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Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
Arithmetic circuit complexity studies the complexity of computing polynomials using only arithmetic operations such as addition, multiplication, subtraction, and division. Polynomials over rings of integers model counting problems.…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
In this paper, we present the computational task-management tool Ganga, which allows for the specification, submission, bookkeeping and post-processing of computational tasks on a wide set of distributed resources. Ganga has been developed…
Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing…
JISA is a software library, written in Java, aimed at providing an easy, flexible and standardised means of creating experimental control software for physical sciences researchers. Specifically, with an emphasis on enabling measurement…
The purpose of these notes is to provide the details of the Jacobian ring computations carried out in [1], based on the computer algebra system Magma [2].
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
We present the SLIM (https://github.com/slimgroup) open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment…
This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
A polynomial ring with rational coefficients is an irreducible representation of Lie algebras of endomorphisms of exterior powers of a infinite countable dimensional $\mathbb{Q}$-vector space. We give an explicit description of it, using…
We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a…
We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum…
We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials.
Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic…
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming…