Algebraic Simplification: A Guide for the Perplexed

Communications of the ACM

Volumn 14, Issue 8, 1971, Pages 527-537

  Moses, Joel ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

algebraic manipulation; algebraic simplification; canonical simplification

Indexed keywords

ALGEBRAIC MANIPULATION;

COMPUTERS, DIGITAL--PROGRAMMING;

EID: 0015111095     PISSN: 00010782     EISSN: 15577317     Source Type: Journal    
DOI: 10.1145/362637.362648     Document Type: Article

References (32)

1. Abrahams, P.W. Application of LISP to sequence prediction. Comm. ACM 9, 8 (Aug. 1966), 551.
2. Brown, W.S., et al. The ALPAK system for non-numerical algebra on a Digital Computer-II. Bell Sys. Tech. J. 43, 2 (Mar. 1964), 785-804.
3. Brown, W.S. Rational exponential expressions and a conjecture concerning p and e. Amer. Math. Monthly 76 (Jan. 1969), 28-34.
4. Caviness, B.F. On canonical forms and simplification. Ph.D. diss., Carnegie-Mellon U., Pittsburgh, Pa., Aug. 1967.
5. Caviness, B.F. On canonical forms and simplification. J. ACM 17, 2 (Apr. 1970), 385-396.
6. Collins, G.P.M., A system for polynomial manipulation. Comm. ACM 9, 8 (Aug. 1966), 578-589.
7. Collins, G. The SAC-I system: An introduction and survey. SYMSAM II, pp. 144-152.
8. Collins, G. Subresultant and reduced polynomial remainder sequences. J. ACM 14, 1 (Jan. 1967), 128-142.
9. Engelman, C. The legacy of MATHLAB 68. SYMSAM II, pp. 29-41.
10. Engeli, M. User's manual for the formula manipulation language SYMBAL. Computer Center, U. of Texas at Austin, 1968.
11. Fateman, R. The user-level semantic matching capability in MACSYMA. Proc. 2nd. Symp. on Symbolic and Algebraic Manipulation, ACM Headquarters, New York, pp. 311-323.
12. Fateman, R. Essays in algebraic simplification. Ph.D. diss., Harvard U., Cambridge, Mass., 1971.
13. Fenichel, R. An on-line system for algebraic manipulation. Ph.D. diss., Harvard U., Cambridge, Mass., 1966.
14. Griesmer, J.H., and Jenks, R.D. scratchpad/1: An interactive facility for symbolic mathematics, symsam II, pp. 42-48.
15. Hall, A.D. The ALTRAN system for rational function manipulation—A survey. Comm. ACM 14, 8 (Aug. 1971), 517-52.
16. Hearn, A. REDUCE: A user-oriented interactive system for algebraic simplification. In Interactive Systems for Experimental Applied Mathematics. Academic Press, New York, 1968, pp. 79-89.
17. Hearn, A. The Problem of Substitution. Proc. 1968 Summer Inst. on Symbolic Math. Comput. IBM, Cambridge, Mass., pp. 3-11.
18. Hearn, A. REDUCE 2: A system and language for algebraic manipulation. Proc. 2nd Symp. on Symbolic and Algebraic Manipulation, ACM Headquarters, New York, pp. 128-135.
19. Korsvold, K. An on-line algebraic simplification program. Artif. Intell. Proj. Memo. no. 37, Stanford U., Stanford, Cal., Nov. 1965.
20. Martin, W., and Fateman, R. The MACSYMA system. SYMSAM II, PP. 59-75.
21. Matijasevic, J.V. Enumerable sets are diophantine. Soviet Math. Dokl., 11, 1970.
22. Minsky, M., and Papert, S. Perceptrons. MIT Press, Cambridge Mass., 1969.
23. Moses, J. Symbolic integration. Report MAC-TR-47, Project MAC, mit, Cambridge, Mass., Dec. 1967. (Available as AD #662-666, Clearinghouse, Springfield, Va. 22151.)
24. Oldehoeft, A. Analysis of constructed mathematical responses by numeric tests for equivalence. Proc. ACM 24th Nat. Conf., 1969, ACM, New York, pp. 117-124.
25. Moses, J., Rothschild, L.P., and Schroeppel, R. A zero-equivalence algorithm for expressions formed by functions definable by first order differential equations. In preparation.
26. Perlis, A., et al. A definition of Formula Algol. Comput. Center, Carnegie-Mellon U., Pittsburgh, Pa., Mar. 1966.
27. Richardson, D. Some unsolvable problems involving functions of a real variable. Ph.D. diss., U. of Bristol, England, 1966.
28. Richardson, D. Some unsolvable problems involving elementary functions of a real variable. J. Symb. Logic 33 (1968), 511-520.
29. Richardson, D. A solution of the identity problem for integral exponential functions. Z. Math Logik u. Grundlagen Math, to appear.
30. Simon, H. The Science of the Artificial. mit Press, Cambridge, Mass., 1969.
31. Tobey, R. Experience with FORMAC algorithm design. Comm. ACM 9, 8 (Aug. 1966), 589-597.
32. Tobey, R., et al. Automatic simplification in FORMAC. Proc. AFIPS 1965 FJCC, Vol. 27, Pt. 1, Spartan Books, New York, pp. 37-57.