Ulrich Pfeifer

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.

The module still compiles fine with Mathematica 5.0 on Linux 2.6 and libc-2.3.2.

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. So MLCloseLink is not accessible; use undef or lexical variables to store links. If you use a global variable and dont force the link close, you will get an optional warning during global 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.

GetByteString

The method does the appropriate MLDisownByteString 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 Stringss 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 perl(1) 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) 1996,1997,1998,2000,2005 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.




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