The sciences of the artificial (3rd ed.)
The sciences of the artificial (3rd ed.)
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Canonical Forms and Simplification
Journal of the ACM (JACM)
The Altran system for rational function manipulation — a survey
Communications of the ACM
PM, a system for polynomial manipulation
Communications of the ACM
Experience with FORMAC algorithm design
Communications of the ACM
Analysis of constructed mathematical responses by numeric tests for equivalence
ACM '69 Proceedings of the 1969 24th national conference
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
SCRATCHPAD/1: An interactive facility for symbolic mathematics
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
REDUCE 2: A system and language for algebraic manipulation
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The SAC-1 system: An introduction and survey
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The user-level semantic matching capability in MACSYMA
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Simplification of algebraic expression by multiterm rewriting rules
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
A system for manipulating polynomials given by straight-line programs
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Introducing symbolic problem solving techniques in the dependence testing phases of a vectorizer
ICS '88 Proceedings of the 2nd international conference on Supercomputing
A differential-equations approach to functional equivalence
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Normal forms for a class of formulas
Journal of Symbolic Computation
Computing A*B (mod N) efficiently in ANSI C
ACM SIGPLAN Notices
Asymptotic expansions of functional inverses
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Symbolic analysis for parallelizing compilers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Journal of the ACM (JACM)
Automatic Error Analysis Using Computer Algebraic Manipulation
ACM Transactions on Mathematical Software (TOMS)
Symbolic Solution of Finite-Difference Equations
ACM Transactions on Mathematical Software (TOMS)
Polynomial manipulation with APL
Communications of the ACM
Communications of the ACM
Towards a general theory of special functions
Communications of the ACM
Applications of symbol manipulation in theoretical physics
Communications of the ACM
Symbolic integration: the stormy decade
Communications of the ACM
Algebraic and symbolic manipulation of Poisson series
Journal of Symbolic Computation
A perspective on symbolic mathematical computing and artificial intelligence
Annals of Mathematics and Artificial Intelligence
IEEE Transactions on Knowledge and Data Engineering
IEEE Expert: Intelligent Systems and Their Applications
Functional programming concepts and straight-line programs in computer algebra
Mathematics and Computers in Simulation
Improving and refining programs by program manipulation
ACM '76 Proceedings of the 1976 annual conference
Extended polynomial algorithms
ACM '73 Proceedings of the ACM annual conference
Limitations in pattern recognition and problem solving
ACM '72 Proceedings of the ACM annual conference - Volume 1
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
Simplification of radical expressions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Canonical representatives for residue classes of a polynomial ideal
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Automatic generation of finite difference equations and fourier stability analyses
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Breuer's grow factor algorithm in computer algebra
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Determining equivalence of expressions in random polynomial time
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Sound and complete qualitative simulation is impossible
Artificial Intelligence
Understanding expression simplification
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On computing with factored rational expressions
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Some problems connected with ambiguous expressions
ACM SIGSAM Bulletin
Course outline: Yale University, New Haven
ACM SIGSAM Bulletin
Symbolic mathematical computation: a survey
ACM SIGSAM Bulletin
Optimization Over a Class of Tree Shape Statistics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Simulation bounds for equivalence verification of polynomial datapaths using finite ring algebra
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
An essential hybrid reasoning system: knowledge and symbol level accounts of KRYPTON
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
ACM Communications in Computer Algebra
Editorial: Macsyma: A personal history
Journal of Symbolic Computation
Hi-index | 48.30 |
Algebraic simplification is examined first from the point of view of a user who needs to comprehend a large expression, and second from the point of view of a designer who wants to construct a useful and efficient system. First we describe various techniques akin to substitution. These techniques can be used to decrease the size of an expression and make it more intelligible to a user. Then we delineate the spectrum of approaches to the design of automatic simplification capabilities in an algebraic manipulation system. Systems are divided into five types. Each type provides different facilities for the manipulation and simplification of expressions. Finally we discuss some of the theoretical results related to algebraic simplification. We describe several positive results about the existence of powerful simplification algorithms and the number-theoretic conjectures on which they rely. Results about the nonexistence of algorithms for certain classes of expressions are included.