How can I get the Automorphism Group of a group G as a Permutationgroup?

Best regards

Kurt Ewald

Hello,

this is the second time I'm writing.

I posted this question in June http://www.mapleprimes.com/questions/201781-System-Of-Parametric-Equations.

This time I have  a similar problem because I'm trying to find a solution for a parametric system of equations but the number of equations and parameters is much bigger and using the tips you gave me last time I couldn't reach any result.

Here is the system:

1) alpha[1]=v*a*u*b ;
2) alpha[2]=v*a*u*(1-b);
3) alpha[3]= v*z*c*(1-a) ;
4) alpha[4]=v*z*(1-a)*(1-c) ;
5) alpha[11]=1/2*v*a* u* b* (-p*u*b+p*u*b*a+b*g-g);
6) alpha[22]=1/2*v*a*u*(1-b)* (p u b-p u b a-b g-p u+p u a);
7) alpha[33] =1/2*v*c*z*(1-a)* (c* (-z*p*a+q)-q);
8) alpha[44]=1/2*v*z*((1-a)*(1-c)* (c*z*p*a-z*p*a-q*c);
9) alpha[12]=v*a*u*b*(1- b)*(-p*u+p*u*a+g) ;
10) alpha[13]=v*a*u*b*z*c*p*(1-a) ;
11) alpha[14]=a*u*b*z*(1-a)*(1-c) ;
12) alpha[23]=a*u*z*c*(1-a)*(1-b);
13) alpha[24]=v*a*u*z*p*(1-a)*(1-b)*(1-c);
14) alpha[34]= v*c*z*(1-a)*(1-c)*(-z*p*a+q);

I have 14 equations/unknowns and 8 parameters (a, b, c, u, v, z, p, q).

I would like to write this system only in terms of alphas. In order to do so, I usually try to find the value for the parameters and the substitute them into the equations (and I have already found b,c,g,q using this technique) but I couldn't manage to find all of them. 

Howveer, as you suggested me, with Maple there is the command "eliminate" that implement exactly what I'm looking for but I can't make it work.

This is my code:

> sys := {alpha[1] = v*a*u*(1-b), alpha[2] = v*a*u*b, alpha[3] = v*z*c*(1-a), alpha[4] = v*z*(1-a)*(1-c), alpha[11] = (1/2)*v*a*u*(1-b)*(p*u*b-p*u*b*a-b*g-p*u+p*u*a), alpha[12] = v*a*u*b*(1-b)*(-p*u+p*u*a+g), alpha[13] =      z*c*a*u*(1-a)*(1-b), alpha[14] = v*z*a*u*p*(1-a)*(1-b)*(1-c), alpha[22] = (1/2)*v*a*u*b*(-p*u*b+p*u*b*a+b*g-g), alpha[23] = v*z*c*a*u*b*p*(1-a), alpha[24] = z*a*u*b*(1-a)*(1-c), alpha[33] = (1/2)*v*c*z*(1-a)*(c*(-z*p*a+q)-q), alpha[34] = v*c*z*(1-a)*(1-c)*(-z*p*a+q), alpha[44] = (1/2)*v*z*(1-a)*(1-c)*(c*z*p*a-z*p*a-q*c)};

> eliminate(sys, {a,b,c, p, q, u, v, z});

> simplify(%, size);

I also tries to substitute in the system the four parameters I already found but still I can't find a solution.

What am I doing wrong? Or the problem is that it is too complicated?

Thank you for your attention,

Elena

I have a Maple program that fits a nonlinear function with 9 parameters to a dataset that contains multiple records; each record gets fitted separately. The records are ordered by a certain experimental variable (an angle of a target). The initial parameters for each fit are the solutions of the previous fit; in this case I get relatively good initial estimates and not too much trouble fitting. I use Statistics:-NonLinearFit to do the actual fitting.

Since this is a bit time consuming and I need to do this a fair amount of times, I'd like to see if I can't speed his up by employing parallel programming.

One way to speed up a fit is to compute the sum of residuals in parallel; is there a way to do this in Maple?

