1998/05/11 by Hyungju Park, Park, Hyungju
Computer Science · Engineering · Mathematics · #13P10 #Advanced Differential Equations and Dynamical Systems #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13P10
paper · pdf · doi:10.48550/arxiv.math/9805053
Latex2e file, 12 pages. Some proofs are improved. A misuse of terminology is corrected
openalex publication_date 1998/05/11 · arxiv created 1998/05/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be an arbitrary field, and C be a curve in An defined parametrically by x1=f1(t),...,xn=fn(t), where f1,...,fn∈ k[t]. A necessary and sufficient condition for the two function fields k(t) and k(f1,...,fn) to be same is developed in terms of zero-dimensionality of a derived ideal in the bivariate polynomial ring k[s,t]. Since zero-dimensionality of such an ideal can be readily determined by a Groebner basis computation, this gives an algorithm that determines if the parametrization ψ=(f1,...,fn): A --> C is a birational equivalence. We also develop an algorithm that determines if k[t] and k[f1,...,fn] are same, by which we get an algorithm that determines if the parametrization ψ=(f1,...,fn): A --> C is an isomorphism. We include some computational examples showing the application of these algorithms.