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HEALPix -- the Hierarchical Equal Area iso-Latitude Pixelization -- is a versatile data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable…
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number…
Libpsht (or "library for Performant Spherical Harmonic Transforms") is a collection of algorithms for efficient conversion between spatial-domain and spectral-domain representations of data defined on the sphere. The package supports…
This work deals with special nested objects arising in massive higher order perturbative calculations in renormalizable quantum field theories. On the one hand we work with nested sums such as harmonic sums and their generalizations…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schr\"odinger equation we…
Many problems in robotics are fundamentally problems of geometry, which lead to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie…
An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica…
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…
It is our intention here only to discuss the nature, complexity and tools concerning the design of Smart Help, an expert help facility for aiding users of Computer Algebra Systems. Although the expert help system presented here has been…
Nowadays the Science progress depends on the numerical calculus, due to the possibility of obtention of solutions using simulations which would be impracticable, or even impossible, to be analitically obtained. In this aspect, it becomes…
A group of satellites, with either homogeneous or heterogeneous orbital characteristics and/or hardware specifications, can undertake a reconfiguration process due to variations in operations pertaining to Earth observation missions. This…
We report on implementations for algorithms treating algebraic and arithmetic properties of hypergeometric functions in the computer algebra system SageMath. We treat hypergeometric series over the rational numbers, over finite fields, and…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system has a universal enveloping Poisson algebra. Finally, we…
This paper introduces Tiramisu, a polyhedral framework designed to generate high performance code for multiple platforms including multicores, GPUs, and distributed machines. Tiramisu introduces a scheduling language with novel extensions…
Pauli matrices and Pauli strings are widely used in quantum computing. These mathematical objects are useful to describe or manipulate the quantum state of qubits. They offer a convenient basis to express operators and observables used in…