Commit d7fd4a50 authored by Benoit Viguier's avatar Benoit Viguier

working on talk CWG

parent 212c3c8d
This diff is collapsed.
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%
% SLIDE 1
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[fragile]{Elliptic Curves 101}
% \newcommand{\PP}{\mathcal{P}}
% \newcommand{\KK}{\mathcal{K}}
% \newcommand{\PK}{x}
% \newcommand{\PKX}{Q}
% \newcommand{\X}{{\bf x}}
% \newcommand{\E}{\mathcal{E}}
% \newcommand{\K}{\mathcal{K}}
% \newcommand{\J}{\mathcal{J}}
\newcommand{\XX}[1]{\ensuremath{{\textbf{x}}(#1)}}
\begin{center}
\begin{tikzpicture}
\newcommand*{\xlen}{-4}
\newcommand*{\ylen}{1.5}
\coordinate (cquoops) at (\xlen, \ylen);
\coordinate (cquosca) at (\xlen, \ylen-0.8);
\coordinate (cquoadd) at (\xlen, \ylen-1.6);
\coordinate (cquoxdbladd) at (\xlen, \ylen-2.4);
\coordinate (cgroupops) at (\xlen, 3*\ylen);
\coordinate (cgroupsca) at (\xlen, 3*\ylen-0.7);
\coordinate (cgroupadd) at (\xlen, 3*\ylen-1.4);
\node [anchor=west] (groupops) at (cgroupops)
{\underline{\emph{Operations on $E: B y^2 = x^3 + A x^2 + x$}}};
\node [anchor=west] (groupsca) at (cgroupsca)
{$\textcolor{rured}{(1)}\,\,P \mapsto [2]P$};
\node [anchor=west] (groupadd) at (cgroupadd)
{$\textcolor{rured}{(2)}\,\,\big\{P,Q\big\}\mapsto P + Q$};
\visible<8->{
\node [anchor=west] (quoops) at (cquoops)
{\underline{\emph{Operations on $\mathbb{P}$}}};
\node [anchor=west] (quosca) at (cquosca)
{$\textcolor{rured}{(1)}\,\,\texttt{xDBL}:\,\XX{P} \mapsto \XX{[2]P}$};
}
\visible<16>{
\node [anchor=west] (quoadd) at (cquoadd)
{$\textcolor{rured}{(2)}\,\,\Big\{\XX{P},\XX{Q}\Big\}
\mapsto \Big\{\XX{P+Q},\XX{P-Q}\Big\}$};
}
\visible<17->{
\node [anchor=west] (quoadd) at (cquoadd)
{$\textcolor{rured}{(2)}\,\,\texttt{xADD} : \Big\{\XX{P},\XX{Q},\XX{P-Q}\Big\}
\mapsto \XX{P+Q}$};
}
\newcommand*{\aaa}{-6}
\newcommand*{\bbb}{7}
\newcommand*{\px}{-1.85}
\newcommand*{\py}{3.4305}
\newcommand*{\dfdxp}{4.2675}
\newcommand*{\dfdyp}{-2*\py}
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\newcommand*{\pyd}{7.4716}
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\newcommand*{\qy}{1.5261}
\newcommand*{\pqx}{1.42956}
\newcommand*{\pqy}{-1.15937}
\newcommand*{\qpx}{4.19886}
\newcommand*{\qpy}{7.4716}
\begin{axis}
[
axis x line = center,
axis line style = thick,
xlabel = $\mathbb{K}$,
axis y line = none,
ticks = none,
xmin=-4,
xmax=8,
ymin=-9,
ymax=9,
samples=200,
domain=-2.9005:5,
smooth
]
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\draw [thick,<-,dashed] ([yshift=-0.8mm]axis cs:\pqx,0) -- (axis cs:\pqx,\pqy);
\draw [thick,<-,dashed] ([yshift=-0.8mm]axis cs:\qpx,0) -- (axis cs:\qpx,-\qpy);
\draw [thick,<-,dashed] ([yshift=0.8mm]axis cs:\qpx,0) -- (axis cs:\qpx,\qpy);
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\only<15->{
\addplot [orange,ultra thick,mark=*] coordinates {(\pqx,0)};
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}
\end{axis}
\end{tikzpicture}
\end{center}
\end{frame}
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%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% beamercolorthemeru.dtx (with options: `package')
%% ---------------------------------------------------------------------------
%% Copyright 2016 Benoit Viguier
%%
%% https://gitlab.science.ru.nl/benoit/rutheme
%%
%% the original template was based on the mtheme
%% (https://github.com/matze/mtheme) by Matthias Vogelgesang
%%
%% This work is licensed under a Creative Commons Attribution-ShareAlike 4.0
%% International License (https://creativecommons.org/licenses/by-sa/4.0/).
%% ---------------------------------------------------------------------------
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%%
%% End of file `beamercolorthemeru.sty'.
This diff is collapsed.
%%
%% This is file `beamerinnerthemeru.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% beamerinnerthemeru.dtx (with options: `package')
%% ---------------------------------------------------------------------------
%% Copyright 2016 Benoit Viguier
%%
%% https://gitlab.science.ru.nl/benoit/rutheme
%%
%% the original template was based on the mtheme
%% (https://github.com/matze/mtheme) by Matthias Vogelgesang
%%
%% This work is licensed under a Creative Commons Attribution-ShareAlike 4.0
%% International License (https://creativecommons.org/licenses/by-sa/4.0/).
%% ---------------------------------------------------------------------------
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%%
%% This is file `beamerouterthemeru.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% beamerouterthemeru.dtx (with options: `package')
%% ---------------------------------------------------------------------------
%% Copyright 2016 Benoit Viguier
%%
%% https://gitlab.science.ru.nl/benoit/rutheme
%%
%% the original template was based on the mtheme
%% (https://github.com/matze/mtheme) by Matthias Vogelgesang
%%
%% This work is licensed under a Creative Commons Attribution-ShareAlike 4.0
%% International License (https://creativecommons.org/licenses/by-sa/4.0/).
%% ---------------------------------------------------------------------------
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sep=0pt,%
leftskip=\ru@frametitle@paddingleft,%
rightskip=\ru@frametitle@padding,%
]{frametitle}%
\ru@frametitlestrut@start%
\insertframetitle%
\nolinebreak%
\ru@frametitlestrut@end%
\end{beamercolorbox}%
}
\setbeamertemplate{frametitle continuation}{%
\usebeamerfont{frametitle}
\romannumeral \insertcontinuationcount