Another way would be to run several fits at the same time. The problem I have with that in this case is that I use the results of the previous fit as starting values for the next fit. I might be able to increase the stride of this scheme; i.e. for 4 processes, use the result of fit 1 as starting point for fit 5; fit 2 for fit 6 etc. But before I embark on this non-trivial change; can Statistics:-NonLinearFit even be used in this way (i.e. is it thread safe)?? My fitting function is an actual function (as opposed to a procedure with local variables) so I don't think the function itself would cause trouble.

I could also contemplate the Grid package; except that I am concerned about the overhead moving the data over to each node (although it would all sit on one machine with 4 processors).

I realize that I may have to do some experimentation by myself, but if there is any experience out there I'd like to know about it...

Mac Dude

restart;
eq:=diff(y(x),x) - y(x)^2 - x*y(x) - x + 1;
r:=dsolve(eq,y(x));
latex(r);

Gives an error "(in fprintf) string expected for string format". The problem seems when the math contains "erf"? Both examples below fail with result that contains this.

Maple 18, on windows 7.

Another example:

restart;
eq:=diff(y(x),x) + a*y(x)*(y(x)-x) - 1;
r:=dsolve(eq,y(x));
latex(r);

Another example, which seems to fail for different reason

restart;
eq:=diff(y(x),x) + a*x*y(x)^3+b*y(x)^2;
r:=dsolve(eq,y(x));
latex(r);

Hi,

With Maplets, it is possible to create popup windows to tell or ask the user something, but only when it is appropriate. That is, it is not there all the time. A particular usage would be to give the user a facilitating question when they have incorrect entries.

Is that possible in some way with Möbius apps also? Or does one have to always keep a blank TextArea available, just a blank space if invisible perhaps but using up space in the presentation nonetheless, to give the student the information?

AOA. I want to plot the graph of the following function 

A new generalized complex representation of Euler gamma function in terms of Dirac delta function, which is

GAMMA(s) = 2*Pi*(sum((-1)^n*Dirac(s+n)/factorial(n), n = 0 .. infinity))

where*s = sigma+i*tau

for differenet values of parameters

Hi everyone,

I was trying to write a Maple sheet to calculate some perturbation theory expension as close to the "book notation" as possible. Lets for example consider a linearly perturbed harmonic oscillator with H = hω(n+1/2) and V = λ(a^†+a), this is one of the classical examples as it can be solved analytically by completing the square. In the Kato formulation (as used in the appended Maple worksheet), as well as in Rayleigh-Schrödinger perturbation theory one uses the projector onto the complement of the unperturbed state. I would like to do this by defining a projector in Maple. I've read the examples concerning projectors in Maple but it seems I have to use a rather ugly workaround by treating the states "below" the unperturbed state and the ones "above" separately. While this is a little annoying in one dimension it becomes a major nuisance in higher dimensions.

My question would be: How do I define the projector onto the complement of some state?

Cheers, Sören

Download kato_perturbation_theory.mw

Hi everyone,

I'm running Maple 18 and MapleSim 6.4 on my macbook pro 13 " with retina display and the GUI is blurred like there is no smoothing or the antialiasing is not working properly. I tried to find something helpfull in the setting but with no luck.

Is there something I can do to fix this?

Thanks

Carlo

convert(50, base, 12);

this can change base for integer, however can not change decimal

assume i change decimal to fraction first and then apply convert base to 12 to numer and denom, and divide again to get decimal

it may get a decimal based on base 12

however, how to make this base 12 operation apply in linear algebra calculation

hi

DirectSearch answer has confused me. How to reduce the residual.
See the program.Direct.mw

Hi Maple users :)

do you know if exists a Maple package in order to perform a Panel method, for instance in the Hess-Smith version, for solving incompressible potential flow over thick 2d and 3d airfoil geometries?

Thank in advance for the help.

I have a matrix then I need to plot its columns as curves on one plot.

how to convert decimal number into given decimal number like algebra

for example, convert 191.715 , given a=12.2, b=3.5

how to find this a^2 + b^3

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);

m2 := Determinant(m-Matrix([[1,0,0],[0,1,0],[0,0,1]]));

1. which family of polynomials do m2 belong to?

2. how to analyze m2?