The Supplementary Material to

Link to the book. Another copy of the material can be found at https://jgluza.us.edu.pl/mbspringer/

In the book examples the following tools have been used:

• AMBRE: https://jgluza.us.edu.pl/ambre/
• PlanarityTest: https://jgluza.us.edu.pl/ambre/planarity/
• MBnumerics: https://jgluza.us.edu.pl/ambre/
• MB, MBresolve, MBasymptotics, barnesroutines: https://mbtools.hepforge.org
• CUBA:http://www.feynarts.de/cuba/
• CernLib: http://cernlib.web.cern.ch/cernlib/
• QMC: https://github.com/mppmu/qmc

These examples are tested under:

• Mathematica 12.0.0.0

For viewing the .nb files one can use Wolfram Player.

• MB.m requires CUBA library for numerical integration and CERNlib for gamma functions.

• To find where the problem is, one can run MBintegrate with the option Debug->True. This option doesn't erase fortran source files, and one can compile them manually to see all errors and warnings.

• For simple tests to be independent on Cernlib and CUBA, one can use MBintegrate with option MaxNIntegrateDim -> your_dim. In this case, MB.m will use the NIntegrate function from Mathematica. Also, one can pass NIntegrate options to MBintegrate.

• MB.m is distributed as it is and without changes since ~2006. To make it works with new libraries and compilers, one should make some changes

• f77 is now a part of gfortran, so you should change in MB.m line962: Run["f77 -O -o", exec, source, "-L. -lmathlib -lkernlib -lcuba"] to Run["gfortran -O -o", exec, source, "-L. -lmathlib -lkernlib -lcuba"].

• MB works by default with Cuba 1.7 or older. It is because function calls are different for different versions (you can check it in Cuba documentation).

You can use the old version or for Cuba 4.x one should modify this part: lines 908-910 and 912-914 from

  "      call vegas(ndim, ncomp, integrand, epsrel, epsabs, flags,\n",
  "     &           mineval, maxeval, nstart, nincrease,\n",
  "     &           neval, fail, integral, error, prob)\n",

  "      call cuhre(ndim, ncomp, integrand, epsrel, epsabs, flags,\n",
  "     &           mineval, maxeval, key, nregions,\n",
  "     &           neval, fail, integral, error, prob)\n",

to

  "      call vegas(ndim, ncomp, integrand, 0, 1,\n",
  "     &           epsrel, epsabs, 0, 0,\n",  
  "     &           mineval, maxeval, nstart, nincrease, 1000,\n",
  "     &           0, \"\", -1,\n",
  "     &           neval, fail, integral, error, prob)\n",

  "      call cuhre(ndim, ncomp, integrand, 0, 1,\n",
  "     &           epsrel, epsabs, 0,\n",
  "     &           mineval, maxeval, key,\n",
  "     &           \"\", -1,\n",
  "     &           nregions, neval, fail, integral, error, prob)\n",

• CERNlib is usually not a problem since it is in any Debian-based Linux distribution repository.

• Nov 2022: first release