Singular

D.15.12 pfd_lib

Library:

pfd.lib

Purpose:

Multivariate Partial Fraction Decomposition

Author:

Marcel Wittmann, e-mail: mwittman@mathematik.uni-kl.de

Overview:

This Library implements an algorithm based on the work of E. K. Leinartas to write rational functions in mutiple variables as a sum of functions with "smaller" numerators and denominators.
This can be used to shorten the IBP reduction coeffcients of multi-loop Feynman integrals. For this application,
we also provide a procedure that applies the algorithm to all entries of a matrix of rational functions given as one (possibly very big) txt-file. If you use the library pfd.lib, please cite the corresponding paper [J. Boehm, M. Wittmann, Z. Wu, Y. Xu, Y. Zhang: 'IBP reduction coefficients made simple'] (preprint 2020).

Procedures:

D.15.12.1 pfd		calculate a partial fraction decomposition of a rational function
D.15.12.2 checkpfd		test if a decomposition is equal to a rational function given by numerator/denominator polynomials
D.15.12.3 evaluatepfd		substitute values in a partial fraction decomposition gotten from pfd
D.15.12.4 displaypfd		print a decomposition gotten as output of pfd
D.15.12.5 displaypfd_long		like display, but denominators are written out
D.15.12.6 getStringpfd		turn a decomposition gotten from pfd into one string
D.15.12.7 getStringpfd_indexed		like getStringpfd, but writes the denominator factors just as q1, q2, ...
D.15.12.8 readInputTXT		read a matrix of rational functions from a txt-file
D.15.12.9 pfdMat		apply pfd to a matrix of rational functions in parallel (using @ref{parallel_lib}) and save result as easy-to-read txt-files.
D.15.12.10 checkpfdMat		test output files of pfdMat for correctness