Parallelization of modular algorithms

DOI10.1016/j.jsc.2011.01.003zbMath1229.13002arXiv1005.5663OpenAlexW2157817077MaRDI QIDQ2430024

Nazeran Idrees, Gerhard Pfister, Stefan Steidel

Publication date: 5 April 2011

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.5663

zbMATH Keywords

decompositionGröbner basesparallel computationmodular computation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Parallel algorithms in computer science (68W10) Parallel numerical computation (65Y05) Numerical algorithms for computer arithmetic, etc. (65Y04)

Related Items

Solving via Modular Methods, Local to Global Algorithms for the Gorenstein Adjoint Ideal of a Curve, Gröbner bases of symmetric ideals, Modular techniques for noncommutative Gröbner bases, Modular computations of standard bases for subalgebras, Usage of modular techniques for efficient computation of ideal operations, On the modular computation of Gröbner bases with integer coefficients, Parallel modular computation of Gröbner and involutive bases, Computing and using minimal polynomials, Ideals Modulo a Prime, The use of bad primes in rational reconstruction

Uses Software

• SINGULAR
• SymbolicData
• PoSSo
• assprimeszerodim.lib
• modstd.lib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localization and primary decomposition of polynomial ideals
• Mapping integers and Hensel codes onto Farey fractions
• Gröbner bases and primary decomposition of polynomial ideals
• A p-adic approach to the computation of Gröbner bases
• A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic \(n\)-roots
• Direct methods for primary decomposition
• On lucky ideals for Gröbner basis computations
• On lucky primes
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Modular algorithms for computing Gröbner bases.
• Radical computations of zero-dimensional ideals and real root counting.
• Solving polynomial equations. Foundations, algorithms, and applications
• Computing the primary decomposition of zero-dimensional ideals
• Some comments on the modular approach to Gröbner-bases
• A Singular Introduction to Commutative Algebra
• P-adic reconstruction of rational numbers