NAME
    Math::ematica - Perl extension for connecting Mathematica(TM)

SYNOPSIS
      use Math::ematica qw(:PACKET :TYPE :FUNC);

WARNING
    This is alpha software. User visible changes can happen any time.

    The module is completely rewritten. Literally no line of the old stuff
    is used (don't ask - I've learned a few things since these days ;-). If
    you are using the old 1.006 version, note that the interface has
    changed. If there is an overwhelming outcry, I will provide some
    backward compatibility stuff.

    Feel free to suggest modifications and/or extensions. I don not use
    Mathematica for real work right now and may fail to foresee the most
    urgent needs. Even if you think that the interface is great, you are
    invited to complete the documentation (and fix grammos and typos). Since
    I am no native English speaker, I will delay the writing of real
    documentation until the API has stabilized.

    I developed this module using Mathematica 3.0.1 on a Linux 2.0.30 box. I
    verified that it still works with Mathematica 4.0 for Solaris. Let me
    know, if it does work with other versions of Mathematica or does not
    work on other *nix flavors.

DESCRIPTION
    The `Math::ematica' module provides an interface to the MathLink(TM)
    library. Functions are not exported and should be called as methods.
    Therefore the Perl names have the 'ML' prefix stripped. Since Perl can
    handle multiple return values, methods fetching elements from the link
    return the values instead of passing results in reference parameters.

    The representation of the data passed between Perl and Mathematica is
    straight forward exept the symbols which are represented as blessed
    scalars in Perl.

Exported constants
    PACKET
         The `PACKET' tag identifies constants used as packet types.

           print "Got result packet" if $link->NextPacket == RETURNPKT;

    TYPE The `TYPE' tag identifies constants used as elements types.

           print "Got a symbol" if $link->GetNext == MLTKSYM;

Exported functions
    FUNC The `FUNC' tag currently only contains the `symbol' function which
         returns the symbol for a given name.

           $sym = symbol 'Sin';

The plain interface
    This set of methods gives you direct access to the MathLink function.
    Don't despair if you don't know them too much. There is a convenient
    layer ontop of them ;-). Methods below are only commented if they do
    behave different than the corresponding C functions. Look in your
    MathLink manual for details.

  `new'

    The constructor is just a wrapper around `MLOpenArgv'.

      $ml = new Math::ematica '-linklaunch', '-linkname', 'math -mathlink';

    The link is automatically activated on creation and will be closed upon
    destruction.

  `ErrorMessage'

      print $link->ErrorMessage;

  `EndPacket'

  `Flush'

  `NewPacket'

  `NextPacket'

  `Ready'

  `PutSymbol'

  `PutString'

  `PutInteger'

  `PutDouble'

  `PutFunction'

  `GetNext'

  `GetInteger'

  `GetDouble'

  `GetString'

    The method does the appropriate `MLDisownString' call for you.

  `GetSymbol'

    The module does the appropriate `MLDisownSymbol' call for you. It also
    blesses the result string into the package `Math::ematica::symbol'.

  `Function'

    Returns the function name and argument count in list context. In scalar
    contex only the function name is returned.

  `GetRealList'

    Returns the array of reals.

The convenience interface
  `PutToken'

    Puts a single token according to the passed data type.

      $link->PutToken(1);               # MLPutInteger

    Symbols are translated to `MLPutFunction' if the arity is provided as
    aditional parameter.

      $link->PutToken(symbol 'Pi');     # MLPutSymbol
      $link->PutToken(symbol 'Sin', 1); # MLPutFunction

  `read_packet'

    Reads the current packet and returns it as nested data structure. The
    implementaion is not complete. But any packet made up of `MLTKREAL',
    `MLTKINT', `MLTKSTR', `MLTKSYM', and `MLTKFUNC' should translate
    correctely. A function symbol `List' is dropped automatically. So the
    Mathematica expression `List[1,2,3]' translates to the Perl expression
    `[1,2,3]'.

    *Mabybe this is *too* convenient?*.

