ApCoCoA-1:HowTo:Run ApCoCoA on a Computing Server

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Introduction

This HowTo shows you how to run ApCoCoA on a Linux server with terminal.


Prerequisites

  • Download ApCoCoA QT and unzip the file. (This HowTo takes ApCoCoA 1.9.0 as an example.)
wget http://www.apcocoa.org/download/apcocoa/linux-x86_64/apcocoa-1.9.0-QT-linux-x86_64.tgz
tar xzvf apcocoa-1.9.0-QT-linux-x86_64.tgz


Run ApCoCoA

Go to the folder ApCoCoA-1.9.0. The contents in the folder are as follows.

ApCoCoA files.jpg

In the following, assume that you are working at the directory ApCoCoA-1.9.0/.


ApCoCoA with Text Interface

Run the following command at terminal to start the ApCoCoA text interface.

./apcocoa_text

ApCoCoA text.jpg

You can run any (Ap)CoCoA command in this interface.

ApCoCoA text1.jpg


ApCoCoAServer

In many cases you also need to run the ApCoCoAServer. Here, assume that you have some terminal tools, like "screen", "tmux", etc., to create new terminal sessions, and that you are able to switch between terminal sessions without having to stop the running program.

Create a new terminal session for the ApCoCoAServer and run the following command to start the ApCoCoAServer.

./ApCoCoAServer

ApCoCoA Server0.jpg

Observe that the ApCoCoAServer is running on the default port 49344 (0xc0c0). One can change the port number to n by using option -p as follows.

./ApCoCoAServer -p n

Now let us switch to the terminal session for the ApCoCoA text interface again. Execute the following commands.

X:="xy";
M:=["xxx","yxy","xyx"];
NCo.IsFinite(X, M); -- Check whether <x,y>/<x^3,yxy,xyx> is finite

The function NCo.IsFinite uses the ApCoCoAServer. You will get the following result in the ApCoCoA text interface.

ApCoCoA text2.jpg

And you can see the following message in the terminal session for the ApCoCoAServer.

ApCoCoA Server1.jpg


ApCoCoA Program Files

Sometimes it is useful to write commands or functions in ApCoCoA program files.

For example, the following function computes Fibonacci numbers. Assume that we write the function in a ApCoCoA program file, say test.coc, in the directory ApCoCoA-1.9.0/.

Define Fib(N)
  If N<=1 Then
    Return 0;
  Elif N=2 Then
    Return 1;
  Else
    Return Fib(N-2)+Fib(N-1);
  EndIf;
EndDefine;

Using the following command, ApCoCoA process

Then we can process the file as batch files and then ask ApCoCoA to process them when it starts.

For example, we have a presentation for SL(3,8) as follows. and we wa put the following commands in a file named SL_3_8.coc.

/* SL(3,8) has a presentation with generators a, b, c, d, e and the following relators
    a^2, b^2, c^7, de, ed,
    (cb)^2,
    (ba)^3,
    (acac^6)^2,
    c^2ac^6ac^5ac,
    dbe^2, 
    (ce)^2cd^2
    aead(ae)^2babd^2,
    eadae^2babd^2(ae)^2babd^2,
    ec^6daecdc^6aca,
    ec^6daecec^6d^2ae^2cd^2,
    ec^6daecec^6d^2ae^2cd^2.
    The following commands check whether the last relator, i.e. ec^6daecec^6d^2ae^2cd^2
    can be rewritten by the others, via Groebner basis techniques.
*/
Use ZZ/(2)[a,b,c,d,e];
G:=[[[a^2], [1]],
    [[b^2], [1]], 
    [[c^7], [1]],
    [[d, e], [1]],
    [[e, d], [1]],
    [[c, b, c, b], [1]],
    [[b, a, b, a, b, a], [1]],
    [[a, c, a, c^6, a, c, a, c^6], [1]],
    [[c^2, a, c^6, a, c^5, a, c], [1]],
    [[b, d, b, e^2], [1]], 
    [[c, e, c, e, c, d^2], [1]],
    [[a, e, a, d, a, e, a, e, b, a, b, d^2], [1]],
    [[e, a, d, a, e^2, b, a, b, d^2, a, e, a, e, b, a, b, d^2], [1]],
    [[e, c^6, d, a, e, c, d, c^6, a, c, a], [1]]];
F:=[ [e,c^6, d, a, e, c, e, c^6, d^2, a, e^2, c, d^2] ];
Gb:=NC.GB(G,31,1,100,5000);
NC.NR(F,Gb);