this is the matlab is it possible to rewrite it in simple maple code

J = rand()+1e-10;

function [M, num, E] = ising(N,J)

B = 0;

M = []; % The total magnetic field of the system

E = []; % The total energy of the system

randTol = 0.1; % The tolerance, dampens the spin flip process

% First we generate a random initial configuration

spin = (-1).^(round(rand(N)));

% Then we let the system evolve for a fixed number of steps

for i=1:1000,

% Calculating the total spin of neighbouring cells

neighbours = circshift(spin, [ 0 1]) + ...

circshift(spin, [ 0 -1]) + ...

circshift(spin, [ 1 0]) + ...

circshift(spin, [-1 0]);

% Calculate the change in energy of flipping a spin

DeltaE = 2 * (J*(spin .* neighbours) + B*spin);

% Calculate the transition probabilities

p_trans = exp(-DeltaE);

% Decide which transitions will occur

transitions = (rand(N) < p_trans ).*(rand(N) < randTol) * -2 + 1;

% Perform the transitions

spin = spin .* transitions;

% Sum up our variables of interest

M = sum(sum(spin));

E = -sum(sum(DeltaE))/2; % Divide by two because of double counting

% Display the current state of the system (optional)

image((spin+1)*128);

xlabel(sprintf('J = %0.2f, M = %0.2f, E = %0.2f', J, M/N^2, E/N^2));

set(gca,'YTickLabel',[],'XTickLabel',[]);

axis square; colormap bone; drawnow;

end

% Count the number of clusters of 'spin up' states

[L, num] = bwlabel(spin == 1, 4);

############################# 

hi.please help me for remove error'' 

Error, illegal use of an object as a name''

thanks

PLATE.mw

Download PLATE.mw

Hi

Hope a nice day for all

restart;

#  *%   define the product of between two operators, and q real number
a*%b = q*b*%a+1;

# First I would like to give a simple for

 a^n*%b;
# and                                    
a*%b^n;

them deduce a general for                                      

b^n*%a^k*%b^N*%a^K-q^(k*N-n*K)*b^N*%a^K*%b^n*%a^k;

 where n, k and k greater than 1 and  n geater than k

Simplification.mw

Thanks for your help

How can i over come convergence error, i am unable to apply approxsoln appropriately and continouation as well. regards

Download ehtasham.mwehtasham.mw

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;

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;
and i wanna to know how to programmate a Gaus Hypegeometric function. Thank You

Hi

We know determinant of a square matrix A[ij] (i,j ∈ {1,2,3}) is equal to the following expression

det(A) = 1/6 * e[ijk] * e[pqr] * A[ip] * A[jq] * A[kr] 

in which e[ijk] is a third order Tensor (Permutation notation or Levi-Civita symbol) and has a simple form as follows:

e[mnr] = 1/2 * (m-n) * (n-r) * (r-m).

The (i,j) minor of A, denoted Mij, is the determinant of the (n − 1)×(n − 1) matrix that results from deleting row i and column j of A. The cofactor matrix of A is the n×n matrix C whose (i, j) entry is the (i, j) cofactor of A,

C[ij]= -1 ^i+j * M[ij]

A^-1=C^T/det(A)

The general form of Levi-Civita symbol is as bellow:

I want to write a program for finding inverse of (NxN) matrix:

N=2 →

restart;
N := 2:
with(LinearAlgebra):
f := (1/2)*(sum(sum(sum(sum((m-n)*(p-q)*A[m, p]*A[n, q], q = 1 .. 2), p = 1 .. 2), n = 1 .. 2), m = 1 .. 2)):
A := Matrix(N, N, proc (i, j) options operator, arrow; evalf((37*i^2+j^3)/(2*i+4*j)) end proc):
f/Determinant(A);

N=3 →

restart;
N := 3:
with(LinearAlgebra):
f := (1/24)*(sum(sum(sum(sum(sum(sum((m-n)*(n-r)*(r-m)*(p-q)*(q-z)*(z-p)*A[m, p]*A[n, q]*A[r, z], m = 1 .. N), n = 1 .. N), r = 1 .. N), p = 1 .. N), q = 1 .. N), z = 1 .. N)):
A := Matrix(N, N, proc (i, j) options operator, arrow; 10*i^2/(20*i+j) end proc):
f/Determinant(A);

The results of above programs are equal to 1 and validation of method is observed.

If we can write the general form of determinant then we can find the inverse of any square non-singular matrices.

