Let A=(a_{i,j}) be an nxn non-singular matrix over GF(2). Assume that we have a positive integer number s and an irreducible polynomial f of degree n over GF(2). 

My question: How to get nxn binary matrices such as A provided that the characteristic polynomial  of these matrices over GF(2) is f and also sum(a_{i,j}) is equal to s with 1<=i<=n and 1<=j<=n.

For example, consider n=8 and s=10 and f= x^8+x^7+x^5+x+1. Then I applied the following Maple code to generate the mentioned matrices. 

restart
with(LinearAlgebra):

randomize(); 
 roll := rand(1 .. 64);
 roll1 := rand(1 .. 8); 
 roll2 := rand(9 .. 16);
 roll3 := rand(17 .. 24);
 roll4 := rand(25 .. 32);
 roll5 := rand(33 .. 40);
 roll6 := rand(41 .. 48);
 roll7 := rand(49 .. 56); 
 roll8 := rand(57 .. 64);

u := 1; while u > 0 do 
L := [roll(), roll1(), roll2(), roll3(), roll4(), roll5(), roll6(), roll7(), roll8(), roll()];
if nops({L[]}) = 10 then
A := Matrix(8, 8, 0); s := 0;
for i to 8 do
for j to 8 do 
s := (i-1)*8+j; 
if evalb(`in`(s, L)) then A[i, j] := 1 end if
end do; end do;
if Determinant(A) <> 0 then
if evalb(`in`(sort(`mod`(Factor(CharacteristicPolynomial(A, x)), 2))[x^8+x^7+x^5+x+1]))
then print(A, sort(`mod`(Factor(CharacteristicPolynomial(A, x)), 2))); 
u := 0 end if; end if; 
unassign('A, s, i, j') 
end if; end do; 
unassign('u, i')

with my computer, it takes less than one minute to generate an 8x8 desired non-singular binary matrix as follows

  \left[
 \begin {array}{cccccccc}
 0&0&1&0&0&0&0&0\\
 0&1&1&0&0&0&0&0\\
 0&0&0&1&0&0&0&0\\
 0&1&0&0&0&0&1&0\\
 1&0&0&0&0&0&0&0\\
 0&0&0&0&1&0&0&0\\
 0&0&0&0&0&0&0&1\\
 0&0&0&0&0&1&0&0
 \end {array} 
 \right]

I wish I could find a systematic method to find these kind of matrices. 

Thanks for any suggestions 

restart;
l := -2;
                               -2
m := 1;
                               1
k := sqrt(-1/(6*beta))/l;
                                    (1/2)
                         1  /   6  \     
                       - -- |- ----|     
                         12 \  beta/     
w := (1/5)*alpha/(beta*l);
                              alpha 
                           - -------
                             10 beta
a[2] := -12*sqrt(-1/(6*beta))*alpha*m^2/(5*l*l);
                                 (1/2)      
                      1  /   6  \           
                    - -- |- ----|      alpha
                      10 \  beta/           
a[0] := 0;
                               0
a[1] := 0;
                               0
F := -l*C[1]/(m*(C[1]+cosh(l*(xi+xi[0]))-sinh(l*(xi+xi[0]))));
                             2 C[1]                      
       --------------------------------------------------
       C[1] + cosh(2 xi + 2 xi[0]) + sinh(2 xi + 2 xi[0])
beta := -2;
                               -2
alpha := 3;
                               3
C[1] := -1/1000;
                               -1 
                              ----
                              1000
xi[0] := 1;
                               1
xi := k*x-t*w;
                        1   (1/2)     3   
                      - -- 3      x - -- t
                        12            20  

u := a[0]+a[1]*F+a[2]*F*F;
   /   (1/2)\//        /   1  
 - \3 3     / |2500000 |- ----
              \        \  1000

          /1  (1/2)     3        /  1   (1/2)     3   \   \
    + cosh|- 3      x + -- t - 2 |- -- 3      x - -- t|[0]|
          \6            10       \  12            20  /   /

          /1  (1/2)     3        /  1   (1/2)     3   \   \\  \
    - sinh|- 3      x + -- t - 2 |- -- 3      x - -- t|[0]||^2|
          \6            10       \  12            20  /   //  /

plot3d(u, x = -3 .. 3, t = -3 .. 3);
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
 

I hope you can help me. I like to use the Workbook feature in Maple 2018. I save variables in one document to use them in another document as well. If, however, the value of the variable changes, I have to delete the variable in the variable manager each time and save it again.
Is there a command I can use to delete and re-save the saved variables?

