Algebraic simplification: a guide for the perplexed
Communications of the ACM
Computers and computations in algebraic number theory
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Factoring polynomials over large finite fields*
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algorithms for partial fraction decomposition and rational function integration
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Integration in Finite Terms with Special Functions: the Error Function
Journal of Symbolic Computation
Symbolic integration of expressions involving unspecified functions
ACM SIGSAM Bulletin
Journal of Symbolic Computation
Integration of elementary functions
Journal of Symbolic Computation
Dagwood: a system for manipulating polynomials given by straight-line programs
ACM Transactions on Mathematical Software (TOMS)
Journal of the ACM (JACM)
The Undecidability of the Existence of Zeros of Real Elementary Functions
Journal of the ACM (JACM)
Analytically Solving Integral Equations by Using Computer Algebra
ACM Transactions on Mathematical Software (TOMS)
Towards a general theory of special functions
Communications of the ACM
Indefinite Integration as a Testbed for Developments in Multi-agent Systems
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Symbolic mathematical computation in a Ph.D. computer science program
SIGCSE '72 Proceedings of the second SIGCSE technical symposium on Education in computer science
An introduction to the Risch integration algorithm
ACM '76 Proceedings of the 1976 annual conference
Applications of symbolic programs to complex analysis
ACM '72 Proceedings of the ACM annual conference - Volume 2
A new REDUCE model for algebraic simplification
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Automatic symbolic solution of differential equations of first order and first degree
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
A study of alternative methods for the symbolic calculation of elliptic integrals
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Computer algebra and numerical integration
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
User-based integration software
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Symbolic mathematical computation in a Ph. D. computer science program
ACM SIGCSE Bulletin
Hypercomputation by definition
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Symbolic integration of a class of algebraic functions
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Implications of symbolic computation for the teaching of mathematics
ACM SIGSAM Bulletin
Course outline: Yale University, New Haven
ACM SIGSAM Bulletin
Factoring multivariate polynomials over algebraic number fields in MACSYMA
ACM SIGSAM Bulletin
A short survey on the state of the art in matching and unification problems
ACM SIGSAM Bulletin
A novel symbolic ordinary differential equation solver
ACM SIGSAM Bulletin
Symbolic mathematical computation: a survey
ACM SIGSAM Bulletin
A Performability Solution Method for Degradable Nonrepairable Systems
IEEE Transactions on Computers
Interactive learning and mathematical calculus
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
| Hi-index | 48.24 |
Three approaches to symbolic integration in the 1960's are described. The first, from artificial intelligence, led to Slagle's SAINT and to a large degree to Moses' SIN. The second, from algebraic manipulation, led to Manove's implementation and to Horowitz' and Tobey's reexamination of the Hermite algorithm for integrating rational functions. The third, from mathematics, led to Richardson's proof of the unsolvability of the problem for a class of functions and for Risch's decision procedure for the elementary functions. Generalizations of Risch's algorithm to a class of special functions and programs for solving differential equations and for finding the definite integral are also described.