@Thomas Richard 

ok I understand. I have made a price request for MapleNet.

Thanks for support

The price for MapleNet Licence bigins at 6000€.

This is too much for me. I am private.

@Thomas Richard 

I explain what my plan is:

The maple code (1 year of work) is producing colered plots. If you click a button randomly 2 coprime integers are choosen which produce a (almost squared) plot of colored polygons.

Herre is an example plot:

Parallel I am building a website and now I want to give the website visitor the possibility to click on a button at a page of my website and then every new click a new polygonplot is shown at that page.

I think the CodeGeneration Tool of Maple is not the solution for that because there are lot of precedures und subprocedures. I am also using several packages:

with(ArrayTools);
with(plots);
with(NumberTheory);
with(ArrayTools);
with(ColorTools);
with(RandomTools[MersenneTwister]);
with(DocumentTools):

Maybe the  commandline option of maple is a possibility.

I have tried Maple Player which works but I recognized that is slower than the Maple Development Tool.

So an Idea is to upload the whole Maple system in the webspace of my domain and let it run there ?!

@Carl Love 

This is test interesting for me.

For understanding your speed test I have tried to copy the code from the grey box but get this message:

iremFrac2a:=proc(n,d, b)     local r1,r,i,li:     li:=NULL:     r:= irem(n*b,d):     if NumberTheory:-AreCoprime(d,b) then       while true do          r1:= irem(b*r,d):          li:=li,[[r,r],[r,r1]],[[r,r1],[r1,r1]]:          if r1=n then break fi:          r:=r1:       end do:     else print("Denom-Base not coprime "): return [] fi:     [li]  end proc  :     iremFrac2b:= proc(n, d, b) local N:= irem(n,d), r:= irem(N*b, d), s;       [if igcd(b,d) = 1 then           (do [[r,r], [r, (s:= irem(b*r, d))]], [[r,s], [s,s]] until (r:= s)=N)      else          print("Denom-Base not coprime")      fi]  end proc  :  d:= nextprime(2^17):  b:= irem(rand(), d);
Error, invalid sequence

We have this problem earlier. When you send me the *.mw file it was  running.

@acer 

Ok I can do that.

Please send me the text of the Question which I wrote this morning, which you have deleted. So I don't have to write it again.

@acer 

It's not a duplicate because the first question was not exact.

In my new question I have describd more exact what I mean.

@Carl Love 

ok now I understand :)

I have measured the speed:

d:=34656
                           d := 34656

b:=3133
                           b := 3133

NULL;
st := time();
iremFrac2(1, d, b);
time() - st;
                               0.

st := time():
iremFrac2old(1, d, b):    # verion with for loop
time() - st;
                               0.

In my program I am using periods < 50 (MultiplicativeOrder(b,d)) and in this case there is not a big gain in speed.

But thank you anyhow, I am learning.

There is another proc wich is to slow somtimes. I will ask this question later.

@Thomas Richard 

This is a good hint :)

I will read this FAQ

@Carl Love 

Thanks for aditional information.

Here you can see how the data (R) is generated.

with other numbers (n,d,b) modlog gives an error.

I think this member-command is a good solution for finding the maximal element in R.

Or do I have to modify somthing in ModularLog(-1, b, d); to have correct result ?

d := 49136;
                           d := 49136

b := 38013;
                           b := 38013

remainders := proc(n, d, b) local r1, r, i, s; r := n; s := NULL; s := 1; for i to d - 1 do r1 := irem(b*r, d); if r1 = n then break; end if; s := s, r1; r := r1; end do; [s]; end proc:

R := remainders(1, d, b);
 R := [1, 38013, 45817, 16101, 9297, 20749, 665, 22741, 3985, 

   44653, 40505, 40005]


maxi:=max(R)
                         maxi := 45817

max[index](R) - 1;
                               2

member(maxi, R, 'p');
p - 1;
                               2

MultiplicativeOrder(b, d)/2;
                               6



ModularLog(-1, b, d);
Error, (in NumberTheory:-ModularLog) no solutions exist

@Thomas Richard 

I have found this for Mac in Preferences, Thanks.

But my question was wrong.

In Maple 2021 I have used 2D-Input with the text-style of Maple-Input (1D) and now want to have the Maple-Input text-Style in the 2D-input worksheet.

@Carl Love 

Thanks both answers.

This is very helpfull for me :)

@acer 

ok,

thanks for reminding me of the your link.

I confess I haven't look there but will do now :)

The ArgPlot()-procedure is very helpfull and produces beautyfull plots.

I like this plot of the Beta-function very much !

I little bit slow in higher resolutions but it does what I was looking for :)

@Carl Love 

Thanks for both answers :)

I have tried to get a plot in a higher resolution with densityplot (without sawtooths when zooming) but didn't fin a way.

The code above gives the plot which I have found here

https://www.ams.org/journals/notices/201106/rtx110600768p.pdf

With other functions for example f(z):=1/(1-z) in the pdf on page 775 it doesnt work. I have tried with 1/(1-z+I y) but this gives another plot than in figure 17 in the pdf.

I am lookinng for a method (or Maple-procedure) to input a complex function and then receive  this phase-plots.

@dharr 

Thanks a lot for all your help :)

@2cUniverse 

Adding a white frame with PadImage for higher resolutions is much too slow for may app.

So I used the method like you did with white rectenagle. I have modified this with PolygonPlot because I dont want to have the black line around the white space.

The only thing wich is not working is to stored the plot as tiff. See attached mw.

NULL;
plottools:-exportplot(cat(dir1, "test1.tiff"), plt);
Warning, unknown plot device
Error, (in plottools:-exportplot) could not write /Users/arno/desktop/whitewall/pb-App Files/tiff/test1.tiff with legacy /Users/arno/desktop/whitewall/pb-App Files/tiff/test1.tiff exporter