The file katsurada.cl contains Common Lisp code implementing the 
approach of H. Katsurada (Am J Math 1999) for computing Fourier 
coefficients of Siegel Eisenstein series. It loads some precomputed 
values from precomputed_misc.cl and precomputed_zetads.cl
See the code itself for a more detailed description and references.

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A Common Lisp interpreter is required to use this code.

We have run the code with GNU CLISP (http://www.clisp.org/),
which can be installed on OS X using Homebrew (http://brew.sh/),
   brew install clisp
and on Ubuntu Linux using apt-get
   sudo apt-get install clisp
or on Windows following the directions at http://www.clisp.org/

The Lisp code can be compiled into machine code or byte code for faster 
execution, if desired.

For example, with clisp, the command 
  clisp -c katsurada.cl -c precomputed_zetads.cl -c precomputed_misc.cl 
produces compiled byte-code of the three .cl files, with extensions .fas

Then one can launch clisp, and use the command
  (load 'katsurada.cl)
to load the source code, or
  (load 'katsurada.fas)
to load the compiled code, or just
  (load 'katsurada)
to let your Lisp implementation decide which to load.

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The file katsurada.cl includes a function cnk for computing the Fourier 
coefficient  c_{n,k}(B,n,k) of the Siegel Eisenstein series of degree n 
and weight k for positive-definite half-integral matrices B, and a function 
fppolys for computing the polynomials F_p(B,X) from Katsurada, a component 
of c_{n,k} that may be of independent interest in some applications.

For these functions the input B is not the matrix itself, but rather a 
representation of the genus symbol of the matrix, as in chapter 15 of 
Conway & Sloane's Sphere Packings, Lattices and Groups; see the file 
precomputed_misc.cl for details of the genus format.

Mathematica code for computing the genus symbol for any positive 
definite symmetric integral matrix (which involves p-adic Jordan 
decompositions) is available at
   http://siegelmodularforms.org/pages/degree3/

Magma also has built-in functions pSignature, Oddity, pExcess for computing 
local invariants, and a function Genus for directly computing the genus of a 
lattice.

In both cases some reformatting of the representation of the genus symbol is 
necessary to use it as input to the Lisp functions. This reformatting can be 
done within Mathematica, within Lisp, or with some other adapter or wrapper 
code, as in the example below.

In this folder there a Perl script makeFpPolys.pl that takes as input a file 
consisting of genus symbols computed in Mathematica, reformats these symbols, 
and produces a Lisp file that loads katsurada.cl then calls the function 
fppolys once for each genus symbol. The Perl script then runs Lisp on this file, 
writing the results to a temp file, then reads in this temp file and reformats 
the results back in Mathematica code, appended to an output file. This output 
file can be used with the EisensteinCoefficient.nb Mathematica file from 
   http://siegelmodularforms.org/pages/degree3/
to compute monic and scaled Fourier coefficients of Siegel Eisenstein series, 
including for positive semi-definite matrices.

This Perl script requires that Perl is installed, and also that the Lisp 
interpreter specified by $mylisp in the Perl script (default value clisp) 
in the path environment variable ($PATH on Unix-like systems, %PATH% on windows). 
Alternatively, $mylisp may be modified to specify the full path.

The Perl script can be run as follows:
   perl makeFpPolys.pl inputfile outputAppendFile

The file fp-input-example.txt is an example input file, with two genus symbols,