26,069 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
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities
involving Bessel functions with half-integer orders and other special
functions. These identities appear in the famous Handbook of Mathematical
Functions, as well as in its successor, the DLMF, but their proofs were lost.
We use generating functions and symbolic summation techniques to produce new
proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl
Symbolic-numeric interface: A review
A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach
HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
We present the Mathematica package HypExp which allows to expand
hypergeometric functions around integer parameters to arbitrary
order. At this, we apply two methods, the first one being based on an integral
representation, the second one on the nested sums approach. The expansion works
for both symbolic argument and unit argument. We also implemented new
classes of integrals that appear in the first method and that are, in part, yet
unknown to Mathematica.Comment: 33 pages, latex, 2 figures, the package can be downloaded from
http://krone.physik.unizh.ch/~maitreda/HypExp/, minor changes, works now
under Window
Technology survey of computer software as applicable to the MIUS project
Existing computer software, available from either governmental or private sources, applicable to modular integrated utility system program simulation is surveyed. Several programs and subprograms are described to provide a consolidated reference, and a bibliography is included. The report covers the two broad areas of design simulation and system simulation
Refined Holonomic Summation Algorithms in Particle Physics
An improved multi-summation approach is introduced and discussed that enables
one to simultaneously handle indefinite nested sums and products in the setting
of difference rings and holonomic sequences. Relevant mathematics is reviewed
and the underlying advanced difference ring machinery is elaborated upon. The
flexibility of this new toolbox contributed substantially to evaluating
complicated multi-sums coming from particle physics. Illustrative examples of
the functionality of the new software package RhoSum are given.Comment: Modified Proposition 2.1 and Corollary 2.
Making big steps in trajectories
We consider the solution of initial value problems within the context of
hybrid systems and emphasise the use of high precision approximations (in
software for exact real arithmetic). We propose a novel algorithm for the
computation of trajectories up to the area where discontinuous jumps appear,
applicable for holomorphic flow functions. Examples with a prototypical
implementation illustrate that the algorithm might provide results with higher
precision than well-known ODE solvers at a similar computation time
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