TSIL-Mma

TSIL-Mma provides a Mathematica interface for the two-loop self-energy integral library TSIL [CPC 174 (2006) 133-151]. TSIL is written by Stephen P. Martin and David G. Robertson.

Building TSIL

First, TSIL must be downloaded and extracted. Afterwards, edit the TSIL Makefile and add -fPIC to TSIL_OPT:

mak TSIL_OPT = -O3 -funroll-loops -fPIC

In addition, we recommend to enable long double precision in the TSIL Makefile (enabled by default):

mak TSIL_SIZE = -DTSIL_SIZE_LONG

Afterwards, run

sh make

Building TSIL-Mma

To build TSIL-Mma, first create a build sub-directory and enter that directory:

sh mkdir build cd build

Then, call cmake to search for the Mathematica installation and for the TSIL library and header files:

sh cmake -DTSIL_DIR=/path/to/tsil -DCMAKE_CXX_FLAGS=-DTSIL_SIZE_LONG ..

The variable CMAKE_CXX_FLAGS must be set to the value of TSIL_SIZE that has been set in the TSIL Makefile (see above):

• If TSIL has been build with long double precision (TSIL_SIZE = -DTSIL_SIZE_LONG), pass to cmake:

mak -DCMAKE_CXX_FLAGS=-DTSIL_SIZE_LONG

This is the default TSIL configuration.

• If TSIL has been build with double precision (TSIL_SIZE = -DTSIL_SIZE_DOUBLE), pass to cmake:

mak -DCMAKE_CXX_FLAGS=-DTSIL_SIZE_DOUBLE

Finally TSIL-Mma can be build by running

sh make

Usage

To call the TSIL functions from Mathematica one has to first include the file src/LibraryLink.m (assuming one is currently in the build directory):

wl Get[FileNameJoin[{"..", "src", "LibraryLink.m"}]];

Afterwards, the TSIL-Mma LibraryLink library must be loaded using the function TSILInitialize[libName]. The function argument libName is the name of the created library, including the path. On Linux the library is called LibraryLink.so, on MacOS it is called LibraryLink.dylib. Thus, on Linux you may write:

wl libName = FileNameJoin[{"src", "LibraryLink.so"}]; TSILInitialize[libName];

When these two steps are done, the TSIL functions can be called, for example:

```wl x = 1; y = 2; z = 3; u = 4; v = 5; s = 10; qq = 1;

(* evaluate all TSIL integral functions *) Print[TSILEvaluate[x, y, z, u, v, s, qq]];

(* individual TSIL integral functions *) Print["A(x,qq) = ", TSILA[x, qq]]; Print["Ap(x,qq) = ", TSILAp[x, qq]]; Print["Aeps(x,qq) = ", TSILAeps[x, qq]]; Print["B(x,y,s,qq) = ", TSILB[x, y, s, qq]]; Print["Bp(x,y,s,qq) = ", TSILBp[x, y, s, qq]]; Print["dBds(x,y,s,qq) = ", TSILdBds[x, y, s, qq]]; Print["Beps(x,y,s,qq) = ", TSILBeps[x, y, s, qq]]; Print["I(x,y,z,qq) = ", TSILI[x, y, z, qq]]; Print["Ip(x,y,z,qq) = ", TSILIp[x, y, z, qq]]; Print["Ip2(x,y,z,qq) = ", TSILIp2[x, y, z, qq]]; Print["Ipp(x,y,z,qq) = ", TSILIpp[x, y, z, qq]]; Print["Ip3(x,y,z,qq) = ", TSILIp3[x, y, z, qq]]; Print["M(x,y,z,u,v,s) = ", TSILM[x, y, z, u, v, s]]; Print["S(x,y,z,s,qq) = ", TSILS[x, y, z, s, qq]]; Print["T(x,y,z,s,qq) = ", TSILT[x, y, z, s, qq]]; Print["Tbar(x,y,z,s,qq) = ", TSILTbar[x, y, z, s, qq]]; Print["U(x,y,z,u,s,qq) = ", TSILU[x, y, z, u, s, qq]]; Print["V(x,y,z,u,s,qq) = ", TSILV[x, y, z, u, s, qq]]; ```

A full example script can be found in example/example.m. It can be run from the build directory as:

wl math -run '<< "../example/example.m"'

Author

TSIL-Mma is written by Alexander Voigt, RWTH Aachen University.

Copying

TSIL-Mma is licenced under the GNU General Public License (GNU GPL) version 3.