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 moderately complicated 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 shellscript that calls the actual program (here mwrank)
• write a wrapper GP script defining a gp routine ellrank calling the shellscript
• make sure the gp script is always loaded on startup

Wrapper shellscript

    #!/bin/sh

    res=`echo "$1 0 0 0 0 0" | mwrank -q -v 0 -o | grep '^\['`
    if test -z "$res"; then
      echo 'error("An error occured in mwrank")'
    else
      echo "$res"
    fi

This passes on its arguments to mwrank (in non-interactive mode, mwrank expects five 0 in a row to signal that input is over), and stores in the variable res the lines beginning with [. In fact, there will be a single such line: mwrank's result. If res is non-empty, mwrank produced a result and we output it.

Otherwise an error occured, and we act accordingly: remember that the output of this file will be read by gp's interpreter, so we do not trigger an error here, we print a command that will trigger it when read by gp.

Make sure this script is executable (chmod 755 gpmwrank), then put it somewhere in your PATH. (This is a list of directories where your shell looks for executable files.)

Wrapper gpscript

    ellrank(e) =
    { my(l = length(e));
      if (type(e) != "t_VEC" || (l != 5 && l != 13 && l != 19),
        error("incorrect type in ellrank")
      );
      extern( Str("gpmwrank ["e[1]","e[2]","e[3]","e[4]","e[5]"]") )
    }

This does some rudimentary error checking then calls gpmwrank and returns its output.

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

Loading ellrank on startup

    read "ellrank.gp"

This causes the ellrank.gp file to be read into gp upon startup, thereby defining ellrank() 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: ellrank.gp tells about its content, whereas lib.gp or extra.gp would not.

    path = "$HOME/pari/gpscripts"

Testing

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

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

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