Opened 13 years ago
Closed 9 years ago
#1236 closed enhancement (duplicate)
tate pairings on elliptic curves -- add to sage
Reported by: | was | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | elliptic curves | Keywords: | |
Cc: | cremona, mariah, aly.deines, jdemeyer | Merged in: | |
Authors: | Reviewers: | David Roe | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Hi, I needed some calculation period benchmark for pairings. I could not find anything build in, but the following implementation solved my problem: http://maths.straylight.co.uk/archives/104
Change History (10)
comment:1 Changed 13 years ago by
comment:2 Changed 13 years ago by
William Stein to sage-support show details 8:35 AM (1 minute ago) Reply On Nov 21, 2007 8:24 AM, Ondrej Certik <ondrej@certik.cz> wrote: > > > I think in the long-run Sage will have to completely implement its own solve > > function, which is better than Maxima's. Thoughts from Ondrej-sympy would be > > appreciated here. > > > Isn't solve supposed to return an analylic solution only? Is there an > analytic solution to this equation? It doesn't seem so to me. I don't like that meaning for solve, since it is misleading to me, and is inconsistent. e.g., what about: sage: solve(x^5 + x^3 + 1, x) [0 == x^5 + x^3 + 1] When there is no explicit solution, maxima usually returns something to explicitly indicate this. Also, as a data point, Maple returns an approximate solution if it doesn't find an exact one: sage: maple.eval('solve(38.40000000*exp(1)^(-1200*t)-9.600000000*exp(1)^(-300*t), t)') '.1540327068e-2' Likewise with Mathematica: sage: mathematica.eval('Solve[0.004*(9600/E^(1200*t) - 2400/E^(300*t)) == 0, t]') Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. {{t -> 0.00154033}} sage: mathematica('x^5 + x^3 + 1 == 0').Solve(x) {{x -> Root[1 + #1^3 + #1^5 & , 1, 0]}, {x -> Root[1 + #1^3 + #1^5 & , 2, 0]}, {x -> Root[1 + #1^3 + #1^5 & , 3, 0]}, {x -> Root[1 + #1^3 + #1^5 & , 4, 0]}, {x -> Root[1 + #1^3 + #1^5 & , 5, 0]}} > My thoughts on these issues are still the same - slowly replacing > Maxima with our own things in Python, that are easy to fix and easy to > extend. But they need to do the same things as Maxima first (and be as > fast as Maxima). Shouldn't we be able to write something that is way faster than Maxima? What do people even benchmark in the context of calculus?
comment:3 Changed 13 years ago by
disregard above comment
comment:4 Changed 12 years ago by
- Component changed from number theory to elliptic curves
- Owner changed from was to davidloeffler
Assigned to new "elliptic curves" component.
comment:5 Changed 12 years ago by
- Owner changed from davidloeffler to (none)
comment:6 Changed 10 years ago by
- Cc cremona mariah aly.deines jdemeyer added
- Report Upstream set to N/A
- Status changed from new to needs_info
should this ticket be closed now that #10912 is fixed?
Paul
comment:7 Changed 10 years ago by
- Status changed from needs_info to needs_review
Weil, Tate and ate pairings are know implemented in sage. I think this ticket may be closed.
The reference
shows implementation using elliptic net. This is not in sage now but this is not needed for the Tate pairing.
comment:8 Changed 10 years ago by
- Milestone changed from sage-4.7.2 to sage-duplicate/invalid/wontfix
comment:9 Changed 9 years ago by
- Status changed from needs_review to positive_review
comment:10 Changed 9 years ago by
- Resolution set to duplicate
- Reviewers set to David Roe
- Status changed from positive_review to closed
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