 0.577070e-4]

 

[.89502732, .8950948190, 0.674990e-4]

 

[.86249795, .8625717020, 0.737520e-4]

 

[.82428488, .8243606355, 0.757555e-4]

 

[.77989071, .7799638580, 0.731480e-4]

 

[.72878132, .7288475200, 0.662000e-4]

 

[.67038351, .6704392900, 0.557800e-4]

 

[.60408269, .6041258120, 0.431220e-4]

 

[.52922015, .5292500040, 0.298540e-4]

 

[.44509054, .4451081856, 0.176456e-4]

 

[.35093889, .3509470278, 0.81378e-5]

 

[.24595805, .2459603111, 0.22611e-5]

 

[.12928542, .1292854830, 0.630e-7]

 

[-0.1e-7, 0., 0.1e-7]

 

[1.0000000, 1, 0.]

 

[.9987075, .9987075410, 0.410e-7]

 

[.9946539, .9946538260, 0.740e-7]

 

[.9875592, .9875591065, 0.935e-7]

 

[.9771225, .9771222065, 0.2935e-6]

 

[.9630194, .9630190630, 0.3370e-6]

 

[.9449015, .9449011655, 0.3345e-6]

 

[.9223945, .9223939070, 0.5930e-6]

 

[.8950954, .8950948190, 0.5810e-6]

 

[.8625722, .8625717020, 0.4980e-6]

 

[.8243613, .8243606355, 0.6645e-6]

 

[.7799644, .7799638580, 0.5420e-6]

 

[.7288483, .7288475200, 0.7800e-6]

 

[.6704399, .6704392900, 0.6100e-6]

 

[.6041262, .6041258120, 0.3880e-6]

 

[.5292503, .5292500040, 0.2960e-6]

 

[.4451084, .4451081856, 0.2144e-6]

 

[.3509472, .3509470278, 0.1722e-6]

 

[.2459606, .2459603111, 0.2889e-6]

 

[.1292855, .1292854830, 0.170e-7]

 

[0.1e-6, 0., 0.1e-6]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

(2)

``


 

Download fourthLINEARBOUD042021.mw
 

NULL

restart

with(LinearAlgebra):

alpha := .985

.985

(1)

for i to 7 do for j from -1 by .1 to 1 do Exact[j] := ((1-j)*(1/2))*exp((1+j)*(1/2)); Y[0] := proc (x) options operator, arrow; -(1/8)*exp(1)+1/2+(-(1/8)*exp(1)-3/4)*x+(1/8)*exp(1)*x^2+((1/8)*exp(1)+1/4)*x^3 end proc; Ics := Z(-1) = 1, Z(1) = 0, (D(Z))(-1) = 0, (D(Z))(1) = -(1/2)*exp(1); exp(x) := convert(taylor(exp(x), x = 0, 25), polynom); f := proc (x) options operator, arrow; ((1/32)*x-5/32)*exp((1/2)*x+1/2) end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; -1/4 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; -1/16 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(f(x)-p(x)*(diff(Y[i-1](x), `$`(x, 3)))-q(x)*(diff(Y[i-1](x), `$`(x, 2)))-r(x)*(diff(Y[i-1](x), x))-u(x)*Y[i-1](x)); s[i] := evalf(dsolve({Ics, eq[i]}, Z(x))); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do

[1.00000001, 1, 0.1e-7]

 

[.99889373, .9987075410, 0.1861890e-3]

 

[.99542387, .9946538260, 0.7700440e-3]

 

[.98930908, .9875591065, 0.17499735e-2]

 

[.98020108, .9771222065, 0.30788735e-2]

 

[.96769238, .9630190630, 0.46733170e-2]

 

[.95132386, .9449011655, 0.64226945e-2]

 

[.93059225, .9223939070, 0.81983430e-2]

 

[.90495743, .8950948190, 0.98626110e-2]

 

[.87384983, .8625717020, 0.112781280e-1]

 

[.83667770, .8243606355, 0.123170645e-1]

 

[.79283435, .7799638580, 0.128704920e-1]

 

[.74170543, .7288475200, 0.128579100e-1]

 

[.68267630, .6704392900, 0.122370100e-1]

 

[.61513924, .6041258120, 0.110134280e-1]

 

[.53850104, .5292500040, 0.92510360e-2]

 

[.45219044, .4451081856, 0.70822544e-2]

 

[.35566578, .3509470278, 0.47187522e-2]

 

[.24842284, .2459603111, 0.24625289e-2]

 

[.13000273, .1292854830, 0.7172470e-3]

 

[0., 0., 0.]

