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Compact Representations: Applications and Recent Results Jacobson, Mike
Description
Compact representations are explicit representations of algebraic numbers or functions, with size polynomial in the logarithm of their height or, respectively, degree. These representations enable much more efficient manipulations of large algebraic numbers or functions than would be possible using a standard representation, and have proved to be useful in a variety of applications. In this talk, we will describe two such applications - how compact representations are essential for short certificates of the unit group and ideal class group of a number field, and how they can be used to speed the resolution of certain Diophantine equations. We will also present recent improvements that reduce the size of compact representations, efforts to generalize these to hyperelliptic function fields, and applications of the latter to speeding the computation of bilinear pairings.
Item Metadata
Title |
Compact Representations: Applications and Recent Results
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-04-16T10:50
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Description |
Compact representations are explicit representations of algebraic
numbers or functions, with size polynomial in the logarithm of their
height or, respectively, degree. These representations enable much
more efficient manipulations of large algebraic numbers or functions
than would be possible using a standard representation, and have
proved to be useful in a variety of applications.
In this talk, we will describe two such applications - how compact
representations are essential for short certificates of the unit group
and ideal class group of a number field, and how they can be used to
speed the resolution of certain Diophantine equations. We will also
present recent improvements that reduce the size of compact
representations, efforts to generalize these to hyperelliptic function
fields, and applications of the latter to speeding the computation of
bilinear pairings.
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Extent |
48 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Calgary
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Series | |
Date Available |
2017-02-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0319154
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International