Welcome to the webpage
of the Mathematica Package HPL
The Mathematica package HPL is
an implementation of the harmonic polylogarithms (HPL) of Remiddi and
Vermaseren. The package contains implementation of
-the product algebra,
-derivatives,
- integration of products of the type x^j/(1-x)^k H(...), x^j/(1+x)^k
H(...), x^j/(1-x^2)^k H(...),
-reduction to more common functions (log's, polylog's, Nielsen
polylog's)
-singular behaviour extraction
-analytic continuation (with control over the sign of the imaginary
parts)
-change of arguments (x = -t,x = tē, x = 1-t, x = 1/t
, x =
t/(t-1), x = (1-t)/(1+t) )
-numerical evaluation on the whole complex plane
-values at argument 1, multiple zeta values (MZV's)
-values at argument i.
A detailed description and many examples can be found in hep-ph/0507152 and in hep-ph/0703052
Most recent version: HPL-2.0
(03-NOV-2011)
List of changes
If you experience problems with the package HPL, please consult the known issues or send a bug report this address.
Installation (Linux, Mac)
There is an installation program with the package. It copies the files
where they belong, updates your init.m file, so that you can load the
package without having to give the whole path.
To install the package, copy the tar file HPL-2.0.tar.gz
to your disk, unpack it with
> gunzip HPL-2.0.tar.gz
> tar -xf HPL-2.0.tar
Change directory to the HPL-2.0 directory
> cd HPL-2.0
Change the permission of the installation script:
> chmod +x HPLInstall
Execute it:
> ./HPLinstall
Follow the instruction...
If you experience problems with the installation script, please consult the known issues or send a bug report this address.
Installation (Windows)
There is no installation script for Windows. It copies the files
where they belong, updates your init.m file, so that you can load the
package without having to give the whole path.
To install the package,
- copy the tar file HPL-2.0.tar.gz
to your disk, where you want the package to be,
-unpack it
-copy and download in the directory HPL-2.0
all the additional tables (see below) you need (this can also be
done afterwards).
The package can be called with
$HPLPath="the:\path\of\the\installation"
(
you might have to escape the \ character :
$HPLPath="the:\\path\\of\\the\\installation" )
Get[ToFileName[{$HPLPath},"HPL.m"]]
If you do not want to type this each time, you can add the following
lines to your init.m file
in the AutoLoad directory
of your Mathematica installation.
$HPLPath="the:\path\of\the\installation"
(
you might have to escape the \ character :
$HPLPath="the:\\path\\of\\the\\installation" )
$Path=Flatten[{$Path,$HPLPath}]
In the next sessions you can then load the package with <<HPL` only.
Additional tables for
weights
higher than 6
The reduction to a minimal set and the values at one and at i require
quite
large tables. In order not to use unnecessarily the memory, the tables
for weight higer than 6 are not included in the basis package (the
HPL-2.0.tar.gz file). If the user needs the HPL's of weight higher than
6, he can simply add the files listed below into the installation
directiory of HPL
and unzip them (>
gunzip MinimalSet?.m.gz). The new tables will be loaded
automatically in the next Mathematica session.
MinimalSet7.m.gz : Rules for the
projection
to the minimal set of HPL of weight 7 (new with version 1.1, please
replace the old with this one).
Compressed size: 112K
Uncompressed size: 1.8 M
MinimalSet8.m.gz : Rules for the
projection
to the minimal set of HPL of weight 8 (new with version 1.1, please
replace the old with this one).
Compressed size: 688K
Uncompressed size: 9.7 M
MinimalSetpm7.m.gz : Rules for the
projection
to the minimal set of HPL of weight 7 with +- weights (new with version
2.0).
Compressed size: 147K
Uncompressed size:
MinimalSetpm8.m.gz : Rules for the
projection
to the minimal set of HPL of weight 8 with +- weights (new with version
2.0).
Compressed size: 752K
Uncompressed size:
h7table.mat.gz : Rules for the HPL's at
argument 1 and MZV's of weight 7 (translated from the summer package of
J. Vermaseren)
Compressed size: 26K
Uncompressed size: 956K
h8table.mat.gz : Rules for the HPL's at
argument 1 and MZV's of weight 8 (translated from the summer package of
J.Vermaseren)
Compressed size: 26K
Uncompressed size: 4.9M
HPLatI7.m.gz : Rules
for the HPL's of weight 7 at
argument i
Compressed size: 5.1M
Uncompressed size:
numHPLatI7.m.gz : auxilliary file to
fasten
the numerical evaluation of HPL's of weight 7 at
argument i
(pleas install along with HPLatI7.m)
Compressed size: 5.1M
Uncompressed size:
Numerical evaluation in FORTRAN
The numerical evaluation of HPL's can be performed with a FORTRAN
program by T.Gehrmann and E.Remiddi called hplog.It can be downloaded here. A complete description can be found at hep-ph/0107173
and in Computer Physics Communications 141 (2001) 296.
Uninstall HPL
Under Linux, run the program
> ./HPLuninstall
in the installation directory of HPL. Under Windows remove the files
of the installation.
Bug reports
Great care has been taking in testing the HPL package. However, if
there were problem left we would appreciate to get bug reports to this address.
---
last update: 6 October 2008