Constructive \(D\)-module theory with \texttt{Singular}

DOI10.1007/s11786-010-0058-xzbMath1217.13011OpenAlexW1984804309MaRDI QIDQ541982

Daniel Andres, Viktor Levandovskyy, Hans Schönemann, Michael Brickenstein, Jorge Martín-Morales

Publication date: 8 June 2011

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

Full work available at URL: https://doi.org/10.1007/s11786-010-0058-x

zbMATH Keywords

\(D\)-modulesBernstein-Sato polynomials\(b\)-functionannihilator idealsnon-commutative Gröbner bases

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) Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10)

Related Items

Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic \(D\)-modules, Modular techniques for noncommutative Gröbner bases, Holonomic functions and prehomogeneous spaces, Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Gröbner systems of PBW algebra, Constructive arithmetics in Ore localizations enjoying enough commutativity, Feynman integral relations from parametric annihilators, Basic Module Theory over Non-commutative Rings with Computational Aspects of Operator Algebras, On Bernstein–Sato ideals for central line arrangements

Uses Software

• Macaulay2
• Plural
• Risa/Asir
• SINGULAR
• slimgb
• Kan
• D-modules

Cites Work

• Algorithms for checking rational roots of \(b\)-functions and their applications
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• Exact linear modeling using Ore algebras
• Non-commutative Gröbner bases in algebras of solvable type
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• Local Bernstein-Sato ideals: algorithm and examples
• B-functions and holonomic systems. Rationality of roots of B-functions
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Algorithms for the \(b\)-function and \(D\)-modules associated with a polynomial
• Noncommutative Gröbner bases and filtered-graded transfer.
• Slimgb: Gröbner bases with slim polynomials
• Gröbner deformations of hypergeometric differential equations
• Stratification associated with local \(b\)-functions
• Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials
• Modules over a ring of differential operators. Study of the fundamental solutions of equations with constant coefficients
• A normal form algorithm for the Brieskorn lattice
• Principal intersection and bernstein-sato polynomial of an affine variety
• Linearity conditions on the Jacobian ideal and logarithmic--meromorphic comparison for free divisors
• On microlocal $b$-function
• Sur le theoreme de finitude de la cohomologie p -adique d'une variete affine non singuliere.
• SINGULAR
• Bernstein–Sato polynomials of arbitrary varieties
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