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

CoFI: The Common Framework Initiative for Algebraic Specification and Development

An open collaborative effort has been initiated: to design acommon framework for algebraic specification and development of software. The rationale behind this initiative is that the lack of such a common framework greatly hinders the dissemination and application of researchresults in algebraic specification. In particular, the proliferationof specification languages, some differing in only quite minor ways from each other, is a considerable obstacle for the use of algebraic methods in industrial contexts, making it difficult to exploit standard examples, case studies and training material. A common framework with widespread acceptancethroughout the research community is urgently needed.The aim is to base the common framework as much as possible on a critical selection of features that have already been explored in various contexts. The common framework will provide a family of specificationlanguages at different levels: a central, reasonably expressive language, called CASL, for specifying (requirements, design, and architecture of) conventional software; restrictions of CASL to simpler languages, for use primarily in connection with prototyping and verification tools; and extensionsof CASL, oriented towards particular programming paradigms,such as reactive systems and object-based systems. It should also be possibleto embed many existing algebraic specification languages in members of the CASL family. A tentative design for CASL has already been proposed. Task groupsare studying its formal semantics, tool support, methodology, and other aspects, in preparation for the finalization of the design

Classification of Higher Dimensional Spacetimes

We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.Comment: 16 pages, 1 Tabl

On the Multi-Language Construction

Modern software is no more developed in a single programming language. Instead, programmers tend to exploit cross-language interoperability mechanisms to combine code stemming from different languages, and thus yielding fully-fledged multi-language programs. Whilst this approach enables developers to benefit from the strengths of each single-language, on the other hand it complicates the semantics of such programs. Indeed, the resulting multi-language does not meet any of the semantics of the combined languages. In this paper, we broaden the boundary functions-based approach a la Matthews and Findler to propose an algebraic framework that provides a constructive mathematical notion of multi-language able to determine its semantics. The aim of this work is to overcome the lack of a formal method (resp., model) to design (resp., represent) a multi-language, regardless of the inherent nature of the underlying languages. We show that our construction ensures the uniqueness of the semantic function (i.e., the multi-language semantics induced by the combined languages) by proving the initiality of the term model (i.e., the abstract syntax of the multi-language) in its category