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Automated geometric reasoning: Dixon resultants, Gröbner bases, and characteristic sets
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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/10.1007/3-540-55602-8_153openalex-snapshot
Proving geometry statements of constructive type
inferredcites →https://doi.org/10.1007/3-540-58156-1_27openalex-snapshot
Algebraic factoring and geometry theorem proving
inferredcites →https://doi.org/10.1007/3-540-60114-7_14openalex-snapshot
A case of automatic theorem proving in Euclidean geometry: the Maclane 83 theorem
inferredcites →https://doi.org/10.1007/3-540-61732-9_60openalex-snapshot
Geometry machines: From AI to SMC
inferredcites →https://doi.org/10.1007/978-1-4612-0913-3openalex-snapshot
Gröbner Bases: A Computational Approach to Commutative Algebra
inferredcites →https://doi.org/10.1007/978-3-7091-6639-0openalex-snapshot
Mechanical Theorem Proving in Geometries
inferredcites →https://doi.org/10.1007/978-3-7091-9459-1_3openalex-snapshot
A Decision Method for Elementary Algebra and Geometry
inferredcites →https://doi.org/10.1007/978-94-009-4037-6openalex-snapshot
Mechanical Geometry Theorem Proving
inferredcites →https://doi.org/10.1007/978-94-009-5225-6_6openalex-snapshot
Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory
inferredcites →https://doi.org/10.1007/bf00248249openalex-snapshot
Automated reasoning in geometry theorem proving with Prolog
inferredcites →https://doi.org/10.1007/bf01224042openalex-snapshot
On the automatic derivation of a set of geometric formulae
inferredcites →https://doi.org/10.1007/bf01231031openalex-snapshot
A new theorem discovered by computer prover
inferredcites →https://doi.org/10.1007/bf01531326openalex-snapshot
Automated production of traditional proofs for theorems in Euclidean geometry I. The Hilbert intersection point theorems
inferredcites →https://doi.org/10.1007/bf01531327openalex-snapshot
Mechanical theorem proving in projective geometry
inferredcites →https://doi.org/10.1007/bf02328448openalex-snapshot
Proving geometry theorems with rewrite rules
inferredcites →https://doi.org/10.1007/bfb0012890openalex-snapshot
Geometer: A theorem prover for algebraic geometry
inferredcites →https://doi.org/10.1016/0004-3702(88)90048-3openalex-snapshot
Wu's method and its application to perspective viewing
inferredcites →https://doi.org/10.1016/0004-3702(88)90050-1openalex-snapshot
A refutational approach to geometry theorem proving
inferredcites →https://doi.org/10.1016/0304-3975(90)90077-uopenalex-snapshot
The parallel numerical method of mechanical theorem proving
inferredcites →https://doi.org/10.1090/conm/029/13openalex-snapshot
Some Recent Advances in Mechanical Theorem-Proving of Geometries
inferredcites →https://doi.org/10.1109/iscv.1995.476984openalex-snapshot
Computing invariants using elimination methods
inferredcites →https://doi.org/10.1109/lics.1993.287601openalex-snapshot
Automated production of traditional proofs for constructive geometry theorems
inferredcites →https://doi.org/10.1109/sfcs.1986.48openalex-snapshot
Proving by example and gap theorems
inferredcites →https://doi.org/10.1112/plms/s2-6.1.468openalex-snapshot
On a Form of the Eliminant of Two Quantics
inferredcites →https://doi.org/10.1112/plms/s2-7.1.49openalex-snapshot
The Eliminant of Three Quantics in two Independent Variables
inferredcites →https://doi.org/10.1137/0213054openalex-snapshot
Cylindrical Algebraic Decomposition I: The Basic Algorithm
inferredcites →https://doi.org/10.1137/0213055openalex-snapshot
Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane
inferredcites →https://doi.org/10.1142/2196#t=tocopenalex-snapshot
Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems
inferredcites →https://doi.org/10.1145/164081.164120openalex-snapshot
The 40 “generic” positions of a parallel robot
inferredcites →https://doi.org/10.1145/164081.164142openalex-snapshot
Automated geometry theorem proving by vector calculation
inferredcites →https://doi.org/10.1145/164081.164144openalex-snapshot
Geometry theorem proving in vector spaces by means of Gröbner bases
inferredcites →https://doi.org/10.1145/190347.190372openalex-snapshot
Algebraic and geometric reasoning using Dixon resultants
inferredcites →https://doi.org/10.1145/220279.220309openalex-snapshot
A complete and practical algorithm for geometric theorem proving (extended abstract)
inferredcites →https://doi.org/10.1145/220346.220370openalex-snapshot
Comparison of various multivariate resultant formulations
inferredcites →https://doi.org/10.1145/237814.237862openalex-snapshot
Sparsity considerations in Dixon resultants
inferredcites →https://doi.org/10.1145/258726.258768openalex-snapshot
Extraneous factors in the Dixon resultant formulation
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/10.1145/96877.96946openalex-snapshot
Methods for mechanical geometry formula deriving
inferredcites →https://doi.org/10.1145/96877.96949openalex-snapshot
Refutational proofs of geometry theorems via characteristic set computation
inferredcites →https://doi.org/10.1515/9783110881271.197openalex-snapshot
Stewart platforms without computer?
inferredcites →https://doi.org/10.1525/9780520348097openalex-snapshot
A Decision Method for Elementary Algebra and Geometry
inferredcites →https://doi.org/10.2140/pjm.1975.56.97openalex-snapshot
The orthocentric simplex as an extreme simplex
inferredcites →https://doi.org/10.2307/2317055openalex-snapshot
The Art of Computer Programming. Volume 2: Seminumerical Algorithms.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/11615798_12openalex-snapshot
Planar Generalized Stewart Platforms and Their Direct Kinematics
inferred← citeshttps://doi.org/10.1007/3-540-44990-6_12openalex-snapshot
Automatic Determination of Geometric Loci. 3D-Extension of Simson-Steiner Theorem
inferred← citeshttps://doi.org/10.1007/978-3-031-98685-7_20openalex-snapshot
PyEuclid: A Versatile Formal Plane Geometry System in Python
inferred← citeshttps://doi.org/10.1007/978-3-540-24616-9_5openalex-snapshot
The SymbolicData GEO Records – A Public Repository of Geometry Theorem Proof Schemes
inferred← citeshttps://doi.org/10.1007/978-3-642-21046-4_3openalex-snapshot
Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving
inferred← citeshttps://doi.org/10.1007/bf02948785openalex-snapshot
Recent advances in automated theorem proving on inequalities
inferred← citeshttps://doi.org/10.1007/s10817-021-09591-2openalex-snapshot
Automated Discovery of Geometric Theorems Based on Vector Equations
inferred← citeshttps://doi.org/10.1007/s11424-019-8347-1openalex-snapshot
On the Mechanization of Straightedge and Compass Constructions
inferred← citeshttps://doi.org/10.1016/b978-044450813-3/50013-8openalex-snapshot
Automated Reasoning in Geometry
inferred← citeshttps://doi.org/10.1016/s0895-7177(03)00115-8openalex-snapshot
A bridge between dynamic geometry and computer algebra
inferred← citeshttps://doi.org/10.1134/s0965542513060092openalex-snapshot
Computer algebra methods in the study of nonlinear differential systems
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