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.

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last update: 6 October 2008