 

[1.00000001, 1, 0.1e-7]

 

[.99870526, .9987075410, 0.22810e-5]

 

[.99464487, .9946538260, 0.89560e-5]

 

[.98753974, .9875591065, 0.193665e-4]

 

[.97708963, .9771222065, 0.325765e-4]

 

[.96297160, .9630190630, 0.474630e-4]

 

[.94483868, .9449011655, 0.624855e-4]

 

[.92231783, .9223939070, 0.760770e-4]

 

[.89500815, .8950948190, 0.866690e-4]

 

[.86247884, .8625717020, 0.928620e-4]

 

[.82426685, .8243606355, 0.937855e-4]

 

[.77987484, .7799638580, 0.890180e-4]

 

[.72876867, .7288475200, 0.788500e-4]

 

[.67037492, .6704392900, 0.643700e-4]

 

[.60407851, .6041258120, 0.473020e-4]

 

[.52922004, .5292500040, 0.299640e-4]

 

[.44509347, .4451081856, 0.147156e-4]

 

[.35094315, .3509470278, 0.38778e-5]

 

[.24596164, .2459603111, 0.13289e-5]

 

[.12928690, .1292854830, 0.14170e-5]

 

[-0.2e-7, 0., 0.2e-7]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

 

[1.00000000, 1, 0.]

 

[.99902820, .9987075410, 0.3206590e-3]

 

[.99581870, .9946538260, 0.11648740e-2]

 

[.98992527, .9875591065, 0.23661635e-2]

 

[.98089421, .9771222065, 0.37720035e-2]

 

[.96826375, .9630190630, 0.52446870e-2]

 

[.95156339, .9449011655, 0.66622245e-2]

 

[.93031319, .9223939070, 0.79192830e-2]

 

[.90402310, .8950948190, 0.89282810e-2]

 

[.87219221, .8625717020, 0.96205080e-2]

 

[.83430805, .8243606355, 0.99474145e-2]

 

[.78984585, .7799638580, 0.98819920e-2]

 

[.73826774, .7288475200, 0.94202200e-2]

 

[.67902206, .6704392900, 0.85827700e-2]

 

[.61154254, .6041258120, 0.74167280e-2]

 

[.53524746, .5292500040, 0.59974560e-2]

 

[.44953895, .4451081856, 0.44307644e-2]

 

[.35380210, .3509470278, 0.28550722e-2]

 

[.24740416, .2459603111, 0.14438489e-2]

 

[.12969376, .1292854830, 0.4082770e-3]

 

[0.1e-7, 0., 0.1e-7]

 

[1.00000002, 1, 0.2e-7]

 

[.99870689, .9987075410, 0.6510e-6]

 

[.99464990, .9946538260, 0.39260e-5]

 

[.98754844, .9875591065, 0.106665e-4]

 

[.97710162, .9771222065, 0.205865e-4]

 

[.96298633, .9630190630, 0.327330e-4]

 

[.94485556, .9449011655, 0.456055e-4]

 

[.92233620, .9223939070, 0.577070e-4]

 

[.89502732, .8950948190, 0.674990e-4]

 

[.86249795, .8625717020, 0.737520e-4]

 

[.82428488, .8243606355, 0.757555e-4]

 

[.77989071, .7799638580, 0.731480e-4]

 

[.72878132, .7288475200, 0.662000e-4]

 

[.67038351, .6704392900, 0.557800e-4]

 

[.60408269, .6041258120, 0.431220e-4]

 

[.52922015, .5292500040, 0.298540e-4]

 

[.44509054, .4451081856, 0.176456e-4]

 

[.35093889, .3509470278, 0.81378e-5]

 

[.24595805, .2459603111, 0.22611e-5]

 

[.12928542, .1292854830, 0.630e-7]

 

[-0.1e-7, 0., 0.1e-7]

 

[1.0000000, 1, 0.]

 

[.9987075, .9987075410, 0.410e-7]

 

[.9946539, .9946538260, 0.740e-7]

 

[.9875592, .9875591065, 0.935e-7]

 

[.9771225, .9771222065, 0.2935e-6]

 

[.9630194, .9630190630, 0.3370e-6]

 

[.9449015, .9449011655, 0.3345e-6]

 

[.9223945, .9223939070, 0.5930e-6]

 

[.8950954, .8950948190, 0.5810e-6]

 

[.8625722, .8625717020, 0.4980e-6]

 

[.8243613, .8243606355, 0.6645e-6]

 

[.7799644, .7799638580, 0.5420e-6]

 

[.7288483, .7288475200, 0.7800e-6]

 

[.6704399, .6704392900, 0.6100e-6]

 

[.6041262, .6041258120, 0.3880e-6]

 

[.5292503, .5292500040, 0.2960e-6]

 

[.4451084, .4451081856, 0.2144e-6]

 

[.3509472, .3509470278, 0.1722e-6]

 

[.2459606, .2459603111, 0.2889e-6]

 

[.1292855, .1292854830, 0.170e-7]

 

[0.1e-6, 0., 0.1e-6]

 

[2., 1, 1.]

