Date of Submission
Spring 2020
Academic Program
Mathematics
Project Advisor 1
Lauren Rose
Abstract/Artist's Statement
In this project we abstract the work of previous bard students by introducing the concept of splines over non-integers, non-euclidean domains, and even non-PIDs. We focus on n-cycles for some natural number n. We show that the concept of flow up class bases exist in PID splines the same way they do in integer splines, remarking the complications and intricacies that arise when abstracting from the integers to PIDs. We also start from scratch by finding a flow up class basis for n-cycle splines over the real numbers adjoin two indeterminates, denoted R[x,y] which necessitate more original techniques.
Open Access Agreement
Open Access
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Cummings, Jacob Tilden, "n-cycle Splines over Sexy Rings" (2020). Senior Projects Spring 2020. 328.
https://digitalcommons.bard.edu/senproj_s2020/328
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