The first step is to install KASH (the KAnt SHell) on your system.
Afterwards you have to download the database package, by downloading
either
database.zip
from this site, or
database.tar.gz from the authors'
remote site.
On a system running under Unix,
to unpack database.zip
from this site, type:
unzip database.zip ;to unpack database.tar.gz from the authors' remote site, type:
gunzip database.tar.gz tar xf database.tar .This creates a directory "Database", which contains all the necessary files.
Edit the first line of the file database.k to contain the path of the
directory Database.
After starting KASH you should write:
Read("Database/database.k").
Now the following commands can be used.
GaloisPolynomial(n,num):this gives all the polynomials of degree n with Galois group "num". (This is the group that one gets by typing "TransitiveGroup(n,num);" in gap or magma.)
GaloisPolynomial(n,num,sig):this gives all the polynomials of degree n with Galois group "num", and "sig" real zeros.
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Description of the files:
All polynomials with GaloisGroup TransitiveGroup(n,num) are contained in the file gntnum; for example, g5t5 contains all S5 (=TransitiveGroup(5,5)) polynomials. The file contains a nested list assigned to the variable "__galpols". Denote by r1 the number of real zeros. Then all the polynomials in "__galpols[(n-r1)/2+1]" have exactly r1 real zeros. For example, "__galpols[1]" contains totally real polynomials. "__galpols[1]" is now a nested list which contains the entries. Each entry is a list of length 2 or 3, where the first entry is always a polynomial, and the second entry is the field discriminant of the field generated by a root of that polynomial. If there is a third entry, this codes the conjugacy class in which complex conjugation lies.
The files "statntnum" (stat5t5 for S5) contain statistical information about the groups. Such a file reads a variable "__stat" containing a list of the following type:
__stat[1] : list of possible signatures (number of real zeros);
__stat[2]
: number of entries for each signature;
__stat[3] : minimal discriminants for
each signature;
__stat[4] : minimal discriminants for classes of involutions
which cannot be characterized by the signature.
The other files contain the KASH program and some group-theoretical data
about the permutation groups.