Unanswered Questions

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

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!

I am not familiar with mathematica syntax. I have this code which is written .np and I would like to translate it efficiently to Maple syntax.I tried FromMmaNotebook but it is not helpful for me. I would be grateful if you would give me a little help me translate the code. I attached the code as diagon.txt (you can change .txt with .nb)

Thank you in advance!diagon.txt

 

How can maple be trusted app when window 10 device guard enabled?

n := 3;
Digits := 10;
R_const := 8.314;
currentdir();
const := [1, 1, 1];
b := 20;
W := readdata("data20.txt", 2);
W := [seq([W[i, 2], W[i, 1]], i = 1 .. nops(W))];
Tempset := seq(W[i, 1], i = 1 .. nops(W));
Rateset := seq(W[i, 2], i = 1 .. nops(W));
Temp := [seq(W[i, 1], i = 1 .. nops(W))];
pdata := plots[pointplot](W, color = red);
pdata;

h[5] := 1;
h[4] := 8.5733287401;
h[3] := 18.059016973;
h[2] := 8.6347608925;
h[1] := 0.2677737343;
p[5] := 1;
p[4] := 9.5733223454;
p[3] := 25.6329561486;
p[2] := 21.0996530827;
p[1] := 3.9584969228;
r := x -> local m; exp(-x)*add(h[m]*x^(m - 1), m = 1 .. 5)/(x*add(p[m]*x^(m - 1), m = 1 .. 5));

q := (i, x) -> -Temp[1]*exp(-E_sim[i]/(R_const*Temp[1])) + E_sim[i]*r(E_sim[i]/(R_const*Temp[1]))/R_const + x*exp(-E_sim[i]/(R_const*x)) - E_sim[i]*r(E_sim[i]/(R_const*x))/R_const;

for i to n do
    R[i] := [seq(1 - exp(-A_sim[i]*const[i]*q(i, Temp[j])/b), j = 2 .. nops(Temp))];
end do;
for i to n do
    Der[i] := [seq(c_sim[i]*A_sim[i]*const[i]*exp(-E_sim[i]/(R_const*Temp[j]))*(1 - R[i][j]), j = 1 .. nops(Temp) - 1)];
end do;
Deriv := add(Der[i], i = 1 .. n);
model := [seq([Temp[i], Deriv[i]], i = 1 .. nops(R[1]))];
objective := add((W[i, 2] - model[i, 2])^2, i = 1 .. nops(Temp) - 1);
with(GlobalOptimization);
infolevel[GlobalOptimization] := 3;
Results := GlobalOptimization[GlobalSolve](objective, {add(c_sim[i], i = 1 .. 3) <= 1}, c_sim[1] = 0.05 .. 0.06, c_sim[2] = 0.85 .. 0.88, c_sim[3] = 0.05 .. 0.6, E_sim[1] = 33880 .. 33890, E_sim[2] = 40220 .. 41230, E_sim[3] = 23230 .. 23235, A_sim[1] = 2453 .. 2455, A_sim[2] = 190 .. 192, A_sim[3] = 1830 .. 1832, timelimit = 7200);
          [GetLastSolution, GlobalSolve, Interactive]

Results := [Float(undefined), [A_sim[1] = 2454.85789978944, 

  A_sim[2] = 190.143107633747, A_sim[3] = 1831.19959951461, 

  E_sim[1] = 33883.8826959700, E_sim[2] = 40796.6139830241, 

  E_sim[3] = 23230.4022199775, c_sim[1] = 0.0558944062681716, 

  c_sim[2] = 0.851532317382881, c_sim[3] = 0.0845465106500359]]


DEV_perc := 100*sqrt(Results[1]/(nops(Temp) - 3*n))/max(Rateset);
       DEV_perc := Float(undefined) + Float(undefined) 

Unsolved for Maple?

Thanks for reading.

I am just evaluating Maple 2021 under Windows 10 and I have something strange happening when I press F1 for Help or I select Maple Help in Help Menu. The first time the help window will appear but if I close it then impossible to view it again by pressing F1 or by selecting it in the Help menu. Also the same for other choices in the help menu like

Maple Help F1
Maple Portal
Study Guides
What's New

But any choices inside On the web will always work.

I am using Windows 10 latest release in french and the keyboard layout in ENG I don't think it is related but just in case someone ask me.

Have you notice the same problem ?

When I use piecewise like this

W :=piecewise(beta>=-Pi/2 and beta<=-Pi/2+Pi/200,1+eps/sin(Pi/200)+eps*cos(Pi/200)/sin(Pi/200)*sin(beta),
     
beta>=-Pi/2+Pi/200 and beta<=Pi/2,1+eps/sin(Pi/200)-eps*cos(Pi/200)/sin(Pi/200)*sin(beta),
      1+eps*(1+cos(beta)));

 

and eval the beta as following,

G:= eval(R,beta=(arctan(diff(f(x,y),y), diff(f(x,y),x))));

the calculation does not run well...because of the undefined

[[-eps sin(t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))),t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))<-Pi/2],[undefined,t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))=-Pi/2],[(eps cos(Pi/200) cos(t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))))/(sin(Pi/200)),t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))<-(99 Pi)/200],[undefined,t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))=-(99 Pi)/200],[-(eps cos(Pi/200) cos(t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))))/(sin(Pi/200)),t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))<Pi/2],[undefined,t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))=Pi/2],[-eps sin(t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))),Pi/2<t_atan2((&PartialD;)/(&PartialD;y) pho(x,y),(&PartialD;)/(&PartialD;x) pho(x,y))]]

Finally, when W is brought into the following formula for calculation, 

R:=   
-M*ElementInt( test(x,y)*((1-co(x,y))*Ha+co(x,y)*Hb))
     +M*ElementInt( test(x,y)*noise)
+M*gamma*(-ElementInt( W^2*( nab(test(x,y))[i] &t nab(f(x,y))[i])))
              +ElementInt( diff(W^2,beta)/2 * ( diff(test(x,y),x)*diff(f(x,y),y)
              -diff(test(x,y),y)*diff(f(x,y),x))):

 

the following error message will appear.

Error: Division by zero at (1)

 

I mentioned a similar problem just recently, but after two days of continuous attempts, I couldn't find a solution.
Look forward to receiving a reply.......

Hello, 

i would like to continue to work on a code which was done With CodeBuilder some years ago.

i often like to print my code to be able to read without any computer.

Problem : the print function on a worksheet with several coderegion doesn t work well.

1) Do you have some ideas to circumvet this issue ,

2) i m thinking about using a text éditor which can give a nice printing with maple. Emacs is far to much complex for me. Consequently, i havé seen that some of you have testéd Sublime text. I think that it may be a good alternative. Do you have ideas about simple text editor that i can use to edit maple code ?
 

thank you for your help 

hi, I wonder why this output is empty because I tried to get solution below partial equation:

restart;
with(PDEtools);
pe := diff(u(t, x, y), t) = u(t, x, y) - diff(u(t, x, y), x $ 2) - diff(u(t, x, y), y $ 2) + (1 + u(t, x, y)*I)*abs(u(t, x, y))*u(t,x,y)^2;                                  
inc := u(0, x, y) = cos(Pi*x/50) - cos(Pi*x/150)*I;
sys := [pe, inc];
   

pdsolve(sys);
 

end after this pdsolve(sys); Maple doesn't show anything

thanks in advance

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