Mitchell Holt
Modular Algorithms for Computation in Simple Algebraic Extension Fields
“A common strategy for addressing the problem of expression swell in the intermediate steps of algorithms
in over the integers is to solve the problem in different in quotient rings of the integers and then recover the result over the integers from these modular results. Examples include the polynomial GCD, polynomial factorisation, rational function interpolation, and solutions of linear systems.
An algebraic extension of Q is called simple if it is generated by the adjuction of a single element that is algebraic over Q. Crucially, these fields may be represented as the quotient of the polynomials in Q by the ideal generated by the minimal polynomial of the algebraic element. This project will investigate using modular algorithms to perform computation in simple algebraic extensions by exploiting this representation.”
Mitchell Holt
The University of Queensland
Mitchell Holt is a fourth year mathematics and computer science student at the University
of Queensland. He is interested in computer algebra – doing maths to write computer code
that does symbolic maths. Mitchell plans to continue studying in the field of computer
algebra.
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