I've been trying to make Julia sets using maple for a project im working on, but the maple help function tells me to embed the image, which does not give me the Plot options or the option to zoom in for a more detailed view.  I have tried using several different image tools, and the only one that seems to output it as a plot is Preview, but then when i zoom in it is in terrible detail and is very pixelated.  I think i just need to use a different output than Embed, but i can't find one that will work, can anyone help please?

Here is the code i've been using:

> with(Fractals:-EscapeTime);

> with(ImageTools);

> bl, ur, c := -2.0-1.5*I, 2.0+1.5*I, -.92+.25*I;

> M := Julia(500, bl, ur, c);

> Embed(M);
 

Thanks

For example, A with a B weighting?

Thanks

QuestionHistogramme.mw

I have written a procedure in which the content is written as either for loop or add commands. Since this procedure need to be evaluated around 1-1.5 lakhs times during iteration (running an iterative method) I need to know which of the two procedure will consume less memory. The whole calculation takes 4 gb. So i am trying to optimize the code. Thank you.

procedure_new.mw

Hey,

I have just started using Maple for my university project and I am follwing this guide https://www.maplesoft.com/support/help/maple/view.aspx?path=DifferentialGeometry%2FTensor%2FKillingVectors to calculate Killing Vectors. My issue is that when I try and define a metric using evalDG, I need to write dx&tdx to mean the tensor product between the two. Maple interperates this as a neutral operator and gives me "Error, invalid neutral operator".

I am not sure where the issue is as I have written exactly the same code as the guide and yet it gives me an error 3 lines in. Is there some issue that I am not aware of as someone who hasn't used Maple before? Any advice would be useful as I am not really sure how it is possible and I need to be able to write the tensor product to define the metric. 

Even for the simplest metric it does not work. My code is:

with(DifferentialGeometry): with(Tensor): with(LieAlgebras):
DGsetup([x, y], M):
g1:=evalDG( dx&tdx):
 

Any help would be greatly appreciated.

Suppose that A is an nxn matrix over the finite field Z:=GF(2,q) for some q. I wan to get the smitform of A over Z. First I used the package  

with(LinearAlgebra[Generic]) 

and after that I applied the command 

S := SmithForm[Z](A)

but the mentioned command made some errors. In fact, I do not how to define commands igcdex, iquo, irem, sign and abs for SmithForm over finite fields.

Thanks for any suggestions 

how I can find solutions for non linear equations.

I want to find non zero solution.

thank you

ZAH.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/ZAH.mw .
 

Download ZAH.mw

I get this problem in a paper published in 2011. there is a table which compares the solution of a differential equation and gives the range of initial guesses. I got confused when saw maple and approximated maple, please any help me 

I'm attaching the link of paper. Please have a look at table 3. 

https://www.sciencedirect.com/science/article/pii/S0098135411000056

Hi, Maple is totally new to me and I found something confusing.

Here is what I have:

And it shows Error, invalid input: unknown uses a 1st argument, A (of type Array(numeric)), which is missing.

But in another similar procedure, I have exactly the same lines but it goes without error. 

I have no idea what is wrong with these 4 lines.

Thank you in advance!

If I add "restart" to a program, then interface(imaginaryunit=j) don't work. Why? 

***********************************
restart;
interface(imaginaryunit = j);
j^2;
************************************
The output is j^2  but the output should be -1. 

 

Dear all,
How can I input different spacesteps in numerical solution of PDE (Heat equation) with pdsolve of Maple?

For example, the x range is x=0..L,
and I'd like to solve the PDE with spacestep1=L/100 for x=0..a and spacestep2=L/10 for x=a..L.

Thank you in advance!

Hi,

How to generate the whole table of quantiles for a normal reduced centered N(0,1)?

restart;
Chargement Statistics
X := RandomVariable(Normal(0, 1));
                            X := _R
Statistics[Quantile](X, 0.1e-1);
                       -2.32634787404074

Download Tensors_-_A_Complete_Guide.mw, or the pdf version with sections open: Tensors_-_A_Complete_Guide.pdf

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft