Maple 18 Questions and Posts

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Hello, 

I have a PDE system. When I use pdsolve it gets me the messege " pdsolve->Warning: System is inconsistent". Is there a way I can see which equations breaks the system down? 
For this system, it's difficult to see from ayeball where the problem is. 
Thank you! 

test.mw

i copy maple code from notepad to maple in maple window,

there is no error

my function in the code

explicit define parameters are Local type

for example

appendto("...");

func1(aaa)

Local aaa;

 

but when i run cmaple to read the code text file in window 8

it return error

missing operator, syntax error

at Local aaa;

originally 

i have defined

Local aaa, ii;

for ii from 1 to nops(aaa) do

etc.

but it has error too,

then i change to one by one

Local aaa;

Local ii;

still have error at Local aaa;

 

I'm displaying a series of point plots as an animation, and would like to update a displayed parameter as well.  I have a nested list L[t] where there's a set of points for each t, and for each t there's also a numerical value M that I'd like to display.  (In my real problem, L[t] is the number of particles in each of several states, and M is the rms deviation from am algebraic probability distribution.)  

The closest I've gotten (for a simple L and M) is the following, but it displays all of the M values in the legend at once:

with(plots); with(Statistics);

L := [[1, 2, 3, 4, 5, 6], [2, 4, 6, 8, 10, 12]];

M := [1, 2];

display([seq(PointPlot(L[t], legend = M[t]), t = 1 .. 2)], insequence = true)

 

I don't need this to be in the legend.  Is there a way to display only the current value of M for each t?  Thanks very much.

Dear All

In following I tried to find symmetries of certain partial differential equation taken from paper "Group classification and exact solutions of generalized modified Boussinesq equation". But the determining equations are not matching with equations obtained in paper.


with(PDEtools)

DepVars := [f(u(x, t)), u(x, t)]; declare(f(u(x, t)), u(x, t))

[f(u(x, t)), u(x, t)]

 

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

 

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

(1)

PDE1 := diff(u(x, t), t, t)-delta*(diff(u(x, t), x, x, t, t))-(diff(f(u(x, t)), x, x))

diff(diff(u(x, t), t), t)-delta*(diff(diff(diff(diff(u(x, t), t), t), x), x))-((D@@2)(f))(u(x, t))*(diff(u(x, t), x))^2-(D(f))(u(x, t))*(diff(diff(u(x, t), x), x))

(2)

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

[xi[x](x, t, u), xi[t](x, t, u), eta[u](x, t, u)]

(3)

declare(G)

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

 

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

(4)

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

{diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta, (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)), 2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)), 2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)), 4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t), 2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta, -(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), -2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta, diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta, 2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta, -(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta, -(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta, -2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta, (diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)), 2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta, diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u), diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x), diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u), diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), x), diff(diff(diff(xi[t](x, t, u), u), x), x), diff(diff(diff(xi[x](x, t, u), t), t), u), diff(diff(diff(xi[x](x, t, u), t), u), u), diff(diff(diff(xi[x](x, t, u), u), u), u), diff(diff(xi[t](x, t, u), u), u), diff(diff(xi[t](x, t, u), u), x), diff(diff(xi[t](x, t, u), x), x), diff(diff(xi[x](x, t, u), t), t), diff(diff(xi[x](x, t, u), t), u), diff(diff(xi[x](x, t, u), u), u), diff(xi[t](x, t, u), u), diff(xi[t](x, t, u), x), diff(xi[x](x, t, u), t), diff(xi[x](x, t, u), u)}

(5)

for EQ in sort([op(DetSys)], length) do EQ = 0 end do

diff(xi[t](x, t, u), u) = 0

 

diff(xi[t](x, t, u), x) = 0

 

diff(xi[x](x, t, u), t) = 0

 

diff(xi[x](x, t, u), u) = 0

 

diff(diff(xi[t](x, t, u), u), u) = 0

 

diff(diff(xi[t](x, t, u), u), x) = 0

 

diff(diff(xi[t](x, t, u), x), x) = 0

 

diff(diff(xi[x](x, t, u), t), t) = 0

 

diff(diff(xi[x](x, t, u), t), u) = 0

 

diff(diff(xi[x](x, t, u), u), u) = 0

 

diff(diff(diff(xi[t](x, t, u), u), u), u) = 0

 

diff(diff(diff(xi[t](x, t, u), u), u), x) = 0

 

diff(diff(diff(xi[t](x, t, u), u), x), x) = 0

 

diff(diff(diff(xi[x](x, t, u), t), t), u) = 0

 

diff(diff(diff(xi[x](x, t, u), t), u), u) = 0

 

diff(diff(diff(xi[x](x, t, u), u), u), u) = 0

 

