#14963: Create a new class for S-units
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Reporter: cremona | Owner: cremona
Type: enhancement | Status: new
Priority: major | Milestone:
Component: number fields | sage-5.12
Keywords: sd51, units, S-units, number | Resolution:
fields | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies: #14489,
Stopgaps: | #14746
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Comment (by cremona):
It was quite easy to extend the functionality of the UnitGroup class to
include S-units, thanks to the pari function bnfsunit (which was already
wrapped) and bnfissunit (which was not). The class constructor requires
that S not be a list, but it can be a tuple or something from which an
element of the number field can be constructed. Note that the pari
function bnfsunit only returns the S-unit generators which are not global
units, and the bnfissunit returns the exponents in the order (1) global
units of infinite order, (2) torsion, (3) other S-units; so some
permutation is required. The new method for number fields is S_unit_group
and is simiar to unit_group: it caches S-unit groups using the tuple S as
key, with separate caches for proof and non-proof options.
The old number field method S_units is probably now redundant; I added a
note there directing users to S_unit_group for great functionality, as we
do for units.
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Ticket URL: <http://trac.sagemath.org/ticket/14963#comment:5>
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