Article

Free access

Analysis of constructed mathematical responses by numeric tests for equivalence

Author:

Arthur E. OldehoeftAuthors Info & Claims

ACM '69: Proceedings of the 1969 24th national conference

Pages 117 - 124

https://doi.org/10.1145/800195.805923

Published: 26 August 1969 Publication History

PDF eReader

Abstract

A method is described to determine if a constructed mathematical response is equivalent to the correct answer specified by the course author. Based on a combination of random evaluation and operator analysis, the method is theoretically justified for a general class of functions. Possible breakdowns due to computer arithmetic are discussed as well as the difficulties encountered when a function fails to fall in the general class. For CAI applications where a response is considered correct if it is equivalent to the correct answer, the method offers two possible advantages: (1) Only one form of the correct answer is specified. (2) Extensive and time consuming manipulation of expressions is avoided.

References

[1]

Bellman, R., "On Proving Theorems in Plane Geometry via Digital Computer", The American Mathematical Monthly, vol. 73, pp. 1107-1109, November, 1966.

Google Scholar

[2]

Bochner, S. and Martin, W.T., "Several Complex Variables", Princeton University Press, 1948.

Google Scholar

[3]

Caviness, B.F., "On Canonical Forms and Simplification", Doctoral Dissertation, Carnegie-Mellon University, May, 1968.

Google Scholar

[4]

Engeli, M.E., "Achievements and Problems in Formula Manipulation", IFIP Congress 68, pp. 79-84.

Google Scholar

[5]

Feingold, S.L. and Frye, C.H., "User's Guide to PLANIT", TM-3055/000/01, System Development Corporation, October, 1966.

Google Scholar

[6]

Gunning, R.C. and Rossi, H. "Analytic Functions of Several Complex Variables", Prentice-Hall, Inc., 1965.

Google Scholar

[7]

Korfhage, R., Hochgesang, G., Oldehoeft, A., Mitzell, M., "PICLS, Purdue Instructional and Computational Learning System", CSD TR 28, Purdue University, October, 1968.

Google Scholar

[8]

Manacher, G.K., "A Content-Evaluating Mode of Computer-Aided Instruction", Interactive Systems for Experimental Applied Mathematics. pp. 286-293, Academic Press, 1968.

Google Scholar

[9]

Martin, W.A., "Symbolic Mathematical Laboratory", Doctoral Dissertation, MAC-TR-36, Massachusetts Institute of Technology, January, 1967.

Google Scholar

[10]

Sammet, J.E., "An Annotated Descriptor Based Bibliography on the Use of Computers for Non-Numerical Mathematics", Computing Reviews, vol. 7, no. 4, pp. B1-B31, July-August, 1966.

Google Scholar

[11]

Sammet, J.E., "Survey of Formula Manipulation", Comm. of the ACM, vol. 9, no. 8, pp. 555-569, August, 1966.

Digital Library

Google Scholar

Cited By

View all

Shackell J(1993)Zero-equivalence in function fields defined by algebraic differential equationsTransactions of the American Mathematical Society10.1090/S0002-9947-1993-1088022-2336:1(151-171)Online publication date: 1993
https://doi.org/10.1090/S0002-9947-1993-1088022-2
Shackle J(1989)A differential-equations approach to functional equivalenceProceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation10.1145/74540.74542(7-10)Online publication date: 17-Jul-1989
https://dl.acm.org/doi/10.1145/74540.74542
Fateman R(1972)Rationally simplifying non-rational expressionsACM SIGSAM Bulletin10.1145/1093522.1093523(8-9)Online publication date: 1-Jul-1972
https://dl.acm.org/doi/10.1145/1093522.1093523
Show More Cited By

Index Terms

Analysis of constructed mathematical responses by numeric tests for equivalence
1. Applied computing
  1. Education
    1. Computer-assisted instruction
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Arbitrary-precision arithmetic
      2. Interval arithmetic

Recommendations

Combined-semantics equivalence of conjunctive queries

Query containment and equivalence are fundamental problems in the context of query processing and optimization. In this paper, we consider combined-semantics equivalence of conjunctive (CQ) queries. The combined-semantics formalism 10,11 generalizes the ...
Equivalence and minimization of conjunctive queries under combined semantics
ICDT '12: Proceedings of the 15th International Conference on Database Theory

The problems of query containment, equivalence, and minimization are fundamental problems in the context of query processing and optimization. In their classic work [2] published in 1977, Chandra and Merlin solved the three problems for the language of ...
Equivalence of SQL queries in presence of embedded dependencies
PODS '09: Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems

We consider the problem of finding equivalent minimal-size reformulations of SQL queries in presence of embedded dependencies [1]. Our focus is on select-project-join (SPJ) queries with equality comparisons, also known as safe conjunctive (CQ) queries, ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

ACM '69: Proceedings of the 1969 24th national conference

August 1969

686 pages

ISBN:9781450374934

DOI:10.1145/800195

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 August 1969

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
98
Total Downloads

Downloads (Last 12 months)48
Downloads (Last 6 weeks)7

Reflects downloads up to 18 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Shackell J(1993)Zero-equivalence in function fields defined by algebraic differential equationsTransactions of the American Mathematical Society10.1090/S0002-9947-1993-1088022-2336:1(151-171)Online publication date: 1993
https://doi.org/10.1090/S0002-9947-1993-1088022-2
Shackle J(1989)A differential-equations approach to functional equivalenceProceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation10.1145/74540.74542(7-10)Online publication date: 17-Jul-1989
https://dl.acm.org/doi/10.1145/74540.74542
Fateman R(1972)Rationally simplifying non-rational expressionsACM SIGSAM Bulletin10.1145/1093522.1093523(8-9)Online publication date: 1-Jul-1972
https://dl.acm.org/doi/10.1145/1093522.1093523
Martin WSammet JTobey RMoses J(1971)Determining the equivalence of algebraic expressions by hash codingProceedings of the second ACM symposium on Symbolic and algebraic manipulation10.1145/800204.806299(305-310)Online publication date: 23-Mar-1971
https://dl.acm.org/doi/10.1145/800204.806299
Moses JSammet JTobey RMoses J(1971)Algebraic simplification a guide for the perplexedProceedings of the second ACM symposium on Symbolic and algebraic manipulation10.1145/800204.806298(282-304)Online publication date: 23-Mar-1971
https://dl.acm.org/doi/10.1145/800204.806298
Oldehoeft AConte S(1971)Experiments with an automated instructional system for numerical methodsCommunications of the ACM10.1145/362759.36279114:10(643-650)Online publication date: 1-Oct-1971
https://dl.acm.org/doi/10.1145/362759.362791
Moses J(1971)Algebraic simplificationCommunications of the ACM10.1145/362637.36264814:8(527-537)Online publication date: 1-Aug-1971
https://dl.acm.org/doi/10.1145/362637.362648
Oldehoeft AConte S(1970)Initial experiences with a program to teach numerical methodsACM SIGNUM Newsletter10.1145/1198456.11984585:2(17-20)Online publication date: 1-Aug-1970
https://dl.acm.org/doi/10.1145/1198456.1198458

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Combined-semantics equivalence of conjunctive queries

Equivalence and minimization of conjunctive queries under combined semantics

Equivalence of SQL queries in presence of embedded dependencies