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)
PM, a system for polynomial manipulation
Communications of the ACM
Experience with FORMAC algorithm design
Communications of the ACM
Solutions of systems of polynomial equations by elimination
Communications of the ACM
Analysis of constructed mathematical responses by numeric tests for equivalence
ACM '69 Proceedings of the 1969 24th national conference
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
IAM, a system for interactive 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 ALTRAN system for rational function manipulation - a survey
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
On Euclid's algorithm and the computation of polynomial greatest common divisors
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
The user-level semantic matching capability in MACSYMA
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
On the problem of recognizing zero
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
REDUCE: a user-oriented interactive system for algebraic simplification
Symposium on Interactive Systems for Experimental Applied Mathematics: Proceedings of the Association for Computing Machinery Inc. Symposium
Edusym—educational symbolic manipulator on a microcomputer
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Implementation of multilinear operators in REDUCE and applications in mathematics
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
How to make AXIOM into a scratchpad
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Determining the Equivalence of Algebraic Expressions by Hash Coding
Journal of the ACM (JACM)
On the Problem of Recognizing Zero
Journal of the ACM (JACM)
An intelligent tutor for high-school algebra
CSC '87 Proceedings of the 15th annual conference on Computer Science
Symbolic mathematical computation—introduction and overview
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Applications of symbol manipulation in theoretical physics
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
Symbolic integration the stormy decade
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The optimization of user programs for an Algebraic Manipulation System
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
FORMAC today, or what can happen to an orphan
ACM SIGSAM Bulletin
An expression analysis package for REDUCE
ACM SIGSAM Bulletin
A discussion and implementation of Brown's REX simplification algorithm
ACM SIGSAM Bulletin
ACM Lisp Bulletin
A Gröbner basis approach to CNF-formulae preprocessing
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Program simplification in genetic programming for object classification
KES'05 Proceedings of the 9th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part III
Simplifying products of fractional powers of powers
ACM Communications in Computer Algebra
Probabilistic equivalence verification approach for automatic mathematical solution assessment
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Automated simplification of large symbolic expressions
Journal of Symbolic Computation
A computer algebra user interface manifesto
ACM Communications in Computer Algebra
An existence lemma for canonical forms in symbolic mathematics
Information Processing Letters
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Algebraic simplification is examined first from the point of view of a user needing 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 non-existence of algorithms for certain classes of expressions are included.