## Sequence data from data file...

I'm trying to make a Least-Squares curve fitting plot.  I need to sequence two rows from a data file I imported (see attached worksheet GR10_20190130_PSA_TESTS.mw).  More specifically, I need to sequence the data in

X:=Row(T,1) with the data in y:=Row(T,2).  It should look like

([41115.0,6.97],[41257.0,18.9],[41270.0,15.67]...[43495.0,4.06]) when complete.  I tried seq[X_k,Y_k], that didn't work.  Also tried using an index of 1 to 25 (the number of elements in each row), that didn't work.  Any help with this appreciated, thanks in advance!

Les

## Animate some statistical concepts ?...

Hi

For educational needs; I try to animated some statistical concepts with simple statistical commands of Maple on 2018. The WorkSheet  in appendix, gives the desired animations, but with rather heavy procedures. Thanks for your help.

## Sorry, but it's a bug !...

Hi !
I made a program that solves a series of system of linear equations of increasing dimension.
Equations with rational numbers. I have a list of equations "liseq1" and a list of variables "lisvar1".
I use the following command :

solve(liseq1,lisvar1) ;

When the equation system reaches dimension 32, Maple gives me the following error message :

"Error, (in LinearAlgebra:-Modular:-IntegerLinearSolve) invalid arguments to iratrecon" .

It is an overdetermined system with 33 equations and 32 unknowns .
The variables are defined with the command:
x: = array (0..31) ;

I managed to work around the problem by replacing the variables with the following commands :

lissub: = seq (x[i] = x||i, i = 0..31) ;
lisvar2: = subs(lissub, lisvar1) ;
liseq2: = subs(lissub, liseq1) ;
solve (liseq2, lisvar2);

If you run the file I sent, Maple sometimes gives the desired answer but in a random way
because if you run the last 3 lines in a different order you will get the answer or the
error message .

Something remains in memory. Sorry, but it's a bug.
I have Windows 10, 64 bit with Maple 2018.2.
Regards .

## Problem using with(CodeGeneration)...

Hello,

I'm a long-time Maple user and have used the CodeGeneration package in the past, but with a recent download of Maple 2018, I'm now getting an error I have never gotten before. Even when I do something simple (see below, for example), I get an error that reads "Error, (in clear) argument  is incorrect or out of order". And I get this error no matter which language I choose. Any help would be much appreciated.

> with(CodeGeneration)

> R(exp(x))

Thanks!

## residue class ring, how do I define the ring F_q[x...

Hello,

I do know how to define the finite field F_q=GF(p,k). But know I am looking at the residue class ring R:= \F_q[x]/(f) with f an arbitrary polynomial in F_q[x]  of degree(f)>1. And I need all the calculations over R. My f will be reducible, so R wont be a field. Can anyone help me how I tell Maple to do the arithmetic in R? With the right remainder calculation? And with [f]=[0], so that the sesidue class of f is the same as the residue class of 0?

Thank you very much for any help!!

## return vs print, How do I reach the print outputs ...

Hello,

I would like to evaluate a funktion f in \F_q[x], where \F_q is a finite field with q=p^k. My algorithm is based on the fast multipoint evaluation algo in J. von zur Gathen/ J. Gerhard Modern Computer Algebra Edition 3. My proc FastEval does the right thing, but I dont know how to reach any of the calculatet values. And I will need all of the values for further procs! I tried it with lists, but (because of the recursive call??) I only get 1 value in the list... Does anyone know how to solve my problem? The return call only stops my proc after the first value has been calculated, that is why i used print.
This is my first question asked in mapleprimes.com, so please excuse any mistakes.. Also I dont know how to put the maple stuff in here correctly??

I would be really really happy if anyone can help me...
Kind regards from Germany
Melanie

\sourceon Maple
istZweierpotenz := proc (n::posint)  #checks if n=2^k for any k in N
local k, nTest;
k := 0; nTest := 1;
while nTest <= n do
if nTest = n then return true
else nTest := 2*nTest; k := k+1
end if
end do;
return false
end proc;

with(ListTools);

