Mathematical Software
A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
A study of the existing linear algebra libraries that you can use from C++
We give a link to a page on the Web on which we deposited a set of eight huge Linear Programming (LP) problems for Intensity-Modulated Proton Therapy (IMPT) treatment planning. These huge LP problems were employed in our recent research and…
In the Python world, NumPy arrays are the standard representation for numerical data. Here, we show how these arrays enable efficient implementation of numerical computations in a high-level language. Overall, three techniques are applied…
We present an XML-based simulation authoring environment. The proposed description language allows to describe mathematical objects such as systems of ordinary differential equations, partial differential equations in two dimensions, or…
Quantum anticipation explorer is a computer program allowing the numerical exploration of quantum anticipation which has been analyzed in arXiv:0810.183v1 and arXiv:1003.1090v1 for H-Atom, equidistant, random and custom spectra. This tool…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
We present a Compression Tool, "GenBit Compress", for genetic sequences based on our new proposed "GenBit Compress Algorithm". Our Tool achieves the best compression ratios for Entire Genome (DNA sequences) . Significantly better…
In this paper we present a Java implementation of the algorithm that computes Buchbereger's and reduced Groebner's basis step by step. The Java application enables graphical representation of the intersection of two surfaces in…
We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
We describe our software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available as a stand-alone serial library, as an external package to PETSc (``Portable, Extensible…
Mathematical learning environments help students in mastering mathematical knowledge. Mature environments typically offer thousands of interactive exercises. Providing feedback to students solving interactive exercises requires domain…
We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…
A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced…
MP is a package of ANSI Standard Fortran (ANS X3.9-1966) subroutines for performing multiple-precision floating-point arithmetic and evaluating elementary and special functions. The subroutines are machine independent and the precision is…
A \emph{Mathematica} Notebook is presented which allows for the transfer or any kind of polynomial expression to \emph{Matlab}. The output is formatted in such a way that \emph{Matlab} routines such as "Root" can be readily implemented.…