In this paper, we review the features in the newly released version of COSY INFINITY, which currently has a base of more than 1000 registered users, focusing on the topics which are new and some topics which became available after the first release of the previous versions 8 and 8.1. The recent main enhancements of the code are devoted to reliability and efficiency of the computation, to verified integration, and to rigorous global optimization. There are various data types available in COSY INFINITY to support these goals, and the paper also reviews the feature and usage of those data types.

http://bt.pa.msu.edu/pub/papers/COSYCAP04/COSYCAP04.pdf

COSY INFINITY Version 9

Building interval software interoperability can be a good solution when re-using high-quality legacy code or when accessing functionalities unavailable natively in one of the software packages. In this work we present the integration of programs based on the interval libraries filib++ and C-XSC into Mathematica via MathLink communication protocol. On some small easily readable programs we demonstrate: i) some details of MathLink technology, ii) the transparency of numerical data communication without any conversion, iii) the advantage of symbolic manipulation interfaces -- the access to the external compiled language functionality from within Mathematica is often even more convenient than from its own native environment.

/pdf/mathematica-connectivity-to-interval-libraries-filib-and-c-2ihk3ge2tx.pdf

Mathematica Connectivity to Interval Libraries filib++ and C-XSC

We propose the collection, standardization, and distribution of a full-featured, production quality library for reliable scientific computing with routines using interval techniques for use by the wide community of applications developers.

/pdf/interval-subroutine-library-mission-imsa0kujj4.pdf

Interval Subroutine Library Mission

Fundamentals of Interval Computing

This work focuses on a mechanism (and software) which communicates (via MathLink protocol) and provides compatibility between the representation of nonlinear functions specified as Mathematica expressions and objects of suitable classes supported by the C-XSC automatic differentiation modules. The application of the developed communication software is demonstrated by MathLink compatible programs embedding in Mathematica the C-XSC modules for automatic differentiation as packages. The design methodology, some implementation issues and the use of the developed software are discussed.

/pdf/communicating-functional-expressions-from-mathematica-to-c-44vm7psrbj.pdf

Communicating functional expressions from mathematica to C-XSC

The COSY Infinity software package by Berz et al. is widely used in the beam physics community. We report execution-based testing of its interval and Taylor model arithmetics. The testing strategy is careful to avoid contamination by inevitable rounding errors. Tests were ported to Sun’s F95 and INTLAB. In each package, we uncovered violations of containment which have all been corrected by their authors. We encourage users of COSY and most other software packages to check author/vendor web sites regularly for possible updates and patches.

Interval Testing Strategies Applied to COSY’s Interval and Taylor Model Arithmetic

Interval Testing Strategies Applied to COSY's Interval and Taylor Model Arithmetic.

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Interval Testing Strategies Applied to COSY’s Interval and Taylor Model Arithmetic

Interval Testing Strategies Applied to COSY's Interval and Taylor Model Arithmetic.