Re: Elliptic Curves and Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg40974] Re: Elliptic Curves and Mathematica
- From: "Richard I. Pelletier" <bitbucket at attbi.com>
- Date: Sat, 26 Apr 2003 03:25:41 -0400 (EDT)
- References: <b7qolq$3ij$1@smc.vnet.net> <200304211058.GAA22418@smc.vnet.net> <b8b9o2$9l5$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
[[ This message was both posted and mailed: see
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In article <b8b9o2$9l5$1 at smc.vnet.net>, Murray Eisenberg
<murraye at attbi.com> wrote:
> Can you supply the tail-end of the Notebook expression from this
> notebook? It was truncated in your message.
sorry about that. i looked at another posting to see what was
customarily kept. since i don't understand exactly what fragments are
essential, i have enclosed the entire nb.
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A. Given the points A,B on the elliptic curve C, compute: 2A, 3A, \
A+B, 2A+B, 3A+B.\
\>", "Subsection"],
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let's get 2A. we get the tangent line at A, and we get the \
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we see the double intersection at A, and the new one is the 1st. \
write it to change the sign of the y-component, though in this case
it's 0:\
\
\>", "Text"],
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but that's interesting. because 2A is the intersection, we don't \
get a third point: the line thru 2A and A is the tangent line at A.\
\>", \
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the first point is 2A, the other two are A. i really don't like 3A \
= 2A, so i guess that A is the intersection, so i change the sign:\
\>", \
"Text"],
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let's go for A+B. here's the line thru the two points, and the \
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\>", "Text"],
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i.e. it looks like we have a tangent at A+B. i have to remind \
myself to flip the sign:\
\>", "Text"],
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"we see 7 distinct points, and add the point at \[Infinity], 0. can i
build \
the group table?\ni think 2B = 0 (vertical tangent at B), 4A=0
(vertical \
tangent at 2A). then A+3A=0 (follows, but also they lie on vertical
line), \
and (2A+B)+(2A+B)=0 (follows, but also vertical tangent at 2A+B), and
finally \
(3A+B)+(A+B) = 0 (follows, but also they lie on vertical line.\nso, we
have \
an element of order 4, and an element of order 2. this is an abelian
group, \
so it's ",
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--
NOTE: email address is rip1 AT attbi DOT com
- References:
- Re: Elliptic Curves and Mathematica
- From: "Richard I. Pelletier" <bitbucket@attbi.com>
- Re: Elliptic Curves and Mathematica