Related papers: LSJK - a C++ library for arbitrary-precision numer…
The evaluation of higher-loop Feynman integrals is at the core of the quest to reduce the uncertainty of theoretical predictions and match experimental data from the LHC and future colliders. pySecDec is a program to evaluate such integrals…
We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
Due to the absence of a library for non-linear function evaluation, so-called general-purpose secure multi-party computation (MPC) are not as ''general'' as MPC programmers expect. Prior arts either naively reuse plaintext methods,…
The fixed-point logic LREC= was developed by Grohe et al. (CSL 2011) in the quest for a logic to capture all problems decidable in logarithmic space. It extends FO+C, first-order logic with counting, by an operator that formalises a limited…
We compute generating functions for the sum of the real-valued character degrees of the finite general linear and unitary groups, through symmetric function computations. For the finite general linear group, we get a new combinatorial proof…
The R package calculus implements C++ optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion,…
The mathematical functions log(x), exp(x), root[n]x, sin(x), cos(x), tan(x), arcsin(x), arctan(x), x^y, sinh(x), cosh(x), tanh(x) and Gamma(x) have been implemented for arguments x in the real domain in a native Java library on top of the…
In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short $S$-sums) arise. They are characterized by…
The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this…
We review the dimensional check problem of the high-level programming languages, discuss the existing solutions, and come up with a new solution suited for scientific and engineering computations. Then, we introduce Univec, our C++ library…
Signals can be interpreted as composed of a rapidly varying component modulated by a slower varying envelope. Identifying this envelope is an essential operation in signal processing, with applications in areas ranging from seismology to…
We describe two new algorithms for the efficient and rigorous computation of Dirichlet L-functions and their use to verify the Generalised Riemann Hypothesis for all such L-functions associated with primitive characters of modulus…
In this paper we analyze the computational costs of various operations and algorithms in algebraic number fields using exact arithmetic. Let $K$ be an algebraic number field. In the first half of the paper, we calculate the running time and…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined…
Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many…
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…
The complete elliptic integral of the first kind (CEI-1) plays a significant role in mathematics, physics and engineering. There is no simple formula for its computation, thus numerical algorithms are essential for coping with the practical…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…