Pivoting in extended rings for computing approximate Gröbner bases

DOI10.1007/s11786-011-0089-yzbMath1252.68356OpenAlexW2042569450MaRDI QIDQ691644

Jean-Charles Faugère, Ye Liang

Publication date: 3 December 2012

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-011-0089-y

zbMATH Keywords

monomial basisapproximate Gröbner basis\(F_5\) algorithmartificial discontinuity

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items (2)

Matrix-F5 algorithms and tropical Gröbner bases computation ⋮ Approximate Gröbner bases, overdetermined polynomial systems, and approximate GCDs

Uses Software

• FGb
• ISOLATE

Cites Work

• Artificial discontinuities of single-parametric Gröbner bases
• Computing border bases
• Stable border bases for ideals of points
• Remarks on automatic algorithm stabilization
• Solving zero-dimensional systems through the rational univariate representation
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Floating point Gröbner bases.
• Characterizations of border bases
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Term Cancellations in Computing Floating-Point Gröbner Bases
• Floating-Point Gröbner Basis Computation with Ill-conditionedness Estimation
• Numerical Polynomial Algebra
• Generalized normal forms and polynomial system solving
• Computer Algebra and Geometric Algebra with Applications
• Finding at least one point in each connected component of a real algebraic set defined by a single equation
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