Effective uniform bounding in partial differential fields

2014/10/31 by James Freitag, Freitag, James, Omar Leon Sanchez +1 · 1 citation
Mathematics · #03C60 #12H05 #12H20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:03C60 #msc:12H05 #msc:12H20

paper · pdf · doi:10.48550/arxiv.1411.0029

arxiv created 2015/10/27 · arxiv updated 2015/10/28

Abstract

Motivated by the effective bounds of ordinary differential equations, we prove an effective version of uniform bounding for partial differential fields with commuting derivations. More precisely, we provide an upper bound for the size of finite solution sets of partial differential polynomial equations in terms of data explicitly given in the equations and independent of parameters. Our methods also produce an upper bound for the degree of the Zariski closure of solution sets, whether they are finite or not.

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