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u) = 0

 

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x) = 0

 

diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u) = 0

 

diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u) = 0

 

diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta = 0

 

4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t) = 0

 

2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)) = 0

 

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)) = 0

 

2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)) = 0

 

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta = 0

 

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

 

2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)) = 0

 

-(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)) = 0

 

-(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)) = 0

 

2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta = 0

 

2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta = 0

 

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

 

-2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

 

2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

 

diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta = 0

 

-2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta = 0

 

-(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta = 0

 

-(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta = 0

 

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)) = 0

 

2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta = 0

 

(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))) = 0

(6)

DetSys1 := dsubs(diff(xi[t](x, t, u), u) = 0, diff(xi[t](x, t, u), x) = 0, diff(xi[x](x, t, u), t) = 0, diff(xi[x](x, t, u), u) = 0, diff(eta[u](x, t, u), u, u) = 0, diff(eta[u](x, t, u), x, u, t) = 0, DetSys)

{0, diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta, (diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))}

(7)

for EQ in sort([op(DetSys1)], length) do EQ = 0 end do

0 = 0

 

diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)) = 0

 

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)) = 0

 

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta = 0

 

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

 

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

 

(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)) = 0

 

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x)) = 0

(8)

The third equation in (8) can simplify last equation. This will give us eta[u][x] = 0as f[u, u] is non zero.

NULL


Download [1116]_Symmetries_Determination.mw[1116]_Group_classification_and_exact_solutions_of_generalized_modified_Boussinesq_equation.pdf

Regards

Good morning, I'm a student and I installed Maple 18 on my PC, as a "Single User Profile". Unfortunately, I had to buy another computer, so now I'm trying to install the program on my new one. Even if I enter my Purchase Code and my details, Maple says that no more activations are left in my account, even if the expiration date is on March 2020. Is it possible to activate again the program? 

Thank you,

Laura

hi...please help me for solve this nonlinear equations with pdsolve

thanksoffcenter2.mw

La := .25; Lb := 0.1e-1

h := 0.4e-2

rho := 7900

E := 0.200e12

nu := .3

ve := 5

g := 9.8

M := .5

Z0 := 0.1e-2

K := 5/6

C := sqrt(E/rho)

NULL

 

PDE[1] := diff(u(x, t), x, x)+(diff(w(x, t), x))*(diff(w(x, t), x, x)) = (diff(u(x, t), t, t))/C^2

diff(diff(u(x, t), x), x)+(diff(w(x, t), x))*(diff(diff(w(x, t), x), x)) = 0.3949999999e-7*(diff(diff(u(x, t), t), t))

(1)

PDE[2] := K*(diff(phi(x, t), x)+diff(w(x, t), x, x))/(2*(1+nu))+(diff(w(x, t), x))*(diff(u(x, t), x, x))+(diff(u(x, t), x))*(diff(w(x, t), x, x))+(3/2)*(diff(w(x, t), x, x))*(diff(w(x, t), x))^2 = (diff(w(x, t), t, t))/C^2

.3205128205*(diff(phi(x, t), x))+.3205128205*(diff(diff(w(x, t), x), x))+(diff(w(x, t), x))*(diff(diff(u(x, t), x), x))+(diff(u(x, t), x))*(diff(diff(w(x, t), x), x))+(3/2)*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2 = 0.3949999999e-7*(diff(diff(w(x, t), t), t))

(2)

 

PDE[3] := diff(phi(x, t), x, x)-6*K*(diff(w(x, t), x)+phi(x, t))/(h^2*(1+nu)) = (diff(phi(x, t), t, t))/C^2

diff(diff(phi(x, t), x), x)-240384.6154*(diff(w(x, t), x))-240384.6154*phi(x, t) = 0.3949999999e-7*(diff(diff(phi(x, t), t), t))

(3)

 

 

#####################################

(4)

at x= La

PDE[a1] := diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-M*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h) = 0

diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-0.6125000000e-6+0.6250000000e-7*(diff(diff(u(x, t), t), t))+0.6250000000e-10*(diff(diff(phi(x, t), t), t)) = 0

(5)

