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Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Computer algebra in Java is a promising field of development. It has not yet reached an industrial strength, in part because of a lack of good user interfaces. Using a general purpose scripting language can bring a natural mathematical…
The R package calculus implements C++ optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion,…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
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…
Language-orientated programming promises to elevate programmer productivity through increased abstrac- tion capabilities. Structural programming environments provide apparatus to reduce the difficulties with syntax. The language workbench,…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
We present the quantum programming language cQPL which is an extended version of QPL [P. Selinger, Math. Struct. in Comp. Sci. 14(4):527-586, 2004]. It is capable of quantum communication and it can be used to formulate all possible quantum…
Quantum computers promise exponential speed ups over classical computers for various tasks. This emerging technology is expected to have its first huge impact in High Performance Computing (HPC), as it can solve problems beyond the reach of…
Template metaprogramming is a popular technique for implementing compile time mechanisms for numerical computing. We demonstrate how expression templates can be used for compile time symbolic differentiation of algebraic expressions in C++…
Even with the increase of popularity of functional programming, imperative programming remains a key programming paradigm, especially for programs operating at lower levels of abstraction. When such software offers key components of a…
In this work we introduce Qumin, a novel quantum programming language with a focus on providing an easy to use, minimalist, high-level, and easily extensible platform for quantum programming. Qumin's design concentrates on encompassing the…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of…
Quantum computing, with its vast potential, is fundamentally shaped by the intricacies of quantum mechanics, which both empower and constrain its capabilities. The development of a universal, robust quantum programming language has emerged…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional…
We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum…
We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for…
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…
A brief characteristic of the specialized computer algebra system GRG_EC intended for symbolic computations in the field of general relativity is given.