Related papers: CGAlgebra: a Mathematica package for conformal geo…
We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a wide range of combinatorial theories, can numerically…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…
PGA (ProGram Algebra) is an algebra of programs which concerns programs in their simplest form: sequences of instructions. Molecular dynamics is a simple model of computation developed in the setting of PGA, which bears on the use of…
A short survey on applications of algebraic geometry in topological data analysis.
We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
A brief characteristic of the specialized computer algebra system GRG_EC intended for symbolic computations in the field of general relativity is given.
The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology
We introduce log-log convex programs, which are optimization problems with positive variables that become convex when the variables, objective functions, and constraint functions are replaced with their logs, which we refer to as a log-log…
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the…
The conformal Galilei algebra (CGA) and the exotic conformal Galilei algebra (ECGA) are applied to construct partial differential equations (PDEs) and systems of PDEs, which admit these algebras. We show that there are no single…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
This is a tutorial in applied and computational topology and topological data analysis. It is illustrated with numerous computational examples that utilize Gudhi library. It is under constant development, so please do not consider this…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in…
Algebraic-geometrical n-orthogonal curvilinear coordinate systems in a flat space are constructed. They are expressed in terms of the Riemann theta function of auxiliary algebraic curves. The exact formulae for the potentials of algebraic…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…