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This paper describes an algorithm to compute the law of the Lie algebra $\mathfrak{g}_{n}$ associated with the Lie group G, formed of all the n× n upper-unitriangular matrices. The goal of this paper is to show the algorithm that computes the law of $\mathfrak{g}_{n}$ and its implementation using the symbolic computation package MAPLE. In addition, the complexity of the algorithm is described. [ABSTRACT FROM AUTHOR]

We introduce algorithms for the computation of homology, cohomology, and related operations on cubical cell complexes, using the technique based on a chain contraction from the original chain complex to a reduced one that represents its homology. This work is based on previous results for simplicial complexes, and uses Serre's diagonalization for cubical cells. An implementation in C++ of the introduced algorithms is available at together with some examples. The paper is self-contained as much as possible, and is written at a very elementary level, so that basic knowledge of algebraic topology should be sufficient to follow it. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze a fast algorithm that determines the possible molecular formulae corresponding to the resolved peaks in the spectral data obtained from a mass analyzer like an FT-ICR-MS. In contrast to our approach, most known algorithms and software that attempt to solve this important problem are brute-force in nature and consequently, highly prone to combinatorial explosion when dealing with the volume of real data. We also present an object-oriented implementation of our algorithm in a general-purpose, user-friendly, interactive, and easily extensible software tool PG C ompound M atch F inder. A run-time performance analysis of our software shows that even when dealing with several billion theoretical possibilities matched against tens of thousands of resolved peaks, a complete analysis using today’s standard desktop machines can take only a few minutes. [ABSTRACT FROM AUTHOR]

It is a difficult task to manually cluster a large software system into loosely coupled modules with a large number of highly cohesive classes. On the other hand clustering is a NP-Hard problem. In this paper the design and implementation of a flexible software environment, called DAGC, to assemble and experiment with genetic clustering algorithms, for software (re)modularization, is described. The main idea behind the design of the DAGC is to define a general genetic clustering algorithm which may invoke different implementations for the parts from an extendable list of components. The DAGC provides visualization facilities to compare and evaluate different genetic clustering algorithms, regarding the two parameters of running time and the quality of clusters generated by the algorithms. [ABSTRACT FROM AUTHOR]