#9334: hilbert symbols!!!
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Reporter: aly.deines | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-wishlist
Component: number fields | Keywords: hilbert symbol
Author: aly.deines | Upstream: N/A
Reviewer: | Merged:
Work_issues: ReST formatting issues |
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Comment(by davidloeffler):
Most of this looks fine, and the docstring formatting is much better; but
there are some technical issues.
- The code in {{{ solver_mod_p }}} is obviously wrong for n > 1: it
calculates the inverse modulo P^n^ but then takes the square root of this
modulo P. You need some kind of Hensel lifting or suchlike to get an
answer that's right modulo P^n^.
- The code in {{{ uniformizer }}} is a mess (e.g. it trivially fails for
any non-principal ideal in a number field of degree > 2, because you've
assumed {{{ self.integral_basis()}}} has length 2). But there's already a
method {{{
sage.rings.number_field.number_field.NumberField_generic.uniformizer }}}
(taking a prime as an argument). I agree that it is worth having
uniformizers accessible via a method of ideals as well, but it should just
be a thin wrapper around the existing code.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:7>
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