Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Functional decomposition ofpolynomials: the tame case
Journal of Symbolic Computation - Special issue on computational algebraic complexity
A fast deterministic algorithm for factoring polynomials over finite fields of small characteristic
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
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
Simple multivariate polynomial multiplication
Journal of Symbolic Computation
Asymptotically fast computation of subresultants
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fast rectangular matrix multiplication and applications
Journal of Complexity
Modern computer algebra
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
Elliptic curves in cryptography
Elliptic curves in cryptography
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases
AAECC-5 Proceedings of the 5th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Improved Sparse Multivariate Polynomial Interpolation Algorithms
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Tellegen's principle into practice
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Complexity results for triangular sets
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Change of order for bivariate triangular sets
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Computing the eigenvalue in the schoof-elkies-atkin algorithm using abelian lifts
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast polynomial factorization and modular composition in small characteristic
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fast arithmetic for triangular sets: From theory to practice
Journal of Symbolic 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
Homotopy techniques for multiplication modulo triangular sets
Journal of Symbolic Computation
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Fast Polynomial Factorization and Modular Composition
SIAM Journal on Computing
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We generalize Kedlaya and Umans' modular composition algorithm to the multivariate case. As a main application, we give fast algorithms for many operations involving triangular sets (over a finite field), such as modular multiplication, inversion, or change of order. For the first time, we are able to exhibit running times for these operations that are almost linear, without any overhead exponential in the number of variables. As a further application, we show that, from the complexity viewpoint, Charlap, Coley, and Robbins' approach to elliptic curve point counting can be competitive with the better known approach due to Elkies.