Algorithm 628: An algorithm for constructing canonical bases of polynomial ideals
ACM Transactions on Mathematical Software (TOMS)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
ACM '73 Proceedings of the ACM annual conference
Some comments on the modular approach to Gröbner-bases
ACM SIGSAM Bulletin
On improving approximate results of Buchberger's algorithm by Newton's method
ACM SIGSAM Bulletin
Implementing the Baumslag-Cannonito-Miller polycyclic quotient algorithm
Journal of Symbolic Computation
On the complexity of computing a Gröbner basis for the radical of a zero dimensional ideal
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A heuristic selection strategy for lexicographic Gröner bases?
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
An improved algorithm for the resolution of singularities
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Gröbner Bases: A Short Introduction for Systems Theorists
Computer Aided Systems Theory - EUROCAST 2001-Revised Papers
Modular algorithms for computing Gröbner bases
Journal of Symbolic Computation
Computer algebra handbook
Complexity results for triangular sets
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
A minimal solution for relative pose with unknown focal length
Image and Vision Computing
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Parallelization of Modular Algorithms
Journal of Symbolic Computation
Usage of modular techniques for efficient computation of ideal operations
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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A method for the p-adic lifting of a Grobner basis is presented. If F is a finite vector of polynomials in @?[x"1,...,x"1] and p is a lucky prime for F (it turns out that there are only finitely many unlucky primes) then in a first step the normalized reduced Grobner basis G^(^0^) for F modulo p is computed, together with matrices Y^(^0^) and R^(^0^) such that Y^(^0^), G^(^0^)=F (mod p) and R^(^0^). G^(^0^)=0(mod p), where the rows of R^(^0^) are the syzygies of G^(^0^) derived from the reduction of the S-polynomials of G^(^0^) to 0. These congruences can be lifted to congruences modulo p^i, for any natural number i, finally leading to the normalized reduced Grobner basis for F in @?[x"1,...,x"1].