  `call'

    Call is the main convenience interface. You will be able to do most if
    not all using this call.

    Note that the syntax is nearly the same as you are used to as *FullForm*
    in Mathematica. Only the function names are moved inside the brackets
    and separated with ',' from the arguments. The method returns the nested
    data structures read by `read_packet'.

      $link->call([symbol 'Sin', 3.14159265358979/2]); # returns something near 1

    To get a table of values use:

      $link->call([symbol 'Table',
                   [symbol 'Sin', symbol 'x'],
                   [symbol 'List', symbol 'x',  0, 1, 0.1]]);

    This returns a reference to an array of doubles.

    You may omit the first `symbol'. *Maybe we should choose the default
    mapping to *Symbol* an require *Strings*s to be marked?*

  `install'

    If you find this too ugly, you may `install' Mathematica functions as
    Perl functions using the `install' method.

      $link->install('Sin',1);
      $link->install('Pi');
      $link->install('N',1);
      $link->install('Divide',2);

      Sin(Divide(Pi(),2.0)) # should return 1 (on machines which can
                            # represent '2.0' *exactely* in a double ;-)

    The `install' method takes the name of the mathematica function, the
    number of arguments and optional the name of the Perl function as
    argument.

      $link->install('Sin',1,'sin_by_mathematica');

    Make shure that you do not call any *installed* function after the
    `$link' has gone. Wild things will happen!

  `send_packet'

    Is the sending part of `call'. It translates the expressions passed to a
    Mathematica package and puts it on the link.

  `register'

    This method allows to register your Perl functions to Mathematica.
    *Registered* functions may be called during calculations.

      sub addtwo {
        $_[0]+$_[1];
      }

      $link->register('AddTwo', \&addtwo, 'Integer', 'Integer');
      $link->call([symbol 'AddTwo',12, 3]) # returns 15

    You may register functions with unspecified argument types using undef:

      sub do_print {
        print @_;
      }
      $link->register('DoPrint', undef);
      $link->call(['DoPrint',12]);
      $link->call(['DoPrint',"Hello"]);

  `main'

    This method allows to have Perl scripts installed in a running
    Mathematica session. The Perl script try.pl might look like this:

      use Math::ematica;
      sub addtwo {
        my ($x, $y) = @_;
  
        $x + $y;
      }
      $ml->register('AddTwo', \&addtwo, 'Integer', 'Integer');
      $ml->main;
  
    Inside the Mathematica do:

      Install["try.pl"]
      AddTwo[3,5];

    Admittedly, adding two numbers would be easier inside Mathematica. But
    how about DNS lookups or SQL Databases?

AUTHOR
    Ulrich Pfeifer <pfeifer@wait.de>

SEE ALSO
    See also the perl(1) manpage and your Mathematica and MathLink
    documentation. Also check the t/*.t files in the distribution.

ACKNOWLEDGEMENTS
    I wish to thank Jon Orwant of *The Perl Journal*, Nancy Blachman from
    *The Mathematica Journal* and Brett H. Barnhart from *Wolfram Research*

    Jon brought the earlier versions of this module to the attention of
    Nancy Blachman. She in turn did contact Brett H. Barnhart who was so
    kind to provide a trial license which made this work possible.

    So subscribe to *The Perl Journal* and *The Mathematica Journal* if you
    are not subscribed already if you use this module (a Mathematica license
    is needed anyway). You would be nice to nice people and may even read
    something more about this module one day ;-)

    Special thanks to Randal L. Schwartz for naming this module.

    Thanks also to Richard Jones for providing a login on a Solaris box so
    that I could check that the module still works with Mathematica 4.0.

Copyright
    The Math:ematica module is Copyright (c) 1996,1997,1998,2000 Ulrich
    Pfeifer. Germany. All rights reserved.

    You may distribute under the terms of either the GNU General Public
    License or the Artistic License, as specified in the Perl README file.

    Mathematica and MathLink are registered trademarks of Wolfram Research.

