Survey of formula manipulation
Communications of the ACM
A differential-equations approach to functional equivalence
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Growth estimates for exp-log functions
Journal of Symbolic Computation
Determining the Equivalence of Algebraic Expressions by Hash Coding
Journal of the ACM (JACM)
Algebraic simplification: a guide for the perplexed
Communications of the ACM
Experiments with an automated instructional system for numerical methods
Communications of the ACM
Algebraic simplification a guide for the perplexed
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Determining the equivalence of algebraic expressions by hash coding
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Rationally simplifying non-rational expressions
ACM SIGSAM Bulletin
Initial experiences with a program to teach numerical methods
ACM SIGNUM Newsletter
| Hi-index | 0.03 |
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.