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Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…

There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists.…

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…

Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…

Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage…

A visual programming language uses pictorial tools such as diagrams to represent its structural units and control stream. It is useful for enhancing understanding, maintenance, verification, testing, and parallelism. This paper proposes a…

We present Matrix Distributed Processing, a C++ library for fast development of efficient parallel algorithms. MDP is based on MPI and consists of a collection of C++ classes and functions such as lattice, site and field. Once an algorithm…

ZKCM is a C++ library developed for the purpose of multiprecision matrix computation, on the basis of the GNU MP and MPFR libraries. It provides an easy-to-use syntax and convenient functions for matrix manipulations including those often…

We review the dimensional check problem of the high-level programming languages, discuss the existing solutions, and come up with a new solution suited for scientific and engineering computations. Then, we introduce Univec, our C++ library…

This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations…

We present programming techniques to illustrate the facilities and principles of C++ generic programming using concepts. Concepts are C++'s way to express constraints on generic code. As an initial example, we provide a simple type system…

We describe a new C++ library for multiprecision arithmetic for numbers in the order of 100--500 bits, i.e., representable with just a few limbs. The library is written in "optimizing-compiler-friendly" C++, with an emphasis on the use of…

We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported…

Sequential Monte Carlo is a family of algorithms for sampling from a sequence of distributions. Some of these algorithms, such as particle filters, are widely used in the physics and signal processing researches. More recent developments…

OpenGM is a C++ template library for defining discrete graphical models and performing inference on these models, using a wide range of state-of-the-art algorithms. No restrictions are imposed on the factor graph to allow for higher-order…

A C++ library, named ZKCM, has been developed for the purpose of multiprecision matrix calculations, which is based on the GNU MP and MPFR libraries. It is especially convenient for writing programs involving tensor-product operations,…

This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into…

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

We present here algorithms for efficient computation of linear algebra problems over finite fields.