SubProdTree := proc (n::posint, u::(seq(anything)))
local k, j, i, M::(polynom(integer, x)), leftList, rightList, kList;
if istZweierpotenz(n) = true then k := log[2](n);
if nops([u]) = n then
for j to nops([u]) do M[0, j-1] := x-u[j]
end do;
for kList from 0 to k do leftList[0, kList] := [M[0, 2*kList]]; rightList[0, kList] := [M[0, 2*kList+1]]
end do;
for i to k do for j from 0 to 2^(k-i)-1 do M[i, j] := M[i-1, 2*j]*M[i-1, 2*j+1]
end do;
for kList from 0 to 2^(k-i-1)-1 do leftList[i, kList]
:= Flatten([[leftList[i-1, 2*kList]], [rightList[i-1, 2*kList]], M[i, 2*kList]]); rightList[i, kList]
:= Flatten([leftList[i-1, 2*kList+1], rightList[i-1, 2*kList+1], M[i, 2*kList+1]])
end do;
if i = k then kList := 0;
leftList[i, kList] := Flatten([[leftList[i-1, 2*kList]], [rightList[i-1, 2*kList]], M[i, 2*kList]])
end if
end do;
return leftList[k, 0]
else
return false
end if
else return false
end if
end proc;

GoDownTree := proc (f::polynom, n::posint, l::list, p::posint)
local func, prim, k, r0, r1, newLeftList, newRightList, numberPoint, newList;
func := f;
prim := p;
numberPoint := n;
k := log[2](numberPoint);
newList := l;
newLeftList := newList[1 .. numberPoint-1];
newRightList := newList[numberPoint .. 2*numberPoint-2];

if not isprime(prim) then return sprintf("%a ist nicht prim", prim)
end if;
if numberPoint < degree(func) then return false
end if;
if numberPoint = 1 then print(func)
else
r0 := evala(mod(Rem(func, newLeftList[-1], x), prim));
r1 := evala(mod(Rem(func, newRightList[-1], x), prim));
GoDownTree(r0, (1/2)*numberPoint, newLeftList, prim);
GoDownTree(r1, (1/2)*numberPoint, newRightList, prim)
end if
end proc;

FastEval := proc (f::polynom, n::posint, p::posint, u::(seq(anything))) local l;
l := SubProdTree(n, u);
GoDownTree(f, n, l, p)
end proc;

G := GF(11, 2);
a := G:-extension;
aOut := G:-ConvertOut(a);
alias(alpha = RootOf(aOut));
l := SubProdTree(8, 1, 2, 3, 4, 5, 6, 7, 8);
GoDownTree(x^2+x+1, 8, l, 11);

GF(11, 2)
/ 2          \
\T  + 6 T + 7/ mod 11
2
T  + 6 T + 7
alpha
[x - 1, x - 2, (x - 1) (x - 2), x - 3, x - 4, (x - 3) (x - 4),

(x - 1) (x - 2) (x - 3) (x - 4), x - 5, x - 6, (x - 5) (x - 6),

x - 7, x - 8, (x - 7) (x - 8), (x - 5) (x - 6) (x - 7) (x - 8),

(x - 1) (x - 2) (x - 3) (x - 4) (x - 5) (x - 6) (x - 7) (x - 8)

]
3
7
2
10
9
10
2
7
FastEval(x^2+x+1, 8, 11, 1, 2, 3, 4, 5, 6, 7, 8);
3
7
2
10
9
10
2
7
\sourceoff

