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Weighted Greatest Common Divisors

Modderman, Robert (2019) Weighted Greatest Common Divisors. Bachelor's Thesis, Mathematics.


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In this thesis, the notion of weighted greatest common divisor (wgcd) will be discussed and redefined for integral domains. We will use the concept of squarefree factorizations to prove existence and uniqueness (up to unit multiplication) for unique factorization domains. We will use Yun's squarefree factorization algorithm to write algorithms for computing wgcd's of polynomials over some fields, of which some will be implemented in the computer algebra system PARI/GP. We will also extend the idea of factoring the usual gcd to compute wgcd's of polynomials over any field and compare the corresponding algorithm to those based on Yun's algorithm.

Item Type: Thesis (Bachelor's Thesis)
Supervisor nameSupervisor E mail
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 17 Jul 2019
Last Modified: 18 Jul 2019 06:24

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