Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
Fast construction of irreducible polynomials over finite fields
Journal of Symbolic Computation
Zeros, multiplicities, and idempotents for zero-dimensional systems
Algorithms in algebraic geometry and applications
Efficient computation of minimal polynomials in algebraic extensions of finite fields
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Challenges of symbolic computation: my favorite open problems
Journal of Symbolic Computation
Using Galois ideals for computing relative resolvents
Journal of Symbolic Computation - Algorithmic methods in Galois Theory
A Gröbner free alternative for polynomial system solving
Journal of Complexity
When Polynomial Equation Systems Can Be "Solved" Fast?
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
In-place Arithmetic for Polinominals over Zn
DISCO '92 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Tellegen's principle into practice
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Modern Computer Algebra
Complexity results for triangular sets
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Complexity issues in bivariate polynomial factorization
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Change of order for bivariate triangular sets
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast arithmetic for triangular sets: From theory to practice
Journal of Symbolic Computation
Computations modulo regular chains
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Fast computation of special resultants
Journal of Symbolic Computation
Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Algebraic Complexity Theory
The modpn library: Bringing fast polynomial arithmetic into Maple
Journal of Symbolic Computation
Homotopy techniques for multiplication modulo triangular sets
Journal of Symbolic Computation
Fast Polynomial Factorization and Modular Composition
SIAM Journal on Computing
On the complexity of solving bivariate systems: the case of non-singular solutions
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We study the complexity of some fundamental operations for triangular sets in dimension zero. Using Las Vegas algorithms, we prove that one can perform such operations as change of order, equiprojectable decomposition, or quasi-inverse computation with a cost that is essentially that of modular composition. Over an abstract field, this leads to a subquadratic cost (with respect to the degree of the underlying algebraic set). Over a finite field, in a boolean RAM model, we obtain a quasi-linear running time using Kedlaya and Umans@? algorithm for modular composition. Conversely, we also show how to reduce the problem of modular composition to change of order for triangular sets, so that all these problems are essentially equivalent. Our algorithms are implemented in Maple; we present some experimental results.