 

[2., .9987075410, 1.001292459]

 

[2., .9946538260, 1.005346174]

 

[2., .9875591065, 1.012440894]

 

[2., .9771222065, 1.022877794]

 

[2., .9630190630, 1.036980937]

 

[2., .9449011655, 1.055098834]

 

[2., .9223939070, 1.077606093]

 

[2., .8950948190, 1.104905181]

 

[2., .8625717020, 1.137428298]

 

[2., .8243606355, 1.175639364]

 

[2., .7799638580, 1.220036142]

 

[2., .7288475200, 1.271152480]

 

[2., .6704392900, 1.329560710]

 

[2., .6041258120, 1.395874188]

 

[2., .5292500040, 1.470749996]

 

[2., .4451081856, 1.554891814]

 

[2., .3509470278, 1.649052972]

 

[2., .2459603111, 1.754039689]

 

[2., .1292854830, 1.870714517]

 

[2., 0., 2.]

(2)

``


 

Download fourthLINEARBOUD042021.mw

 

 

 

PLS FIND ATTACHED A MAPLE CODE TO SOLVE SOME BOUNDARY VALUE PROBLEM, BUT IT JUMP SOME ITERATION WITHOUT EVALUATION WHICH END UP WITH INACCURATE SOLUTION.

> restart;
> with(LinearAlgebra);
> exp(1) := 2.7182818284590452354;
> alpha := .975;
> NULL;
> st := time[real]();
> for i to 4 do for j from 0 by .1 to 4-exp(1) do Exact[j] := evalf(ln(exp(1)+j)); Y[0] := proc (x) options operator, arrow; 1+x/exp(1)+(1/4)*((exp(1))^2-8*exp(1)+24*ln(2)*exp(1)-32)*x^2/(exp(1)*(16-8*exp(1)+(exp(1))^2))+(1/4)*(16*ln(2)*exp(1)-16-8*exp(1)+(exp(1))^2)*x^3/((-64+48*exp(1)-12*(exp(1))^2+(exp(1))^3)*exp(1)) end proc; Ics := Z(0) = 1, (D(Z))(0) = 1/exp(1), Z(4-exp(1)) = evalf(ln(4)), (D(Z))(4-exp(1)) = 1/4; f := proc (x) options operator, arrow; 0 end proc; p := proc (x) options operator, arrow; 0 end proc; q := proc (x) options operator, arrow; 0 end proc; r := proc (x) options operator, arrow; 0 end proc; u := proc (x) options operator, arrow; 0 end proc; eq[i] := diff(Z(x), `$`(x, 4)) = (1-alpha)*(diff(Y[i-1](x), `$`(x, 4)))+alpha*(-6*convert(taylor(exp(-4*Y[i-1](x)), x = 0, 20), polynom)); s[i] := dsolve({Ics, eq[i]}, Z(x)); Y[i] := unapply(op(2, s[i]), x); App[j] := evalf(Y[i](j)); Er[j] := abs(App[j]-Exact[j]); print([App[j], Exact[j], Er[j]]) end do end do; time[real]()-st;
 

Dear maple users 

Greetings.

I hope you are all fine.

In this code, I am solving the PDEs via pdsolve with numeric.

There is some mistake in the boundary condition and pdsolve.

Kindly help me that to get the solution for this PDE.

Waiting for your reply.

In this problem h(z) is piecewise 

 

Bc:   

code:JVB.mw

 

Note: z=0.5:

My question is whether any special interest groups exist in the Maple Cloud?  If so, is there a public listing of these groups?

Hello,

I would like to understand how i can construct module with submodules.

In the maple help, this chapter should answer perfectly to my need : https://www.maplesoft.com/support/help/Maple/view.aspx?path=ProgrammingGuide/Chapter11

At this page, there is a package called Shapes which should be very useful for me.

However, i don't understand 1 point at the moment about the package architecture of this example of package.

Why there is a submodule also called Shapes inside the module Shapes ? In other words, why the different submodules point, segment, circle, square, triangle have not be constructed directly under the module Shapes but under the submodule Shapes?

I thank you in advance for your help.

Hey everyone,

I see I can use SimpleLieAlgebraData to create Lie algebras of types A, B, C, D, and also G2 and F4. Is there a built-in way to generate E6, E7, and E8? If not, is there any plan to add these?

Thanks!

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