Now I try to write the mentioned program.

restart;
with(linalg):
N := 7:
Digits := 40:
e := product(product(signum(a[j]-a[i]), j = i+1 .. N), i = 1 .. N):
ML := product(A[a[k], b[k]], k = 1 .. N):
s[0] := e*subs(`$`(a[q] = b[q], q = 1 .. N), e)*ML:
for i to N do
s[i] := sum(sum(s[i-1], a[i] = 1 .. N), b[i] = 1 .. N)
end do:
A := Matrix(N, N, proc (i, j) options operator, arrow; evalf((3*i+j)/(i+2*j)) end proc): # arbitrary matrix
CN:=simplify(s[N]/det(A));

Therefore det(A)= CN^-1 * e[a1,a2,..an] * e [b1,b2,.., bn] * A[a1,b1] * A[a2,b2] * ... * A[an,bn].

The correction coefficient is CN(for N)/CN(for N-1) = N!/(N-1)! =N.

restart:
with(linalg): N := 4: Digits := 20:
e := product(product(signum(a[j]-a[i]), j = i+1 .. N), i = 1 .. N):
ML := product(A[a[k], b[k]], k = 1 .. N):
s[0] := e*subs(`$`(a[q] = b[q], q = 1 .. N), e)*ML:
for r to N do s[r] := sum(sum(s[r-1], a[r] = 1 .. N), b[r] = 1 .. N) end do:
A := Matrix(N, N, proc (i, j) options operator, arrow; evalf((3*i+2*j)/(i+2*j)) end proc):
DET:=S[N]:
for x to N do for y to N do
e := product(product(signum(a[j]-a[i]), j = i+1 .. N-1), i = 1 .. N-1):
ML := product(AA[a[k], b[k]], k = 1 .. N-1):
S[0, x, y] := e*subs(`$`(a[q] = b[q], q = 1 .. N-1), e)*ML:
for r to N-1 do S[r, x, y] := sum(sum(S[r-1, x, y], a[r] = 1 .. N-1), b[r] = 1 .. N-1) end do:
f[y, x] := (-1)^(x+y)*subs(seq(seq(AA[t, u] = delrows(delcols(A, y .. y), x .. x)[t, u], t = 1 .. N-1), u = 1 .. N-1), S[N-1, x, y])
end do: end do:
Matrix(N, N, f)/(DET)*(24/6);
A^(-1);

CN for N=4 and N=3 is 24 and 6 respectively i.e. CN(4)/CN(3)=24/6.

When I use bellow procedure the error "(in S) bad index into Matrix" is occurred.

Please help me to write this algorithm by using procedure.

Thank you 

restart; with(linalg): Digits := 40: n := 7:
S := proc (N) local e, ML, s, i:
e := product(product(signum(a[j]-a[i]), j = i+1 .. N), i = 1 .. N):
ML := product(A[a[k], b[k]], k = 1 .. N):
s[0] := e*subs(`$`(a[q] = b[q], q = 1 .. N), e)*ML:
for i to N do s[i] := sum(sum(s[i-1], a[i] = 1 .. N), b[i] = 1 .. N) end do
end proc:
A := Matrix(n, n, proc (i, j) options operator, arrow; evalf((3*i+j)/(i+2*j)) end proc): # arbitrary matrix
CN := simplify(S(n)/det(A))

This is the coding till i do dhe decryption process. 

Do(plaintext=GetProperty("message",value));
Do(plaintext=convert(GetProperty("message",value),name));
Do(plaintextInt = convert(plaintext, bytes));
Do(plaintextBin = `~`[convert](plaintextInt, binary));
Do(plaintextBin2 = map2(nprintf, "%07d", plaintextBin));
Do(n0 = plaintextBin2[]);
Do(length1 = length(n0));
Do(plaintextCode = cat("", plaintextBin2[]));
Do(length2 = length(plaintextCode));
Do(z = convert(plaintextCode, decimal, binary));
Do(z1 = z+1);
Do(z2 = z1+%sk1);
Do(z3 = convert(z2, base, 2));
Do(b = cat("", z3[]));
Do(z4 = length(b));
Do(z5 = [Bits:-GetBits(-z2, -1 .. 0, bits = z4)]);
Do(z6 = cat("", z5[]));
Do(z7 = convert(z6, decimal, binary));
Do(%C = `mod`(Power(z7, %txte), %txtN));
Do(%C1 = `mod`(Power(%sk1, %txte), %txtN));

Do(%m = `mod`(Power(%C, %d), %N));

Do(%sk2=`mod`(Power(%C1,%d),%N));

Then nw i need to decrypt back to the original message with the coding:

Do(z8 = [Bits:-GetBits(-%m,-1 .. 0, bits = z4)]);
Do(c = cat("", z8[]));
Do(z9 = convert(c, decimal, binary));
Do(z10 = z9-sk2);
Do(z11 = z10-1);
Do(z12 = [Bits:-GetBits(z11, -1 .. 0, bits = length2)]);
Do(d = cat("", z12[]));
Do(plaintextBin2 = [StringTools:-LengthSplit(d, length1)]);
Do(plaintextInt2 = `~`[convert](plaintextBin2, decimal, binary));
Do(%message1 = convert(plaintextInt, bytes));

when i execute the program it shows the error

so how should I solve this as although i think that it should be problem of parsing the number z4 in the sentence that i highlighed, but whenever i correct it it still can't work.Thus anyone who know please help.Thanks.