PDE[a2] := diff(phi(x, t), x)-12*M*Z0*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h^3) = 0

diff(phi(x, t), x)-0.4593750000e-3+0.4687500000e-4*(diff(diff(u(x, t), t), t))+0.4687500000e-7*(diff(diff(phi(x, t), t), t)) = 0

(6)

PDE[a3] := w(x, t) = 0

w(x, t) = 0

(7)

NULL

############################################

``

at x=0 NULL

(8)

PDE[b1] := u(x, t) = 0 

PDE[b2] := w(x, t) = 0

PDE[b3] := diff(phi(x, t), x) = 0

diff(phi(x, t), x) = 0

(9)

################################################

at t=0 for x= [0,La]

u(x, t) = 0

u(x, t) = 0

(10)

w(x, t) = 0

w(x, t) = 0

(11)

phi(x, t) = 0

phi(x, t) = 0

(12)

diff(phi(x, t), t) = 0

diff(phi(x, t), t) = 0

(13)

diff(w(x, t), t) = 0

diff(w(x, t), t) = 0

(14)

diff(phi(x, t), t, t) = 0

diff(diff(phi(x, t), t), t) = 0

(15)

diff(w(x, t), t, t) = 0

diff(diff(w(x, t), t), t) = 0

(16)

######################################################

at t=0 for x= [0,La)

diff(u(x, t), t) = 0

diff(u(x, t), t) = 0

(17)

diff(u(x, t), t, t) = 0

diff(diff(u(x, t), t), t) = 0

(18)

###################################################

at t=0 for x=La

NULL

diff(u(x, t), t) = -ve

diff(u(x, t), t) = -5

(19)

diff(u(x, t), t, t) = g

diff(diff(u(x, t), t), t) = 9.8

(20)

NULL

NULL

 

Download offcenter2.mw

Hello guys, i would like to do parallel computation in my code written in the Maple18. The question that can help me is:

Given a procedure that compute an function g, where g = f1+f2+f3+f4+f5+f6+f7+f8, i would like to compute all fi at same time.
Now, i´m using " grid:-seq('f[i]',[i=1,2,3,4,5,6,7,8])" and it works very well. However, i think that for my case an better solution should be;
Calculate the f1 in core 1, f2 in core 2, f3 in core 3 ... f8 in core 8 at same time, and after this, to sum all results(f1+f2+f3+..+f8). How i can do this?

Att,

Griffith.

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


Here, I attached my maple code. I need to find root. I am using fsolve. But I am not geting the root. Please any one help me... to find the root.

reatart:NULL``

m1 := 0.3e-1;

0.3e-1

(1)

m2 := .4;

.4

(2)

m3 := 2.5;

2.5

(3)

m4 := .3;

.3

(4)

be := .1;

.1

(5)

rho := .1;

.1

(6)

ga := 25;

25

(7)

a := 3.142;

3.142

(8)

q := .5;

.5

(9)

z[0] := 3;

3

(10)

x[0] := 1.5152;

1.5152

(11)

w[0] := 1.1152;

1.1152

(12)

a1 := be*z[0];

.3

(13)

a2 := be*x[0];

.15152

(14)

a3 := rho*w[0];

.11152

(15)

a4 := rho*z[0];

.3

(16)

a5 := rho*w[0];

.11152

(17)

a6 := rho*z[0];

.3

(18)

b1 := a1*a4*ga+a4*ga*m1;

2.475

(19)

D1 := a1+m1+m2+m3+m4;

3.53

(20)

D2 := a1*m2+a1*m3+a1*m4-a2*ga+a3*ga+m1*m2+m1*m3+m1*m4+m2*m3+m2*m4+m3*m4;

1.92600

(21)

D3 := a1*a3*ga+a1*m2*m3+a1*m2*m4+a1*m3*m4-a2*ga*m1-a2*ga*m4+a3*ga*m1+a3*ga*m4+m1*m2*m3+m1*m3*m4+m2*m3*m4+m1*m2*m3;

1.4499000

(22)

D4 := a1*a3*a4*ga+a1*m2*m3*m4-a2*ga*m1*m4+a3*ga*m1*m4+m1*m2*m3*m4;

.3409200

(23)

G1 := -a1*a6-a6*m1-a6*m2-a6*m3;

-.969

(24)

G2 := -a1*a6*m2-a1*a6*m3+a2*a6*ga-a3*a6*ga+a4*a5*ga-a6*m1*m2-a6*m1*m3-a6*m2*m3;

.549300

(25)

G3 := -a1*a3*a6*ga-a1*a6*m2*m3+a2*a6*ga*m1-a3*a6*ga*m1-a6*m1*m2*m3;

