Effective uniform bounding in partial differential fields

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Motivated by the effective bounds found in [12] for ordinary differential equations, we prove an effective version of uniform bounding for fields with several 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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)308-336
JournalAdvances in Mathematics
Early online date11 Nov 2015
StatePublished - Jan 2016