Adapting Real Quantifier Elimination Methods for Conflict Set Computation

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

FormCalc 8: Better Algebra and Vectorization

We present Version 8 of the Feynman-diagram calculator FormCalc. New features include in particular significantly improved algebraic simplification as well as vectorization of the generated code. The Cuba Library, used in FormCalc, features checkpointing to disk for all integration algorithms.Comment: 7 pages, LaTeX, proceedings contribution to ACAT 2013, Beijing, China, 16-21 May 201

A computer algebra user interface manifesto

Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and allowing easy fine grain control over the form of the result even by amateurs. This wizard integrates ideas including: * flexible subexpression selection; * complete control over the ordering of variables and commutative operands, with well-chosen defaults; * interleaving the choice of successively less main variables with applicable function choices to provide detailed control without incurring a combinatorial number of applicable alternatives at any one level; * quick applicability tests to reduce the listing of inapplicable transformations; * using an organizing principle to order the alternatives in a helpful manner; * labeling quickly-computed alternatives in dialog boxes with a preview of their results, * using ellipsis elisions if necessary or helpful; * allowing the user to retreat from a sequence of choices to explore other branches of the tree of alternatives or to return quickly to branches already visited; * allowing the user to accumulate more than one of the alternative forms; * integrating direct manipulation into the wizard; and * supporting not only the usual input-result pair mode, but also the useful alternative derivational and in situ replacement modes in a unified window.Comment: 38 pages, 12 figures, to be published in Communications in Computer Algebr

Digital waveguide modeling for wind instruments: building a state-space representation based on the Webster-Lokshin model

This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations for the refined acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature). The purpose of this work is to build low-cost digital simulations in the time domain based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a Kelly-Lochbaum network of input/output systems and delays. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in the time domain. The method is applied to a real trombone, and results of simulations are presented and compared with measurements. This method seems to be a promising approach in term of modularity, complexity of calculation and accuracy, for any acoustic resonators based on tubes