-.3409200

(26)

A1 := w^(4*q)*cos(4*q*a*(1/2))+D1*w^(3*q)*cos(3*q*a*(1/2))+D2*w^(2*q)*cos(2*q*a*(1/2))+D3*w^q*cos((1/2)*q*a)+D4;

-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200

(27)

B1 := w^(4*q)*sin(4*q*a*(1/2))+D1*w^(3*q)*sin(3*q*a*(1/2))+D2*w^(2*q)*sin(2*q*a*(1/2))+D3*w^q*sin((1/2)*q*a);

-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5

(28)

A2 := -w^(3*q)*a6*cos(3*q*a*(1/2))+G1*w^(2*q)*cos(2*q*a*(1/2))+G2*w^q*cos((1/2)*q*a)+G3;

.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200

(29)

B2 := -w^(3*q)*a6*sin(3*q*a*(1/2))+G1*w^(2*q)*sin(2*q*a*(1/2))+G2*w^q*sin((1/2)*q*a);

-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5

(30)

C := .27601200;

.27601200

(31)

Q1 := 4*C^2*(A2^2+B2^2);

.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2

(32)

Q2 := -4*C*A2*(A1^2-A2^2+B1^2-B2^2-C^2);

-1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)

(33)

Q3 := (A1^2-A2^2+B1^2-B2^2-C^2)^2-4*C^2*B2^2;

((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)^2-.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2

(34)

V := simplify(-4*Q1*Q3+Q2^2);

-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2)

(35)

x := (-Q2+sqrt(V))/(2*Q1);

(1/2)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)

(36)

E := -2*A1*C*x-A1^2+A2^2-B1^2+B2^2-C^2;

-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1

(37)

y := -E/(2*C*B1);

-1.811515442*(-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)/(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)

(38)

``

fsolve(x^2+y^2 = 1, w)

fsolve((1/4)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))^2/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)^2+3.281588197*(-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)^2/(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2 = 1, w)

(39)

``

 

Download root.mw

Hello guys,

I was just playing around with the Shanks transformation of a power series, when I noticed that polynomials aren't evaluated as I would expect.
I created this minimal working example; the function s should evaluate for z=0 to a[0], however it return simply 0.
Is there something I messed up?

restart

s := proc (n, z) options operator, arrow; sum(a[k]*z^k, k = 0 .. n) end proc;

proc (n, z) options operator, arrow; sum(a[k]*z^k, k = 0 .. n) end proc

(1)

series(s(n, z), z = 0)

series(a[0]+a[1]*z+a[2]*z^2+a[3]*z^3+a[4]*z^4+a[5]*z^5+O(z^6),z,6)

(2)

The value of s in z=0 should be a[0], however it returns 0:

s(n, 0)

0

(3)

s(1, 0)

0

(4)

Download evaluate_sum.mw

 

Thanks for your help,

Sören

Dear All

Using Lie algebra package in Maple we can easily find nilradical for given abstract algebra, but how we can find all the ideal in lower central series by taking new basis as nilradical itself?

Please see following;

 

with(DifferentialGeometry); with(LieAlgebras)

DGsetup([x, y, t, u, v])

`frame name: Euc`

(1)
Euc > 

VectorFields := evalDG([D_v, D_v*x+D_y*t, 2*D_t*t-2*D_u*u-D_v*v+D_y*y, t*D_v, D_v*y+D_u, D_t, D_x, D_x*t+D_u, 2*D_v*x+D_x*y, -D_t*t+2*D_u*u+2*D_v*v+D_x*x, D_y])

[_DG([["vector", "Euc", []], [[[5], 1]]]), _DG([["vector", "Euc", []], [[[2], t], [[5], x]]]), _DG([["vector", "Euc", []], [[[2], y], [[3], 2*t], [[4], -2*u], [[5], -v]]]), _DG([["vector", "Euc", []], [[[5], t]]]), _DG([["vector", "Euc", []], [[[4], 1], [[5], y]]]), _DG([["vector", "Euc", []], [[[3], 1]]]), _DG([["vector", "Euc", []], [[[1], 1]]]), _DG([["vector", "Euc", []], [[[1], t], [[4], 1]]]), _DG([["vector", "Euc", []], [[[1], y], [[5], 2*x]]]), _DG([["vector", "Euc", []], [[[1], x], [[3], -t], [[4], 2*u], [[5], 2*v]]]), _DG([["vector", "Euc", []], [[[2], 1]]])]

