#9334: Implement Hilbert symbols over number fields
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Reporter: aly.deines | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: number fields | Keywords: hilbert symbol
Author: aly.deines | Upstream: N/A
Reviewer: David Loeffler, John Cremona | Merged:
Work_issues: ReST formatting issues, and more |
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Comment(by aly.deines):
Here are the changes I've made so far:
1. in generalized_legendred_symbol I test for primality first
2. instead of K(2).valuation(P) I just test that n is odd
3. I've changed RunTime Errors to ValueErrors
4. I return +/- 1 as sage integers
5. I test if P|self and if so return 0 (as a sage integer)
6. in generalized_hilbert_symbol I deleted iprime
7. I did the calculation and have hard coded jprime^2
8. I've replace ^ with ** where necessary in _voight_alg_6_2
9. Things should work for fractions
10. generalized_hilbert_symbol should also accept a,b, divisible by p
One question I have, does anyone know about hensel lifting in sage?
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9334#comment:14>
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