The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On Canonical Forms and Simplification
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Algebraic simplification: a guide for the perplexed
Communications of the ACM
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Using basis computation to determine pseudo-multiplicative independence
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
ESSAYS IN ALGEBRAIC SIMPLIFICATION
ESSAYS IN ALGEBRAIC SIMPLIFICATION
Algorithms for polynomials over a real algebraic number field.
Algorithms for polynomials over a real algebraic number field.
Algorithms for elementary transcendental function arithmetic.
Algorithms for elementary transcendental function arithmetic.
Factoring multivariate polynomials over algebraic number fields in MACSYMA
ACM SIGSAM Bulletin
Detecting algebraic dependencies between unnested radicals (extended abstract)
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Algorithm 628: An algorithm for constructing canonical bases of polynomial ideals
ACM Transactions on Mathematical Software (TOMS)
On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On the normalization of numbers and functions defined by radicals
Journal of Symbolic Computation
Automated simplification of large symbolic expressions
Journal of Symbolic Computation
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In this paper we discuss the problem of simplifying unnested radical expressions. We describe an algorithm implemented in MACSYMA that simplifies radical expressions and then follow this description with a formal treatment of the problem. Theoretical computing times for some of the algorithms are briefly discussed as is related work of other authors.