相关论文: Specialized computer algebra system for applicatio…
We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special…
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…
Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…
In connection with generalized cluster algebras we introduce a certain generalization of the celebrated Rogers dilogarithm, which we call the Rogers dilogarithms of higher degree. We show that there is an identity of these generalized…
In this paper we shall analyse the structure of the Cauchy Problem (CP briefly) for General Relativity (GR briefly) by applying the theory of first order symmetric hyperbolic systems.
The aim of this paper is to propose a strategy to implement the Minimal Model Program in modern computer algebra systems.
On behalf of the development team, I review the capabilities of the BAGEL program package in this article. BAGEL is a newly-developed full-fledged program package for electronic-structure computation in quantum chemistry, which is released…
The computer algebra system CHEVIE is designed to facilitate computations with various combinatorial structures arising in Lie theory, like finite Coxeter groups and Hecke algebras. We discuss some recent examples where CHEVIE has been…
We describe the architecture of an evolving algebra partial evaluator, a program which specializes an evolving algebra with respect to a portion of its input. We discuss the particular analysis, specialization, and optimization techniques…
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…
Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
We study the theory specialisations in algebraic geometry from a model theoretic viewpoint. In particular we investigate universality and maximality of specialisations in algebraic geometry.