Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Algorithms for computer algebra
Algorithms for computer algebra
Zeros, multiplicities, and idempotents for zero-dimensional systems
Algorithms in algebraic geometry and applications
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Modern computer algebra
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
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
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Complexity results for triangular sets
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Sharp estimates for triangular sets
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 regular chains in positive dimension
Theoretical Computer Science
Algebraic Complexity Theory
Algorithms for computing triangular decomposition of polynomial systems
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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We give bit-size estimates for the coefficients appearing in triangular sets describing positive-dimensional algebraic sets defined over Q. These estimates are worst case upper bounds; they depend only on the degree and height of the underlying algebraic sets. We illustrate the use of these results in the context of a modular algorithm. This extends the results by the first and the last author, which were confined to the case of dimension 0. Our strategy is to get back to dimension 0 by evaluation and interpolation techniques. Even though the main tool (height theory) remains the same, new difficulties arise to control the growth of the coefficients during the interpolation process.