[ One has a permutation group and wants to export its irreducible 
representations to fortran. ]

I wrote a naive method to do this in GAP:

http://www.ms.uky.edu/~jack/2012-08-19-GAPToFortranIrreps.g.txt

The documentation is in the file.  Save this file in the directory from which 
you call GAP (probably with a short name, like fortran.g), then read it into 
gap with:

gap> Read("fortran.g");

Then you can have it create one file per matrix in an easily readable format 
for fortran using:

gap> ExampleUsage( SymmetricGroup(4) );

This function especially is meant to be easy for you to change. The file format 
is three lines: first line is the dimension of the matrix, second line is the 
entries of the matrix in column major order, and third line is the name of the 
group element (meant to be ignored by fortran).

You will need Frank Luebeck's unreleased futil package, available from 
http://www.math.rwth-aachen.de/~Frank.Luebeck/gap/FUtil/

And unless he updates it, you'll need to change two lines in 
futil/gap/Decimal.gi to change the name "Exp" to "ExpFutil" since these days 
there is already a function called Exp.

The function to rewrite over the real field can be unreasonably slow because it 
uses no theory; if you need this to work on larger groups, you'll need to use 
theory.  The function to rewrite a representation as unitary (keeping real reps 
real) does not fit into the GAP philosophy, so I recommend only using it to 
export to fortran.


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