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Khovanskii-Gröbner Basis

Ehrmann, Daniel (2020) Khovanskii-Gröbner Basis. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In this thesis a natural generalization and further extension of Gröbner theory using Kaveh and Manon's Khovanskii basis theory is constructed. Suppose A is a finitely generated domain equipped with a valuation v with
a finite Khovanskii basis. We develop algorithmic processes for computations regarding ideals in the algebra A. We introduce the notion of a Khovanskii-Gröbner basis for an ideal J in A and give an analogue of the Buchberger algorithm for it (accompanied by a Macaulay2 code). We then use Khovanskii-Gröbner bases to suggest an algorithm to solve a system of equations from A. Finally we suggest a notion of relative tropical variety for an ideal in A and
sketch ideas to extend the tropical compactification theorem to this setting.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Ehrmann, Danieldae45@pitt.edudae45
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairKaveh,
Committee MemberHales,
Committee MemberManon,
Committee MemberConstantine,
Date: 8 June 2020
Date Type: Publication
Defense Date: 20 November 2019
Approval Date: 8 June 2020
Submission Date: 1 May 2020
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 83
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Algebra, Gröbner Basis, Gröbner Bases, Algorithm, Khovanskii Basis, Khovanskii Bases, Algebraic Geometry
Date Deposited: 08 Jun 2020 16:10
Last Modified: 08 Jun 2020 16:10


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