How to use extern: the example of mwrank

The extern routine allows gp to call an arbitrary program, and feed its result to the interpreter. This mechanism passes arguments to the external program as character strings, and reads its output as if it had been typed directly into gp. It is powerful, and simpler than the tight integration provided by install, which is more appropriate for heavy-duty usage of low level routines.

Unfortunately, using extern involves a number of interface problems which will vary from one application to the next. In this page, we shall use John Cremona's mwrank package as a simple case study. Given an elliptic curve E over Q, mwrank returns the rank of the free part of the group of its rational points, and a set of points generating a subgroup of finite index in this group.

We assume henceforth that you have a working version of mwrank installed on your computer.

• write a wrapper GP script defining a gp routine mwrank calling the shellscript
• make sure the gp script is always loaded on startup

Wrapper gpscript

  mwrank(E)=
  {
    my(cmd=Str("echo '", E[1..5], "' | mwrank -q -o -v 0"));
    eval(externstr(cmd)[2]);
  }

This calls mwrank feeding the first 5 arguments of the elliptic curve structure (containing the Weierstrass model) and returns the second component of its output.

Put this file somewhere in your GP path. (See the path default in the manual.)

Loading mwrank on startup

    read "mwrank.gp"

This causes the mwrank.gp file to be read into gp upon startup, thereby defining mwrank() routine in all gp sessions!

Of course, the names of the file and function do not have to coincide. They were chosen as above for consistency and self-documentation: mwrank.gp tells about its content, whereas lib.gp or extra.gp would not.

    path = "$HOME/pari/gpscripts"

Testing

    ? mwrank([0,-1,1,-10,-20])
    %1 = [[0], []]

    ? mwrank([0,0,1,-1,0])
    %2 = [[1], [[0, 0]]]

    ? mwrank([1,0,0,0,1])
    %3 = [[2], [[1, 1], [3/4, 7/8]]]