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Automated reasoning in differential geometry and mechanics using the characteristic set method

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-52885-7_89openalex-snapshot

Ritt-Wu's decomposition algorithm and geometry theorem proving

inferredcites →https://doi.org/10.1007/978-94-009-4037-6openalex-snapshot

Mechanical Geometry Theorem Proving

inferredcites →https://doi.org/10.1007/bf00245819openalex-snapshot

A procedure to prove statements in differential geometry

inferredcites →https://doi.org/10.1007/bf01209162openalex-snapshot

Zur Nullstellentheorie der Polynomideale

inferredcites →https://doi.org/10.1007/bf01553889openalex-snapshot

On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving

inferredcites →https://doi.org/10.1007/bf02328448openalex-snapshot

Proving geometry theorems with rewrite rules

inferredcites →https://doi.org/10.1007/bf02551378openalex-snapshot

Elimination in control theory

inferredcites →https://doi.org/10.1007/bfb0077689openalex-snapshot

A constructive theory of differential algebraic geometry based on works of J.F. Ritt with particular applications to mechanical theorem-proving of differential geometries

inferredcites →https://doi.org/10.1016/b978-0-12-080550-1.50009-3openalex-snapshot

Differentially closed fields: a model-theoretic tour

inferredcites →https://doi.org/10.1090/coll/014openalex-snapshot

Differential Equations from the Algebraic Standpoint

inferredcites →https://doi.org/10.1090/coll/033openalex-snapshot

Differential Algebra

inferredcites →https://doi.org/10.1145/32439.32479openalex-snapshot

Geometry theorem proving using Hilbert's Nullstellensatz

inferredcites →https://doi.org/10.1145/32439.32480openalex-snapshot

Automated geometry theorem proving using Buchberger's algorithm

inferredcites →https://doi.org/10.1360/ya1978-21-2-159openalex-snapshot

ON THE DECISION PROBLEM AND THE MECHANIZATION OF THEOREM-PROVING IN ELEMENTARY GEOMETRY

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/3-540-45084-x_2openalex-snapshot

Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems

inferred← citeshttps://doi.org/10.1007/3-540-45410-1_10openalex-snapshot

Reasoning about Surfaces Using Differential Zero and Ideal Decomposition

inferred← citeshttps://doi.org/10.1007/3-540-61732-9_60openalex-snapshot

Geometry machines: From AI to SMC

inferred← citeshttps://doi.org/10.1007/978-1-4612-4088-4_5openalex-snapshot

A Survey of Geometric Reasoning Using Algebraic Methods

inferred← citeshttps://doi.org/10.1007/978-3-319-66320-3_14openalex-snapshot

Characteristic Set Method for Laurent Differential Polynomial Systems

inferred← citeshttps://doi.org/10.1007/978-3-642-80350-5_55openalex-snapshot

A Method for Proving Theorems in Differential Geometry and Mechanics

inferred← citeshttps://doi.org/10.1007/bf00881835openalex-snapshot

Automated reasoning in differential geometry and mechanics using the characteristic set method

inferred← citeshttps://doi.org/10.1007/bf00885765openalex-snapshot

An extension of a procedure to prove statements in differential geometry

inferred← citeshttps://doi.org/10.1007/s00200-002-0110-4openalex-snapshot

Resolvent Representation for Regular Differential Ideals

inferred← citeshttps://doi.org/10.1007/s00200-008-0079-8openalex-snapshot

Probabilistic algorithms for computing resolvent representations of regular differential ideals

inferred← citeshttps://doi.org/10.1007/s10208-015-9249-9openalex-snapshot

Sparse Differential Resultant for Laurent Differential Polynomials

inferred← citeshttps://doi.org/10.1007/s11424-011-8267-1openalex-snapshot

An application of Ritt-Wu’s zero decomposition algorithm to the pseudo null Bertrand type curves in Minkowski 3-space

inferred← citeshttps://doi.org/10.1007/s11424-016-5040-5openalex-snapshot

A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity

inferred← citeshttps://doi.org/10.1007/s11424-019-8343-5openalex-snapshot

Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems

inferred← citeshttps://doi.org/10.1007/s11425-008-0053-8openalex-snapshot

Mechanical theorem proving in the surfaces using the characteristic set method and Wronskian determinant

inferred← citeshttps://doi.org/10.1007/s11704-007-0001-8openalex-snapshot

Mathematics mechanization and applications after thirty years

inferred← citeshttps://doi.org/10.1016/b978-012734760-8/50022-3openalex-snapshot

References

inferred← citeshttps://doi.org/10.1016/b978-044450813-3/50013-8openalex-snapshot

Automated Reasoning in Geometry

inferred← citeshttps://doi.org/10.1016/j.jsc.2007.05.005openalex-snapshot

A characteristic set method for ordinary difference polynomial systems

inferred← citeshttps://doi.org/10.1016/j.jsc.2008.02.010openalex-snapshot

Characteristic set method for differential–difference polynomial systems

inferred← citeshttps://doi.org/10.1016/s0747-7171(03)00068-3openalex-snapshot

Implicitization of differential rational parametric equations

inferred← citeshttps://doi.org/10.1016/s0898-1221(00)00332-1openalex-snapshot

Involutive directions and new involutive divisions

inferred← citeshttps://doi.org/10.1023/a:1005819428156openalex-snapshot

Clifford Algebraic Reduction Method for Automated Theorem Proving in Differential Geometry

inferred← citeshttps://doi.org/10.1090/s0002-9947-2013-05633-4openalex-snapshot

Intersection theory in differential algebraic geometry: Generic intersections and the differential Chow form

inferred← citeshttps://doi.org/10.1145/1993886.1993922openalex-snapshot

Sparse differential resultant

inferred← citeshttps://doi.org/10.1145/2429135.2429158openalex-snapshot

Sparse differential resultant for laurent differential polynomials

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