(2)
Euc > 

L1 := LieAlgebraData(VectorFields)

_DG([["LieAlgebra", "L1", [11]], [[[1, 3, 1], -1], [[1, 10, 1], 2], [[2, 3, 2], -1], [[2, 5, 4], 1], [[2, 6, 11], -1], [[2, 7, 1], -1], [[2, 8, 4], -1], [[2, 9, 5], -1], [[2, 9, 8], 1], [[2, 10, 2], 1], [[3, 4, 4], 3], [[3, 5, 5], 2], [[3, 6, 6], -2], [[3, 8, 8], 2], [[3, 9, 9], 1], [[3, 11, 11], -1], [[4, 6, 1], -1], [[4, 10, 4], 3], [[5, 10, 5], 2], [[5, 11, 1], -1], [[6, 8, 7], 1], [[6, 10, 6], -1], [[7, 9, 1], 2], [[7, 10, 7], 1], [[8, 9, 4], 2], [[8, 10, 8], 2], [[9, 10, 9], 1], [[9, 11, 7], -1]]])

(3)
Euc > 

DGsetup(L1)

`Lie algebra: L1`

(4)
L1 > 

MultiplicationTable("LieTable"):

L1 > 

N := Nilradical(L1)

[_DG([["vector", "L1", []], [[[1], 1]]]), _DG([["vector", "L1", []], [[[2], 1]]]), _DG([["vector", "L1", []], [[[4], 1]]]), _DG([["vector", "L1", []], [[[5], 1]]]), _DG([["vector", "L1", []], [[[6], 1]]]), _DG([["vector", "L1", []], [[[7], 1]]]), _DG([["vector", "L1", []], [[[8], 1]]]), _DG([["vector", "L1", []], [[[9], 1]]]), _DG([["vector", "L1", []], [[[11], 1]]])]

(5)
L1 > 

Query(N, "Nilpotent")

true

(6)
L1 > 

Query(N, "Solvable")

true

(7)

Taking N as new basis , how we can find all ideals in lower central series of this solvable ideal N?

 

Download [944]_Structure_of_Lie_algebra.mw

Regards

i'm using maple in a research but i want to add a recursive function h_m(t) in 2 case : if m is integer positive and not, 
la formule est donnée comme suit :  if (mod(m,1) = 0  and m>0) then  h:=proc(m,t)  local  t ;  h[0,t]:=t ;   for  i from -4 to  m  by  2 do  h [m,t]:= h[0, t]-(GAMMA(i/(2)))/(2*GAMMA((i+1)/(2)))*cos(Pi*t)*sin(Pi*t)  od:  fi:  end; 
  if (mod(m,1) = 0  and m>0) then  h:=proc(m,t)  local  t ;  h[0,t]:=t ;   for  i from -4 to  m  by  2 do  h [m,t]:= h[0, t]-(GAMMA(i/(2)))/(2*GAMMA((i+1)/(2)))*cos(Pi*t)*sin(Pi*t)  od:  fi:  end;
and i wanna to know how to programmate a Gaus Hypegeometric function. Thank You

 

Dear All

I have downloaded second version of DGApplications to work with abstract Lie algebra. The file is actually .mla file and it is executale(as when we open it, a prompt ask, "do you want to execute this file"), but when I press ok for execution, a file open with command like as

"march('open',"C:\\Users\\Manjit\\Downloads\\DGApplications.mla");",

what should I do after this, is it a some sort installation procedure. I keep all my Maple file in E drive with following path:

E:\Maple work\General Maple Workout

Please guide me in simple way, as I failed to install Maple package many times.

Regards

I'm trying to implement the QR algorithm to find the Eigenvalues of the input matrix which will be forwarded to another implementation (of the SVD alg.) to find the singular values. My implementation goes as follows:

1. feeding input: A::Matrix(datatype=float) # a bidiagonal matrix
2. construct input matrix for the QR alg. of matrix A and Z (zeros of size A): C := Matrix([[Z,Transpose(A)],[A,Z]], datatype=float); # therefore C should be symmetric
3. find the eigenvalues of matrix C with an implementation of the QR alg.:

for k from 1 to 400 do
Q, R := QRDecomposition(C);
C:=R.Q;
end do:

At this point, the eigenvalues of C should be placed in the diagonal of the matrix, but they're randomly placed around the diagonal, with only ~0 elements (like 2,xxx * 10^(-13)) in the diagonal.

If anyone knows how to resolve this, let the knowledge flow through. Any help will be appriciated, thanks in advance.

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