### D.15.15 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 multiple variables as a sum of functions with "smaller" numerators and denominators.
  This can be used to shorten the IBP reduction coefficients 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.15.15.1 pfd |  | calculate a partial fraction decomposition of a rational function
> D.15.15.2 checkpfd |  | test if a decomposition is equal to a rational function given by numerator/denominator polynomials
> D.15.15.3 evaluatepfd |  | substitute values in a partial fraction decomposition gotten from `pfd`
> D.15.15.4 displaypfd |  | print a decomposition gotten as output of `pfd`
> D.15.15.5 displaypfd_long |  | like `display`, but denominators are written out
> D.15.15.6 getStringpfd |  | turn a decomposition gotten from `pfd` into one string
> D.15.15.7 getStringpfd_indexed |  | like `getStringpfd`, but writes the denominator factors just as `q1`, `q2`, ...
> D.15.15.8 readInputTXT |  | read a matrix of rational functions from a txt-file
> D.15.15.9 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.15.15.10 checkpfdMat |  | test output files of `pfdMat` for correctness

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