Related papers: Symbolic computations in differential geometry
In recent years, compositional symbolic execution (CSE) tools have been growing in prominence and are becoming more and more applicable to real-world codebases. Still to this day, however, debugging the output of these tools remains…
We describe an algorithm and a C++ implementation that we have written and made available for calculating the fully nonlinear evolution of 5D braneworld models with scalar fields. Bulk fields allow for the stabilization of the extra space.…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
functionalObjects.h allows the C++ programmer performing common mathematical calculations to use a more symbolic syntax rather than an algorithmic syntax. This is not as ambitious as a symbolic manipulation program such as Mathematica; it…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are presented. The algorithms can be used to test the…
We propose a new diagrammatic modeling language, DML. The paradigm used is that of the category theory and in particular of the pushout tool. We show that most of the object-oriented structures can be described with this tool and have many…
Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…
In this paper we will present SDeval, a software project that contains tools for creating and running benchmarks with a focus on problems in computer algebra. It is built on top of the Symbolic Data project, able to translate problems in…
The representation of polynomials by arithmetic circuits evaluating them is an alternative data structure which allowed considerable progress in polynomial equation solving in the last fifteen years. We present a circuit based computation…
Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of…
This report is devoted to some C++ codes implementing the implicit LU class algorithms for solving linear determined, and undetermined systems with $n$ variables and $m$ equations. A main program used in part of the numerical test is given…