I need to do Huffman Coding by using Document Tools thus i can produce user interface by using coding that referred in this post by Alec Mihailovs. Below is the coding and Document Tools interface:

Do(plaintext=GetProperty("message2",value));
Do(plaintext=convert(GetProperty("message2",value),name));
Do(Freq = proc (message) options operator, arrow; map(proc (x) options operator, arrow; rhs(x) = lhs(x) end proc, {StringTools:-CharacterFrequencies(message)}) end proc);
Do(Fr = Freq(plaintext));
Do(HuffmanTree = proc (message) options operator, arrow; if nops(message) <= 1 then rhs(message[]) else procname(`union`(message[3 .. -1], {lhs(message[1])+lhs(message[2]) = [rhs(message[1]), rhs(message[2])]})) end if end proc);
Do(HT = HuffmanTree(Fr));
Do(HuffmanCoding = proc (message, r := "") if message::string then message = r else procname(message[1], cat(r, 0)), procname(message[2], cat(r, 1)) end if end proc);
Do(HD = HuffmanCoding(HT));
Do(C = table([HD]));
Do(HC = cat(map(proc (x) options operator, arrow; C[x] end proc, StringTools:-Explode(message))[])

It still can get result for first part of the coding.During execute the second part of the coding(as bolded), it produces error ,the error show below.So how should I modified so that the error won't pop out @Alec Mihaivols

restart:with(plots):
eq:=(diff(f(eta),eta$2))-a*f(eta)+b*(1+diff(f(eta),eta)^2)^(-1/2)=0;
bc:=f(1)=0,D(f)(0)=0;
ans := dsolve(eq);

hi.how i can determind  eignvalue of matrix in the form parametric?

thanks1.mw

Download 1.mw

Hi everybody,

how about a little arithmetical challenge?

known quantities : Z, t, epsilon : reals

let W = X+Y*t    X, Y integers, t real (t with unlimited precision)

let W = Z + epsilon (epsilon < 1/W), Z real (Z with unlimited precision)

W and Z have same decimal expansion ( W - Integerpart[W], Z - IntegerPart[Z] ), up to a certain "rank" (determined by the precision : epsilon)

Y*t and Z have same decimal expansion, up to a certain "rank".

The problem : build an algorithm to find the integer Y, using the "usable" decimal expansion of Z.

Thanks in advance for your contributions!

how to convert system of differential equations to differential form for evalDG?

[a(t)*(diff(c(t), t))+b(t), a(t)*(diff(b(t), t))+c(t)*(diff(b(t), t)), a(t)*(diff(c(t), t))+a(t)*(diff(b(t), t))+b(t)];

when i try eliminate dt which is the denominator

eliminate([a(t)*dc(t) + b(t)*dt,a(t)*db(t)+dt*c(t)*db(t),a(t)*dc(t)+a(t)*db(t)+b(t)*dt],dt);

[{dt = -a(t)/c(t)}, {a(t)*(c(t)*dc(t)-b(t)), a(t)*(db(t)*c(t)+c(t)*dc(t)-b(t))}]

i got two solutions, which one is correct?

a(t)*(c(t)*dc(t)-b(t)), a(t)*(db(t)*c(t)+c(t)*dc(t)-b(t))

does it mean that two have to use together to form a differential form?

update1

with(DifferentialGeometry):
DGsetup([a,b,c], M);
X := evalDG({a*(c*D_c-b), a*(D_b*c+c*D_c-b(t))});
Flow(X,t);
Flow(X, t, ode = true);

got error when run with above result

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 need this equation solve by maple

eql := alap*[(la(a)^4+6*la(a)+1+alap*(la(a)^4-1)/difl1)*la(a)*j(a)-((la(a)^2+1)*(1+2/difl)+la(a)^2-1)*intdj/a^4+[(4*(la(a)^4-1))/difl-8*la(a)^2]*intdj/a^2]-(4*(la(a)^2+1))*intdj/a^4+(4*(la(a)^4-1))*intdj1/a^2 = 0;