how to calculate the shorting routing path in cayley graph?

i search that it is related with knuth bendix

In the following code, the evalf prints -32.16... 

restart; S := 8;

sigma := 8/sqrt(2*Pi);

iprec := 151;

evalf(log[2](-(sum(log(round(2^iprec*exp(-j^2/(2*sigma^2)))/2^iprec*exp(-j^2/(2*sigma^2))))*round(2^iprec*exp(-j^2/(2*sigma^2)))/2^iprec, j = 0 .. 7))));

Change the last line to evalf[20](log[2](....)), and re-run *just that line*. It now prints -66.67...

Change the last line to evalf[200](log[2](...)) and re-run *just that line* again. It now prints -151.24... (I have strong evidence to support that the true value is near -151, so I believe this answer.)

Now remove the precision indicator from the command completely and re-run just the last line. It *still* prints -151.24...!

My two questions are: why do I need evalf[200] to get the first three digits of the answer to be correct? and why does setting the evalf precision and then removing it cause the previous precision to persist?

hello everyone. I have an undergradute project i'm currently working on and I'm stuck where I have to use the Differential Transforms Method to solve a problem with boundary conditions at infinity

restart;

Digits := 5;

F[0] := 0; F[1] := 0; F[2] := (1/2)*A; T[0] := 1; T[1] := B; M := 2; S := 1;

for k from 0 to 10 do F[k+3] := (2*(sum((r+1)*F[r+1]*(k+1-r)*F[k+1-r], r = 0 .. k))-T[k]-3*(sum((k+1-r)*(k+2-r)*F[r]*F[k+2-r], r = 0 .. k))-M*(k+1)*F[k+1])*factorial(k)/factorial(k+3);

T[k+2] := (-3*(sum((k+1-r)*F[r]*T[k+1-r], r = 0 .. k))-S*T[k])*factorial(k)/factorial(k+2)

end do; f := 0; t := 0;

for k from 0 to 10 do

f := f+F[k]*x^k;

t := t+T[k]*x^k end do;

print(f);
print(t);

but the problem is that i cant seem to evaluate

or higer diagonal pade-approximant. any help will be greatly appreciated. thank you.

Please help, here is my code:

findproot:=proc(f,var,k)
local i,g,B,n,L,tk;

readlib(rootbound):readlib(realroot):
B:=rootbound(f,var);
g:=expand(subs(var=B*var,f));
if B<1 then g:=numer(g);fi;
n:=degree(g,var);
L:=zero_one(g,var,n,1/B/2^k);
tk:=k+1:
while has(L,0) do
L:=zero_one(g,var,n,1/B/2^tk);
tk:=tk+1:
od:
if L=[] then RETURN([]);fi;
L:=map(proc(x,y) [op(1,x)*y,op(2,x)*y];end,L,B);
end:

I dont know why i cant run this code, it always report: 

Error, (in findproot) improper op or subscript selector

Hello, i am recently doing a lot of my (really simple) equation manipulations with Maple and would like to include an expectation operator E( ) in my symbolic equations. As maple threads E() as a function, differentiating is not very convenient, as i have to replace all D(E) ... manually. I tried defining some properties of E() via the define() function, but when trying to set the behavior of d E(f(x))/dx I am not sure how to use (diff()=result) in the define() function. Any help or ideas are greatly appreciated!

How can I solve this equation 18 *9^(x^2 + 2* x) + 768* 4^((x + 3)* (x - 1)) - 5 *6 ^((x + 1)^2)?

I tried

restart:

A:=18 *9^(x^2 + 2* x) + 768* 4^((x + 3)* (x - 1)) - 5 *6 ^((x + 1)^2);
solve(A=0);

I see that, the equation has three solutions: x = -2, x = -1 and x = 0. I check

f:=x->18 *9^(x^2 + 2* x) + 768* 4^((x + 3)* (x - 1)) - 5 *6 ^((x + 1)^2);

f(-2);

f(-1);

f(0);

Another question, Maple can not solve inequality 

18 *9^(x^2 + 2* x) + 768* 4^((x + 3)* (x - 1)) - 5 *6 ^((x + 1)^2) > = 0.

PS. We can easy to solve the above inequality with Mathematica

Reduce[18 9^(x^2 + 2 x ) + 768 4^((x + 3) (x - 1)) - 5 6 ^((x + 1)^2) >= 0 , x, Reals]

I got x <= -2 || x == -1 || x >= 0

How to generate all basis of a set? (rather an the one basis that basis generates)

Hi all,

Please help in writing finite difference algorithm for a nonlinear PDE using Maple.

for a[j], b[j] known at time n, I want to compute A[j]  for a[j] at time n+1 according to the equation below

EQs:=A[j]-theta*tau*(A[j-1]-2*A[j]+A[j+1])=a[j]+sqrt(a[j])*b[j]*h^2/tau+(1-theta)*tau*(a[j-1]-2*a[j]+a[j+1]) ;

Thanks in advance.

Thanks.

hi guys , i have this warning for solving a complicated equation with 7 parameters. how can i overcome to this warning ?

Download sol.mw

thanks

Dear I want to define a general operator D for Fractional derivative whose behave like this

(D^alpha)(t^beta) = GAMMA(1+beta)*t^(beta-alpha)/GAMMA(1+beta-alpha)

How to generate an undirected graph with a given set of its verticies and a given list/set of the degrees of its verticies?

guys, i have this equation which a, n, c, phi[0] are parameters and r is variable. maple solved this equation with n=0,c=c,phi[0]=5/4-1/4 c but i obtained another solution for this equation : a = 1, c = 5, n = 1, phi[0] = 1 ( you can check). 

how can i get all solutions for a equation like this ?

Download eq000.mw

Hello,

Concerning the 3D visualization of my multibody systems, in the visualization windows, i can see both :
- the display of geomtry of the elements which has been defined as simple forms (as cylindrical geometry)
- the display of the geometry of the elements where the display of the geometry has been defined with CAD.

However, concerning the 3D animation, i have only see the components where the display of the geometry is defined as simple forms (as cylindrical geometry).

Have you some ideas why I can not see the elements which has been defined with CAD ?

For your information, the CAD geometries have been defined with STL files and, in the CAD geometry component, I let the box "Transparent" empty.

Thank you for your help

As I am beginner in maple, how to verify Bianchi Identities?

For Riemannian manifold,

1) R(X, Y)*Z+R(Y, Z)*X+R(Z, X)*Y = 0 

2) ((&nabla;)[X]R)(Y,Z)W+((&nabla;)[Y]R)(Z,X)W+((&nabla;)[Z]R)(X,Y)W=0

I am not getting how to define vector fields. From my previous question I understood defining vector fields particularly. From that post I tried to verify the proof, but I cant. Please tell me about how to define vector fields without taking examples.

Thank in advance.