On multivariate rational function decomposition

DOI10.1006/jsco.2000.0529zbMath1043.12006OpenAlexW2002352305MaRDI QIDQ697481

Rosario Rubio, David Sevilla, Jaime Gutierrez

Publication date: 17 September 2002

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.2000.0529

zbMATH Keywords

algorithmsmultivariate rational functionstranscendence degree oneunirational field

Mathematics Subject Classification ID

Related Items (15)

\texttt{PTOPO}: computing the geometry and the topology of parametric curves ⋮ Effective differential Lüroth's theorem ⋮ Implicitization using univariate resultants ⋮ A partial solution to the problem of proper reparametrization for rational surfaces ⋮ Computation of unirational fields ⋮ Common composites of triangular polynomial systems and hash functions ⋮ Decomposition of ordinary differential polynomials ⋮ On the decomposition of rational functions ⋮ Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis ⋮ On the problem of proper reparametrization for rational curves and surfaces ⋮ Hyperelliptic curves with reduced automorphism group \(A_{5}\) ⋮ On Ritt's decomposition theorem in the case of finite fields ⋮ Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields ⋮ An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography ⋮ Detecting real singularities of a space curve from a real rational parametrization

Cites Work

• Reduced Gröbner bases under composition
• Basic algorithms for rational function fields
• A note on separated factors of separated polynomials
• Recognizing simple subextensions of purely transcendental field extensions
• A note on a theorem of Fried and MacRae
• A rational function decomposition algorithm by near-separated polynomials
• Unirational fields of transcendence degree one and functional decomposition
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