Results 31 to 40 of about 396 (66)
gTybalt - a free computer algebra system [PDF]
, 2003 This article documents the free computer algebra system "gTybalt". The program is build on top of other packages, among others GiNaC, TeXmacs and Root.
Weinzierl, Stefan
core +1 more source
, 2015 We present an algebraic framework to represent indefinite nested sums over hypergeometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been extended to a ring theory in which also the ...
Schneider, Carsten
core +1 more source
Special functions, transcendentals and their numerics [PDF]
, 2017 Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented.
Ablinger, Jakob +3 more
core +2 more sources
The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$ [PDF]
, 2018 We calculate the two-mass QCD contributions to the massive operator matrix element $A_{gg,Q}$ at $\mathcal{O} (\alpha_s^3)$ in analytic form in Mellin $N$- and $z$-space, maintaining the complete dependence on the heavy quark mass ratio.
Ablinger, J. +5 more
core +4 more sources
Symbolic and Numerical Analysis in General Relativity with Open Source Computer Algebra Systems
, 2018 We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general ...
Birkandan, Tolga +3 more
core +1 more source
General $\varepsilon$-representation for scalar one-loop Feynman integrals
, 2015 A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms of higher ...
Bluemlein, Johannes +2 more
core +1 more source
Calculation of Massless Feynman Integrals using Harmonic Sums [PDF]
, 2006 A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums. Algorithms for the
Bekavac, Stefan
core +1 more source
Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces [PDF]
, 2015 This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large ...
De Loera, Jesús A. +2 more
core +3 more sources
Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences
, 2017 Analyzing and reasoning about safety properties of software systems becomes an especially challenging task for programs with complex flow and, in particular, with loops or recursion.
Humenberger, Andreas +2 more
core +1 more source
, 2015 Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable $N$ and the ...
Ablinger, J. +5 more
core +1 more source