197 research outputs found
Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language
The traditional split-up into a low level language and a high level language
in the design of computer algebra systems may become obsolete with the advent
of more versatile computer languages. We describe GiNaC, a special-purpose
system that deliberately denies the need for such a distinction. It is entirely
written in C++ and the user can interact with it directly in that language. It
was designed to provide efficient handling of multivariate polynomials,
algebras and special functions that are needed for loop calculations in
theoretical quantum field theory. It also bears some potential to become a more
general purpose symbolic package
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs
This paper presents an experimental performance study of implementations of
three symbolic algorithms for solving band matrix systems of linear algebraic
equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient
matrices. The only assumption on the coefficient matrix in order for the
algorithms to be stable is nonsingularity. These algorithms are implemented
using the GiNaC library of C++ and the SymPy library of Python, considering
five different data storing classes. Performance analysis of the
implementations is done using the high-performance computing (HPC) platforms
"HybriLIT" and "Avitohol". The experimental setup and the results from the
conducted computations on the individual computer systems are presented and
discussed. An analysis of the three algorithms is performed.Comment: 7 pages, 9 tables, 4 figure
Kira - A Feynman Integral Reduction Program
In this article, we present a new implementation of the Laporta algorithm to
reduce scalar multi-loop integrals---appearing in quantum field theoretic
calculations---to a set of master integrals. We extend existing approaches by
using an additional algorithm based on modular arithmetic to remove linearly
dependent equations from the system of equations arising from
integration-by-parts and Lorentz identities. Furthermore, the algebraic
manipulations required in the back substitution are optimized. We describe in
detail the implementation as well as the usage of the program. In addition, we
show benchmarks for concrete examples and compare the performance to Reduze 2
and FIRE 5.
In our benchmarks we find that Kira is highly competitive with these existing
tools.Comment: 37 pages, 3 figure
Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic
polylogarithms up to w = 8 at an absolute accuracy of
or better. Using algebraic and argument relations the numerical representation
can be limited to the range . We provide replacement
files to map all harmonic polylogarithms to a basis and the usual range of
arguments to the above interval analytically. We also
briefly comment on a numerical implementation of real valued cyclotomic
harmonic polylogarithms.Comment: 19 pages LATEX, 3 Figures, ancillary dat
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