## 1500 Reputation

19 years, 104 days

## Thank You....

@jm@france-paris.org I am not trying to use goto. I never use it. I dug it up for a way to test the STOP button. Often I lose sessions because STOP button does not accomplish.

## Maple 2017....

@C_R My Maple 2017 does not stop when I use the stop button repeatedly. That is why I ask. Perhaps there is config options to consider.

## Thank You....

@Carl Love I wrote this in Maple 5.4. There is only ilog10 in it.

## ilog[2]...

@May You can replace ilog[2](n) with a recursive procedure L2:

L2:=proc(n) if n=1 then 0 elif n>1 then 1+procname(iquo(n,2)) else 'procname(args)' fi end;

OR You can replace 2^ilog[2](n) with L2P:

L2P:=proc(n) if n=1 then 1 elif n>1 then 2*procname(iquo(n,2)) else 'procname(args)' fi end;

then

J:=(n->(2*(n-L2P(n))+1));

Mission accomplished.

## Thank You....

@Rouben Rostamian  At last a clear presentation.

## What is the problem here?...

@smithss Looking at your original image:

C:=black, red, yellow, pink, brown, purple, blue, green, orange;
L:=[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]], [[1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], [[1, 3], [4, 3], [5, 3], [7, 3], [1, 4], [4, 4], [5, 4], [7, 4]], [[2, 3], [3, 3], [6, 3], [2, 4], [3, 4], [6, 4]], [[1, 5], [3, 5], [5, 5], [7, 5], [1, 6], [3, 6], [5, 6], [7, 6]], [[2, 5], [4, 5], [6, 5], [2, 6], [4, 6], [6, 6]], [[1, 7], [2, 7], [7, 7], [1, 8], [2, 8], [7, 8], [1, 9], [2, 9], [7, 9]], [[3, 7], [5, 7], [3, 8], [5, 8], [3, 9], [5, 9]], [[4, 7], [6, 7], [4, 8], [6, 8], [4, 9], [6, 9]];

plots[display](seq(seq(plots[textplot]([[op(i),op(j, [C])]],color=op(j,[C])),i=op(j,[L])),j=1..nops([C])));

Is there a problem here?

I suspect you want to permute points in each vertical line, so each horizontal line does not have the same color twice.

## Lookup ?combinat[randperm]...

@smithss What you describe is a permutation of colors on lines x=1, x=2, ... Collect all the colors on the line into a list and use combinat[randperm] or combinat[permute], whichever you prefer.

## Typo....

@Rouben Rostamian  You meant:

return  z((-x+sqrt(3)*y)/2,(-sqrt(3)*x-y)/2);

## Gfun....

@Carl Love I used gfun. Nice form, thank you.

[(1/2*I*(1+3*X(0)+2*Y(0))+1/2*X(0)+1/2)/GAMMA(k+1)*(-I)^k+(-1/2*I*(1+3*X(0)+2*Y(0))+1/2*X(0)+1/2)/GAMMA(k+1)*I^k-1/GAMMA(k+1), (1/2*I*(-2-5*X(0)-3*Y(0))+1/2*Y(0)-1/2)/GAMMA(k+1)*(-I)^k+(-1/2*I*(-2-5*X(0)-3*Y(0))+1/2*Y(0)-1/2)/GAMMA(k+1)*I^k+1/GAMMA(k+1)]

## Also......

General solution is:

G:=[proc (n) options operator, arrow; (((-9/2+9/2*(-1)^n)*RootOf(_Z^2+1)+3/2*(-1)^n+3/2)*RootOf(_Z^2+1)^n-1)/GAMMA(n+1) end, proc (n) options operator, arrow; ((15/2-15/2*(-1)^n)*RootOf(_Z^2+1)*RootOf(_Z^2+1)^n+1)/GAMMA(n+1) end];
map(evala@G, [\$0..10]);

@Carl Love Which Maple versions support this form?

## Simplier....

@C_R Here is a formula slightly better than the other:

plot((2^(1/2)*EllipticF((1-1/(sin(x0)+1))^(1/2)*2^(1/2),1/2*2^(1/2)*(sin(x0)+1)^(1/2))), x0 = 0 .. Pi/2, view = [0 .. Pi/2, 0 .. 10]);
this is:
Int(1/sqrt(sin(x0)-sin(x)),x=0..x0) = 2^(1/2)*EllipticF((1-1/(sin(x0)+1))^(1/2)*2^(1/2),1/2*2^(1/2)*(sin(x0)+1)^(1/2));

## References....

@Axel Vogt Thank You. That sounds promising. Would this be a textbook reference?

## Symmetric polynomials....

@Carl Love I was working with Groebner Basis and the result suggested symmetric polynomials as basis. To my surprise I found cyclic polynomials among them and also the fact that Maple has no refrences for these two classes of polynomials (is this correct?)

Anyhow. The case is 3 variable case and so I find cyclic polynomials can be reduced to a linear combination of cyclic polynomials of the form x^n*y+y^n*z+z^n*x, coefficients in symmetric polynomials.

## Symmetric polynomials....

@vv I meant algebraic relationships akin to those of symmetric polynomials. I take it matrix operations are unavoidable.

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