NDLI: A Computer Program for the Nonnumerical Testing and Reduction of Sets of Algebraic Partial Differential Equations

Content Provider	ACM Digital Library
Author	Brans, Carl H.
Copyright Year	1967
Abstract	A program is described which enables a digital computer to perform the formal algebraic manipulations and differentiations required to test a set of algebraic partial differential equations for consistency, and, if the set is consistent, to reduce the equations in it to such an extent that the nature of the arbitrary functions uniquely generating all local, analytic solutions is apparent upon inspection. The computer performs these operations on polynomials in a nonnumerical sense, treating variables and derivatives of variables precisely as they are treated in the symbolic operations of algebra and calculus. The language which permits the computer to deal with variables and polynomials in this fashion is described. The general mathematical problem of testing and reduction of sets of algebraic partial differential equations is briefly described together with the techniques available for resolving it as adapted to this computer language. A brief description of the FORTRAN program itself is also given. The motivation for the development of this program was the study of the Einstein gravitational equations in general relativity. It has been shown that these equations can be invariantly reduced to a finite number of sets of algebraic partial differential equations, and the problem of testing and reducing these sets led to this program. The program reported on in this paper has been successfully tested for comparatively simple problems, some of which are described here, but must be further developed for the relativity applications.
Starting Page	45
Ending Page	62
Page Count	18
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/321371.321375
Journal	Journal of the ACM (JACM)
Volume Number	14
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1967-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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

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