Related papers: Computer algebra in Julia
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
We develop a framework which aims to simplify the analysis of quantum states and quantum operations by harnessing the potential of function programming paradigm. We show that the introduced framework allows a seamless manipulation of…
The Gisela framework for declarative programming was developed with the specific aim of providing a tool that would be useful for knowledge representation and reasoning within real-world applications. To achieve this, a complete integration…
We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some…
Proprietary closed-source software is still the norm in advanced process control. Transparency and reproducibility are key aspects of scientific research. Free and open-source toolkit can contribute to the development, sharing and…
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight…
We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer…
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived…
In many problems that involve multiple decision making agents, optimal choices for each agent depend on the choices of others. Differential game theory provides a principled formalism for expressing these coupled interactions and recent…
The aim of this article is to show, how computer algebra can be used when applying Liu's procedure. Although Mathematica (a commercial product by Wolfram Research Inc.) is used, it is possible to use other computer algebra systems as well.
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
What would you teach if you had only one course to help students grasp the essence of computation and perhaps inspire a few of them to make computing a subject of further study? Assume they have the standard college prep background. This…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…
The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment, thereby enabling the R user…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Dynamic programming languages face semantic and performance challenges in the presence of features, such as eval, that can inject new code into a running program. The Julia programming language introduces the novel concept of world age to…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
In emerging scientific computing environments, matrix computations of increasing size and complexity are increasingly becoming prevalent. However, contemporary matrix language implementations are insufficient in their support for efficient…