## Using RAND to simulate coin toss...

Trying to simulate tossing 10 coins. What  am i doing rong? Thanks

 >
 >
 >
 (1)
 >
 >
 >
 (2)
 >

## Fix error missing operation...

restart;
solve({12 beta k^2 w alpha[2]+k alpha[2]^2, 56 beta k^2 m w alpha[2]+4 beta k^2 w alpha[1]-4 A k^2 alpha[2]+8 k m alpha[2]^2+2 k alpha[1] alpha[2]0, 104 beta k^2 m^2 w alpha[2]+16 K beta k^2 w alpha[2]+16 beta k^2 m w alpha[1]-20 A k^2 m alpha[2]+28 k m^2 alpha[2]^2-2 A k^2 alpha[1]+14 k m alpha[1] alpha[2]+2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2], 56 k alpha[2]^2 m^3+42 k alpha[1] alpha[2] m^2+6 m (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+96 w k^2 beta alpha[2] m^3+40 w k^2 beta alpha[2] K m-40 A k^2 alpha[2] m^2-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]+4 w k^2 beta alpha[1] K+4 (8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m+24 w k^2 beta alpha[1] m^2,70 k alpha[2]^2 m^4+70 k alpha[1] m^3 alpha[2]+15 m^2 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+5 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m+80 w k^2 beta alpha[2] K m^2-40 A k^2 alpha[2] m^3+44 w k^2 beta alpha[2] m^4+4 w k^2 beta alpha[2] K^2-2 A k^2 alpha[1] K+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]+16 w k^2 beta alpha[1] K m+6 (8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m^2+16 w k^2 beta alpha[1] m^3-4 w k^2 beta beta[1] m+2 A k^2 beta[1]+4 w k^2 beta beta[2],56 k alpha[2]^2 m^5+70 k alpha[1] alpha[2] m^4+20 m^3 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+10 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^2+80 w k^2 beta alpha[2] K m^3-20 A k^2 alpha[2] m^4+8 w k^2 beta alpha[2] m^5+4 (4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m+24 w k^2 beta alpha[1] K m^2+4 (8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m^3+4 w k^2 beta alpha[1] m^4+2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]-4 w k^2 beta beta[1] m^2+4 w k^2 beta beta[1] K+4 A k^2 beta[1] m-8 w k^2 beta beta[2] m+4 A k^2 beta[2],28 k alpha[2]^2 m^6+42 k alpha[1] alpha[2] m^5+15 m^4 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+10 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^3+40 w k^2 beta alpha[2] K m^4-4 A k^2 alpha[2] m^5+6 (4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m^2+16 w k^2 beta alpha[1] K m^3+(8 K beta k^2 w alpha[2]-2 A k^2 alpha[1]) m^4+3 (2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]) m-8 w k^2 beta beta[1] K m+2 A k^2 beta[1] m^2+2 A k^2 beta[1] K+2 k alpha[0] beta[2]+k beta[1]^2-2 w beta[2]+16 w k^2 beta beta[2] K+(8 K beta k^2 w beta[1]+4 A k^2 beta[2]) m,8 k alpha[2]^2 m^7+14 k alpha[1] alpha[2] m^6+6 m^5 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+5 (-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^4+8 w k^2 beta alpha[2] K m^5+4 (4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m^3+4 w k^2 beta alpha[1] K m^4+3 (2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]) m^2+2 (2 A K k^2 beta[1]+2 k alpha[0] beta[2]+k beta[1]^2-2 w beta[2]) m-4 w k^2 beta beta[1] K m^2+4 w k^2 beta beta[1] K^2-8 w k^2 beta beta[2] K m+4 A k^2 beta[2] K+2 k beta[1] beta[2],k m^8 alpha[2]^2+2 k m^7 alpha[1] alpha[2]+m^6 (2 k alpha[0] alpha[2]+k alpha[1]^2-2 w alpha[2])+(-4 A K k^2 alpha[2]+2 k alpha[0] alpha[1]+2 k alpha[2] beta[1]-2 w alpha[1]) m^5+(4 K^2 beta k^2 w alpha[2]-2 A K k^2 alpha[1]+k alpha[0]^2+2 k alpha[1] beta[1]+2 k alpha[2] beta[2]-2 w alpha[0]) m^4+(2 k alpha[0] beta[1]+2 k alpha[1] beta[2]-2 w beta[1]) m^3+(2 A K k^2 beta[1]+2 k alpha[0] beta[2]+k beta[1]^2-2 w beta[2]) m^2+(4 K^2 beta k^2 w beta[1]+4 A K k^2 beta[2]+2 k beta[1] beta[2]) m+12 w k^2 beta beta[2] K^2+k beta[2]^2},{k,w, alpha[0], alpha[1], beta[1], alpha[2], beta[2]});
Error, missing operation

## finding vector structures in trig expressions...

I get trig expressions which are long but contain structure,  The simplest example might be the following which is nothing but a.b where a and b are two unit vectors in polar coordinates.

cos(&theta;a)*cos(theta;b)+sin(&theta;a)*cos(&phi;a)*sin(theta;b)*cos(phi;b)
+sin(&theta;a)*sin(&phi;a)*sin(theta;b)*sin(phi;b)

Whereas the above is easy to identify, in general the structures are not evident.

Question 1  Is there a way to extract such vectors from long trig expressions? I am most interested in identifying inner, cross and outer products of unit vectors contained in these expressions.

Question 2 I would like to apply trig formulae, double angles etc, selectively.  That is apply the formula to only some of the quantities present, say only on the angles theta;a, and theta;b, but not on the phi's.  How is that done?

Thanks

## Random number generators and memory...

I tried three commands for uniform random distribution. The memory used by sequence created by Generate(distribution(Uniform(0, 1))) is very high. But this is the command which can bring randomness while doing metropolis algorithm. The other two commands consume very less memory but cannot bring randomness. I need the one which can inject randomness and at the same time uses less memory. Thank you.

DISTRIBUTION.mw

## How to get an nxn binary matrix with some limitati...

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

## fix the plot command...

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

## Workbook mode, variables...

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?

## How can I zoom into Julia Sets with Maple?...

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