how to solve optimal system of vector   fields in lie theory in maple?

What is a suitable replacement for eliminate?

Here is my code:

In the older versions of Maple the first example of eliminate would return same result as the solve example, but with current version I need to resort to the second example.

Hi, I need to calculate some discrete variational problems, but it's a hard work just by hand.

Is there any toolboxes about the discrete variational computation? Or how to design a program to do that?

In particular, I need to realize the functions:

1. the linearized operator and the adjoint operator of some expressions.

       For example:

       the linearized operator of u(n,m+1)u(n+1,m) is u(n+1,m)Tm+u(n,m+1)Tn

       the adjoint operator is u(n+1,m-1)T^(-1)m+u(n-1,m+1)T^(-1)n,

       (The latter is just the discrete Euler operator.)

      Tm, Tn is the shift operator, T^(-1) is the inverse operator of T.

2. discrete Euler-Lagrange equation.

I am not familar with the maple, please help!

Thanks.

How do I introduce the first derivative of M when i<> k and aij when i <> j and aii in Maple?

Am trying to teach myself "circle inversion" to solve circle geometry problems.  Towards this end I wrote a Maple 7 program to draw a Pappus chain of circles.  Pappus lived around 200AD, and I read that he considered this problem ancient!  

   The output diagram may not come out on this forum, but it comes out as a collection of tangential circles, and I have no problems with that.  In drawing the circles I was thinking of using the infinity symbol.  The following line uses the infinity, but with a minus sign.  Maple is "happy" with this and outputs square braces, suggesting an empty list?  I changed the program by omitting the -ve sign - and Maple came up with an error message.  I would have expected the output to include the value zero  ie [0]  I think it is just that the infinity symbol is not allowed in the seq command. 

[seq( i, i=0..-infinity )];  #???  why the -?,

In the next part I define X, Y and rad as the coordinates and radii of a sequence of circles: subscript i, ranging from start to nterm, (for the number of terms).  These are set at 1 and 286.   The program works OK with these values, but if the variable start is changed to zero, 0, it doesn't work.  I thought I might have a division by zero, but can't find one.  I also drew a circle with a radius of zero - no problem!  (...except it's difficult to see:-))   

   My main puzzle is why does it come up with the error message "invalid subscript selector" when the variable start is set to 0?

With i=start=0 I am asking it to draw a circle of radius zero at some specified coords - but it doesn't like it!  

  Any comments would be appreciated.  Merry Christmas.

David

restart:

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

# Pappus Chain of circles

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

with(plots):

with(plottools):

#Maple 7

#r is ratio of AC/AB = diam of large circle, to a smaller internally tangential one

r:=1.35:

#Why will start=0 not work?

start:=1:

#nterm=286 is smallest value where axes have "true" origin of (0.0)

#nterm<= 285 puts "x-axis" below y=-0.6

nterm:=286:

X := [seq( 0.5*r*(1+r)/(((i*(1-r))^2)+r), i=start..nterm )]:

Y := [seq( i*r*(1-r)/(((i*(1-r))^2)+r), i=start..nterm )]:

rad:=[seq(0.5*r*(1-r)/((i*(1-r))^2+r), i=start..nterm)]:

[seq( i, i=0..-infinity )];  #???  why the -?

#Gives [] output with -ve sign:  empty list?  Why is 0 not included?

# Not allowed to use with seq

#ccc:=[seq(circle([X[i],Y[i]],rad[i]), i=1..5)]:  #nops(X))]:

ccc:=[seq(circle([X[i],Y[i]],rad[i]), i=start..nterm)]:

#c := circle([1,1], 0, color=red):

#plots[display](c, scaling=constrained);

plots[display](ccc, scaling=constrained);

OUTPUT

Hello

Long time asker of minimization problems here.

Following on from my question on 2D packing.

I found this "solved" problem for packing 3D items efficiently. See Illustration 6.13

https://www.researchgate.net/file.PostFileLoader.html?id=59938b635b49527571134c33&assetKey=AS%3A527790252490752%401502846410852

Some discrepancies with constraint set-up (first one), number of variables and the optimized solution.

3DbinPack2.mw

Hello

When I export a worksheet table as HTML,MATH EXPRESSIONS: GIF the resulting .html file is 100% readable.

screenshot:

But when i send the html file to myself over email, I get gibberish

The (acer) code for the top is... .....Equation(Standings[id]:-mu &+- Standings[id]:-sigma....

and below opponents rating: ....Cell(Equation(thetable[id][':-losses'][r][1] &+- thetable[id][':-losses'][r][2],......

Anyone shed?

Does any body have example of maple code for solving optimal control problem in deterministic model using Pontryagin's maximum (or minimum) principle?

Say I want to use multiples commands on an expression

simplify(expand(eval(expr,x=y+1)))

Now similar I could use

(simplify@expand)(expr)

but how do I do it with sth like eval which needs extra arguments

(simplify@expand@eval(x->y, x=y+1))(f)

??

t := 5;
                               5
u := exp((1/2)*x-2*t*(1/3));
                            /1     10\
                         exp|- x - --|
                            \2     3 /
plot(u(x), x = -4 .. 4);

this is the exact solution graph

while below is the approximate solution graph

h := -1;
                               -1
t := 5;
                               5
u := exp((1/2)*x)*(1+t*(27*h^4+108*h^3+240*h^2+256*h)/2^7+t^2*(27*h^4+24*h^3+168*h^2)/2^7+(1/3)*t^3*(9*h^4+16*h^3)/2^6+(1/4)*t^4*h^4/2^4);
                         6877    /1  \
                         ---- exp|- x|
                         192     \2  /
plot(u(x), x = -4 .. 4);

Please help me

Please, anyone with usefull informations to hint me. Looking forward to your favorable response. 

Thanking you in advance

Hello,

how could I force Maple to solve this pde

pdsolve(y*(diff(f(x, y, z, w), x))-x*(diff(f(x, y, z, w), y))+w*(diff(f(x, y, z, w), z))-z*(diff(f(x, y, z, w), w)) = 0)

When I hit enter, it happens nothing.

Below is MAPLE code to simplify a series.  MAPLE expresses the result in terms of functions which many people are not familiar with.  Is there a way to express the answer in terms of more conventional functions expecially if N is a positive integer?

Download simplify.mw

Request help in solving the equation:

Eq_H_1 := C[11*m]*(int((t-(j-1)*T)*alpha*(-alpha*(K*T*beta+T*beta*j-K*T-T*beta-T*j-beta*t+T+t))^(-beta/(beta-1))*exp(-R[m]*t), t = (j-1)*T .. (K+j-1)*T))

Thanks