the paper focuses on means of defining parameterized type categories and algorithms built on such types in Mathematica. symbolicalgorithms based on category theory have the advantage of systematically dealing with do...
详细信息
ISBN:
(纸本)9780769527406
the paper focuses on means of defining parameterized type categories and algorithms built on such types in Mathematica. symbolicalgorithms based on category theory have the advantage of systematically dealing with domains, categories, operators over them by creating general contexts Of expressing algorithms, which can be applied by parameterizing them with various domains, using the same algorithm definition. While similar approaches have been previously presented by the author, the present paper aims at a stronger focus on algorithm characteristics defined on categorical principles and giving a more general framework for implementing Mathematica algorithms based on genetic principles and category theory. the paper also discusses run time efficiency aspects for these generic implementations.
In my PhD thesis 1965 and the subsequent publication 1970 in Aequationes Mathematicae, I introduced the notion of Grobner bases and proved a characterization theorem for Grobner bases on which an algorithm for constru...
详细信息
ISBN:
(纸本)9781538626269
In my PhD thesis 1965 and the subsequent publication 1970 in Aequationes Mathematicae, I introduced the notion of Grobner bases and proved a characterization theorem for Grobner bases on which an algorithm for constructing Grobner bases can be based. the main idea for the theorem and the algorithm was the notion of \"�S-polynomials\"�. Most of the subsequent work on the algorithmic theory of Grobner bases, including the implementation of the Grobner bases technology in mathematical software systems like Mathematica, Maple, etc. was based on this approach.
We propose general preprocessing techniques to reshape dense multivariate polynomials over finite fields, in order to minimize the cost of memory accesses, while preserving sufficient parallelism, so as to reduce the ...
详细信息
ISBN:
(纸本)9781665465458
We propose general preprocessing techniques to reshape dense multivariate polynomials over finite fields, in order to minimize the cost of memory accesses, while preserving sufficient parallelism, so as to reduce the running time of polynomial multiplication in multi-threaded implementations.
We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computa...
详细信息
ISBN:
(纸本)9780769546308
We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computations in Maple, C++ and Linux. Results of our computing experiences are presented in a table of Section 2 and in Section 6.
An important and challenging computational problem is to identify and include the missing compatibility (integrability) conditions for general systems of partial differential equations. the inclusion of such missing c...
详细信息
ISBN:
(纸本)9798350394139;9798350394122
An important and challenging computational problem is to identify and include the missing compatibility (integrability) conditions for general systems of partial differential equations. the inclusion of such missing conditions is executed by the application of differential-elimination algorithms. Differential equations arising during modeling generally contain both exactly known coefficients and coefficients known approximately from data. We focus on our recent work on approximate differential-elimination methods and in particular their application to the determination of approximate symmetries. We illustrate this with applications to a class of Schrodinger equations.
In this paper we study the ladder operators for little q-Jacobi polynomials and for polynomials orthogonal with respect to a generalized q-Jacobi weight. We also briefly discuss the computational aspects in the comput...
详细信息
ISBN:
(纸本)9781479930357
In this paper we study the ladder operators for little q-Jacobi polynomials and for polynomials orthogonal with respect to a generalized q-Jacobi weight. We also briefly discuss the computational aspects in the computer algebra system Mathematica (***).
Widespreading and enabling machine processing of old prints relevant to a particular cultural area can be achieved using modern research infrastructures. this paper outlines the architecture of a distributed environme...
详细信息
ISBN:
(纸本)9781538626269
Widespreading and enabling machine processing of old prints relevant to a particular cultural area can be achieved using modern research infrastructures. this paper outlines the architecture of a distributed environment for optical character recognition customized for a collection comprising scanned books in old Romanian language and it also presents the preliminary results of our experiments.
the principal benefit introduced by distributed systems is the ability to use the computation power and processing capabilities of multiple processing nodes in order to solve problems infeasible on a single machine. F...
详细信息
ISBN:
(纸本)9780769539645
the principal benefit introduced by distributed systems is the ability to use the computation power and processing capabilities of multiple processing nodes in order to solve problems infeasible on a single machine. For symboliccomputingthese advantages are particularly useful. In order to create a successful distributed system to support symbolic computations is important to have a deep understanding of the way the computer algebra specialists interact with a symboliccomputing system. In this paper we investigate general processing capabilities of symboliccomputing systems related to control flow and we emphasize several execution patterns. the impact that workflow management functionalities have over general execution patterns in symboliccomputing are also investigated.
We present a denotational semantics designed with metric spaces and continuations for an abstract concurrent language embodying two new features: the semantics of parallel composition is based on the concept of maxima...
详细信息
ISBN:
(纸本)9780769546308
We present a denotational semantics designed with metric spaces and continuations for an abstract concurrent language embodying two new features: the semantics of parallel composition is based on the concept of maximal parallelism, and computations are specified by means of multiset rewriting rules. To the best of our knowledge, this is the first paper that presents a metric denotational semantics for this combination of features, encountered also in membrane computing.
We define the functional inverse of the Gamma function. It is a multivalued function, and we define its branches. We present its basic properties, included series approximations, asymptotic results and numerical evalu...
详细信息
ISBN:
(纸本)9781538626269
We define the functional inverse of the Gamma function. It is a multivalued function, and we define its branches. We present its basic properties, included series approximations, asymptotic results and numerical evaluation.
暂无评论