NDLI: A view on the future of symbolic computation

Please wait, while we are loading the content...

A view on the future of symbolic computation

D-finiteness: algorithms and applications

On a finite kernel theorem for polynomial-type optimization problems and some of its applications

Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula

Signature of symmetric rational matrices and the unitary dual of lie groups

Sum of roots with positive real parts

Algebraic general solutions of algebraic ordinary differential equations

Adherence is better than adjacency: computing the Riemann index using CAD

Fast algorithms for polynomial solutions of linear differential equations

Non complete integrability of a magnetic satellite in circular orbit

Symmetric and semisymmetric graphs construction using G-graphs

Picard--Vessiot extensions for linear functional systems

On using bi-equational constraints in CAD construction

Hybrid symbolic-numeric integration in multiple dimensions via tensor-product series

A BLAS based C library for exact linear algebra on integer matrices

Structure and asymptotic expansion of multiple harmonic sums

Lifting techniques for triangular decompositions

Computing the multiplicity structure in solving polynomial systems

Algorithms for the non-monic case of the sparse modular GCD algorithm

Computing μ-bases of rational curves and surfaces using polynomial matrix factorization

Efficient computation of the characteristic polynomial

Selfintersections of a bézier bicubic surface

A procedure for proving special function inequalities involving a discrete parameter

Generalized Loewy-decomposition of d-modules

On computing nearest singular hankel matrices

A reliable block Lanczos algorithm over small finite fields

Schur partition for symmetric ternary forms and readable proof to inequalities

Affine transformations of algebraic numbers

Architecture-aware classical Taylor shift by 1

On the complexity of factoring bivariate supersparse (Lacunary) polynomials

Generic matrix multiplication and memory management in linBox

Exact analytical solutions to the nonlinear Schrödinger equation model

Half-GCD and fast rational recovery

Application of Wu's method to symbolic model checking

Probabilistic algorithms for computing resultants

Generalized normal forms and polynomial system solving

Domains and expressions: an interface between two approaches to computer algebra

Symbolic-numeric completion of differential systems by homotopy continuation

Algorithms for symbolic/numeric control of affine dynamical systems

Finding telescopers with minimal depth for indefinite nested sum and product expressions

Multivariate power series multiplication

Partial degree formulae for rational algebraic surfaces

Computing the rank and a small nullspace basis of a polynomial matrix

Approximation of dynamical systems using s-systems theory: application to biological systems

Generalized laplace transformations and integration of hyperbolic systems of linear partial differential equations

Preconditioners for singular black box matrices

Solving second order linear differential equations with Klein's theorem

Deterministic equation solving over finite fields

Stability analysis of biological systems with real solution classification

An open problem on metric invariants of tetrahedra

Admissible orderings and finiteness criteria for differential standard bases

A view on the future of symbolic computation

Content Provider	ACM Digital Library
Author	Buchberger, Bruno
Abstract	Since approximately 1960, symbolic computation added algebraicalgorithms (polynomial algorithms, simplification algorithms forexpressions, algorithms for integration, algorithms for theanalysis of algebraic structures like groups etc.) to numerics andprovided both numerical and algebraic algorithms in the frame ofpowerful integrated mathematical software systems like Macsyma,Reduce,., Mathematica, Maple,. Various wonderful tools likegraphics, notebook facilities, extensible two-dimensional syntaxetc. greatly enhanced the attractivity of these systems formathematicians, scientists, and engineers. Over the recent decades,sometimes based on very early work in the 19th century, new anddeep research results in various branches of mathematics have beendeveloped by the symbolic computation research community which ledto an impressive variety of new algebraic algorithms.In parallel, in a different community, based on new and deepresults in mathematical logic, algorithms and systems for automatedtheorem proving were developed. In the editorial for the Journal ofSymbolic Computation (1985), I tried to offer this journal as acommon forum for both the computer algebra and the computationallogic community and for the interaction and merge of the twofields. In fact, in some specific theorem proving methods (as, forexample, decision methods for the first order theory of real closedfields and decision methods for geometry), algebraic techniquesplay an important role. However, we are not yet at a stage whereboth worlds, the world of computational algebra (thealgorithmization of the object level of mathematics) and the worldof computational logic (the algorithmization of the meta-level ofmathematics) would find there common frame in terms of integratedmathematical software systems.In the talk, I will sketch a view on future symbolic computationthat hopefully will integrate numerics, computer algebra, andcomputational logic in a unified frame and will offer softwaresystems for supporting the entire process of what could be called"mathematical theory exploration" or "mathematical knowledgemanagement". In this view, symbolic computation is not only aspecific part of mathematics but, rather, will be specific way ofdoing mathematics.This will have drastic effects on the way howresearch, education, and application in mathematics will bepossible and the publication, accumulation, and use of mathematicalknowledge will be organized. We envisage a kind of "Bourbakism ofthe 21st century", which will be very different --- and partly inopposition to --- the Bourbakism of the 20th century.
Starting Page	1
Ending Page	1
Page Count	1
File Format	PDF
ISBN	1595930957
DOI	10.1145/1073884.1073885
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-07-24
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in