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mskalsi

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How to write vector fileds corresponding...

mskalsi 290 Maple 18
infinitesimal
July 10 2016
0 0

Dear All

It is well known that the package "PDEtools" is helpful in finding infinitesimal transformations for PDEs which I illustrate as follow:


> 

with(PDEtools):
> 

DepVars := [u(x, y, t)]

[u(x, y, t)]

 (1)
> 

declare(u(x, y, t)):

u(x, y, t)*`will now be displayed as`*u

 (2)
> 

U := diff_table(u(x, y, t)):
> 

PDE1 := U[t, x]+(3/2)*u(x, y, t)*U[x, x]+(3/2)*U[x]^2+(1/4)*U[x, x, x, x]+(3/4)*sigma*U[y, y] = 0:
> 

G := [seq(xi[j](x, y, t, u), j = [x, y, t]), seq(eta[j](x, y, t, u), j = [u])]:
> 

declare(G):

eta(x, y, t, u)*`will now be displayed as`*eta

  

xi(x, y, t, u)*`will now be displayed as`*xi

 (3)
> 

DetSys := DeterminingPDE(PDE1, G, integrabilityconditions = false):
> 

pdsolve(DetSys)

{eta[u](x, y, t, u) = (1/9)*(-2*(diff(diff(diff(_F1(t), t), t), t))*y^2-4*(diff(diff(_F2(t), t), t))*y+6*sigma*(-(3/2)*(diff(_F1(t), t))*u+(1/2)*(diff(diff(_F1(t), t), t))*x+diff(_F3(t), t)))/sigma, xi[t](x, y, t, u) = (3/2)*_F1(t)+_C1, xi[x](x, y, t, u) = (1/6)*(-2*(diff(diff(_F1(t), t), t))*y^2-4*(diff(_F2(t), t))*y+3*sigma*((diff(_F1(t), t))*x+2*_F3(t)))/sigma, xi[y](x, y, t, u) = (diff(_F1(t), t))*y+_F2(t)}

 (4)

The set (4) gives infinitesimal transformations. How we can write  vector fields corresponding to arbitrary constant C1and arbitrary functions "F1(t), F2(t), F3(t) "?"" 

> 

``


Download Writing_Vector_fields.mw

Regards

How I can improve aesthetic look of my 3...

mskalsi 290 Maple 18
plot export 3d
June 25 2016
2 9

Dear All

I have 3D plot

 

> 

y := 0; 1; z := 0

0

  

0

 (1)
> 

plot3d(abs((2*(-exp(-t-x-z)+exp(t+x+z)))/(exp(-t-x-z)+tanh((1+I)*t+(1/2-1/2*I)*y+z)+exp(t+x+z))), x = -5 .. 5, t = -5 .. 5)

 
> 

``

How I can Improve this plot so that it look more aesthetic ?

Secondly, the resulotion of plot is not so good, and when I export this plot as jpeg file, quality of resolution deteriotate even more, I mean pixel tear out on zooming the image. How I fix this issue which I guess might be due to wrong way of exporting plot ?

Download Improving_3D-_plot.mw

Regards

Isomophism between Lie algebras...

mskalsi 290 Maple 18
liealgebra isomorphism
June 17 2016
1 9

My query is related to Maple packages "Lie algebra" and "DifferentialGeometry", I wonder can these packages help me to check isomophism between to Lie algebras, for example, suppose I have a 4-dim Lie algebra with commutation relations:

[e2, e3] = e3, [e2, e4] = - e4, [e3, e4] = - e1 

and another 4-dim Lie algebra with commutation relations

[e2, e3] = e1, [e4, e2] = e2, [e3, e4] = - e3

Can I check for isomophism between these Lie algebras if there is any using Lie algebra package ?

 

Regards

Sharing content between worksheets...

mskalsi 290 Maple 18
worksheet import
May 30 2016
1 4

Is it possible to share contents between two different Maple worksheets ? Suppose for example, I want to use certain expression number (10) of  Worksheet 1 in worksheet 2, can I call that expression (10) in worksheet 2 ? I am asking this question because copying expressions between different worksheets is not easy task, sometime we unable copy expressions when they are too large. In my case after carrying out very tedious and lengthy calculations Maple stopped responding, now I have an idea that if I import last output of present worksheet in new worksheet may be I could continue my calculations.

Regards

Forcing Maple to give desired output...

mskalsi 290 Maple 18
output
May 30 2016
1 1


Suppose I type certain math expression like as follow:

> 

F^5*alpha[5]+F^4*G*gamma[1]+F*G^4*gamma[3]+G^5*beta[5]+F^4*alpha[4]+G^4*beta[4]+F^3*alpha[3]+F^2*G*gamma[2]+F*G^2*gamma[4]+G^3*beta[3]+F^2*alpha[2]+F*G*gamma[5]+G^2*beta[2]+F*alpha[1]+G*beta[1]+delta[0]

F^5*alpha[5]+F^4*G*gamma[1]+F*G^4*gamma[3]+G^5*beta[5]+F^4*alpha[4]+G^4*beta[4]+F^3*alpha[3]+F^2*G*gamma[2]+F*G^2*gamma[4]+G^3*beta[3]+F^2*alpha[2]+F*G*gamma[5]+G^2*beta[2]+F*alpha[1]+G*beta[1]+delta[0]

 (1)

But when I enter this expression, Maple gives totally different look to this expression, can I force Maple to print similar looking expression as I typed in command line ? I mean without change of  position of intermediates and coefficients.


Download Forcing_Maple_Output.mw

Regards

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