@Carl Love 

Made me think for a while...

It satisfies Maple's requirements that the Matrix elements be 1...m, m=number of coprimes and the labels are the coprimes to n in 1..n-1

Thanks.

@dharr 

Thanks for helping me understand this.

@dharr 

I read the wiki article thinking or order rather than mod n.

sorry for the noise. I seem to do a lot of that lately.

I stumbled on this with the code below. I should have printed ord+1. If  I had done that,
I would not have the problem...

for idx from 1 to 40 do
Mmult := Matrix(idx,idx,(i,j)-> i*j mod (idx+1)):
try
  Gmult := CayleyTableGroup(Mmult):
  print("group of order ",idx+1," exists");
catch "invalid input":
  ##print("group of order ",idx," does not exist");
end try;
end do:

@dharr 

Gauss Theorem on the existence of cyclic groups of order n in the wiki article
Multiplicative_group_of_integers_modulo_n says:

"The group (Z/nZ)* is cyclic if and only if n is1, 2, 4, p^k or 2*p^k, where p is an odd prime
and k > 0. For all other values of n the group is not cyclic."

MultGroup12.mw

Maple says the group (Z/nZ)* of order 12 is Abelian and Cyclic.

Am I doing something wrong?

@dharr 

This is often the first example of a group:

v:={1,-1,I,-I};M:=Matrix(4,4,(i,j) -> v[i]*v[j] );

G := Group(M); ## invalid input
G := CayleyTableGroup(M); ## also invaid input

How do I create this group?

Thanks all.

I can create (Z/4Z)* two ways,

G:=SmallGroup(4,1);

-or-

G := Group(Matrix(4,4,[[1,2,3,4],[2,4,1,3],[3,1,4,2],[4,3,2,1]]))

These both produce (Z/4Z)*. I have not found how to for (Z/7Z)*

But, for (Z/4Z)+,

  G := Group(Matrix(4,4,[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]]))

produces an invalid input error.

@acer 

Sorry for my earlier omission.

I go back and forth with emacs and xmaple. I attempted to have a setup that would work for either.

Now that I know the problem, I can correct for it.

Thanks for the input.

@Thomas Dean 

I installed Windows 10 on an unused disk and installed Maple 2022.

The plot problem does not happen.

I have suspected the Java used under the Linux installation behaves differently than the windows 10 installation.

I see some strangeness in how things behave.

@Thomas Richard

I often use emacs or command line maple. I goto xmaple when I have some problem like this.

@Thomas Richard

Did you try toggling Dislay -> Plot Display? I can not imagine how this would effect hardware calculations.

Setting Digits to 20 does resolve the problem.

Maxima does not have a problem plotting this. Gnuplot does fine.

I believe acer uses windows. Correct?

I believe there is some disconnect, (in java?) that brings out some effects in the Linux platforms. I seem to have some strangeness...

I have a spare disk and access to windows. Maybe I will add a disk to my system and install Maple 2021 under windows to see if there are differences.

@acer 

What OS? What plot device? Has to some difference...but, what?

interface ->Dislay ->PlotDisplay is'inline'.  plotdevice is maplet and the plot appears in a popup maplet.

Changing inline to window and apply to session seems to fix the problem. Changing Plot Display back to inline makes the plot appear inline.

restart restored the incorrect behavior.

I have Ubuntu 20.04.

> interface(plotdevice)
                             maplet

> interface(version)
 Standard Worksheet Interface, Maple 2022.2, Linux, October 23  2022 Build ID 1657361

@Carl Love

Sorry for the noise.

This code does not work on my Maple 2022.

Please post a worksheet, using the green arrow at the upper right.

@segfault 

A simpler way will be to open each *.mw file with xmaple and then use:

  File -> Export As -> and select *.mpl (Maple Input) as the output file name.

I do this frequently and have never had a problem.

Ubuntu 20.04, over many versions of maple.

I mostly use maplev mode with emacs...