Deterministic normal position transformation and its applications

DOI10.1016/j.tcs.2020.07.025zbMath1456.13017OpenAlexW3044060291MaRDI QIDQ2006776

Benyamin M.-Alizadeh, Amir Hashemi

Publication date: 12 October 2020

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

Full work available at URL: https://doi.org/10.1016/j.tcs.2020.07.025

zbMATH Keywords

Gröbner basespolynomial idealsdeterministic algorithmshape lemmanormal position

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 (1)

DetNorPos.mpl

Uses Software

• Kronecker
• Bertini
• ISOLATE

Cites Work

• Algorithms for computing triangular decomposition of polynomial systems
• Evaluation techniques for zero-dimensional primary decomposition
• Gröbner bases and primary decomposition of polynomial ideals
• Factoring polynomials with rational coefficients
• The membership problem for unmixed polynomial ideals is solvable in single exponential time
• Solving zero-dimensional systems through the rational univariate representation
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• On the stability of Gröbner bases under specializations
• Deterministic genericity for polynomial ideals
• Solving polynomial equations. Foundations, algorithms, and applications
• Gröbner bases of ideals defined by functionals with an application to ideals of projective points
• A concise proof of the Kronecker polynomial system solver from scratch
• 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
• A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases
• An FGLM-like algorithm for computing the radical of a zero-dimensional ideal
• Using Algebraic Geometry
• Numerical Polynomial Algebra
• A zero structure theorem for polynomial-equations-solving and its applications
• A Gröbner free alternative for polynomial system solving
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