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Abstract: We examine what is necessary to allow generic libraries to be used naturally in a multi-language, potentially distributed environment. Language-neutral library interfaces usually do not support the full range of programming idioms that are available when a library is used natively. We investigate how to structure the language bindings of the neutral interface to achieve a better expressibility and code re-use. We furthermore address how language-neutral interfaces can be extended with import bindings to recover the desired programming idioms. We also address the question of how these extensions can be organized to minimize the performance overhead that arises from using objects in manners not anticipated by the original library designers. Our approach is to treat a library as a software component and to view the problem as one of component extension. We use C++ as an example of a mature language, with libraries using a variety of patterns, and use the Standard Template Library as an example of a complex library for which efficiency is important. By viewing the library extension problem as one of component organization, we enhance software composibility, hierarchy maintenance and architecture independence. [Copyright &y& Elsevier]

We study online classification of isolated handwritten symbols using distance measures on spaces of curves. We compare three distance-based measures on a vector space representation of curves to elastic matching and ensembles of SVM. We consider the Euclidean and Manhattan distances and the distance to the convex hull of nearest neighbors. We show experimentally that of all these methods the distance to the convex hull of nearest neighbors yields the best classification accuracy of about 97.5%. Any of the above distance measures can be used to find the nearest neighbors and prune totally irrelevant classes, but the Manhattan distance is preferable for this because it admits a very efficient implementation. We use the first few Legendre-Sobolev coefficients of the coordinate functions to represent the symbol curves in a finite-dimensional vector space and choose the optimal dimension and number of bits per coefficient by cross-validation. We discuss an implementation of the proposed classification scheme that will allow classification of a sample among hundreds of classes in a setting with strict time and storage limitations. [ABSTRACT FROM AUTHOR]

We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over R[x] or C[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9. [ABSTRACT FROM AUTHOR]

Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given. [ABSTRACT FROM AUTHOR]