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main.tex
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\input{misc/preamble}
\title{素数判定法と素因数分解アルゴリズム}
\author{}
\date{}
\makeindex
\begin{document}
\setcounter{notesNum}{1}
\maketitle
\begin{multicols}{2}
\setcounter{tocdepth}{3}
\tableofcontents
\end{multicols}
\newpage
\section{整数と素数}
\subsection{数論の最初の一歩}
\input{tex/first_step}
\subsection{試し割}
\input{tex/trial_division}
\subsection{平方差法}
\input{tex/fermat_factorization}
\section{概論}
\subsection{素因数分解}
\input{tex/outline_factorization}
\section{剰余と群}
\subsection{剰余}
\input{tex/modulo}
\subsection{群}
\input{tex/group}
\subsection{Pollardの$p-1$法}
\input{tex/p_minus_1}
\subsection{剰余類に含まれる因数}
\input{tex/divisors_lenstra}
\section{平方剰余}
\subsection{平方剰余と平方非剰余}
\input{tex/quadratic_residue}
\subsection{Miller-Rabinテスト}
\input{tex/miller_rabin}
\subsection{拡張Riemann予想とMillerテスト}
\input{tex/riemann_miller}
\section{原始根}
\subsection{Lucasテスト}
\input{tex/lucas_test}
\subsection{Pepinテスト}
\input{tex/pepin_test}
\subsection{Pocklingtonテスト}
\input{tex/pocklington_test}
\section{Fibonacci数列}
\subsection{Fibonacci数列とLucas数列}
\input{tex/fibonacci}
\subsection{環と体}
\input{tex/ring}
\subsection{2次Frobeniusテスト}
\input{tex/quadratic_frobenius_primality_test}
\subsection{Lucas-Lehmerテスト}
\input{tex/lucas_lehmer_primality_test}
\subsection{Williamsの$p+1$法}
\input{tex/p_plus_1}
\subsection{実装}
\input{tex/implementation_frobenius_test}
\section{2次形式}
\subsection{2次形式とは}
\input{tex/intro_quadratic_form}
\subsection{類群$\mathcal{C}(D)$}
\input{tex/class_number}
\subsection{類数公式}
\input{tex/class_number_formula}
\subsection{Shanksの baby-step giant-step}
\input{tex/baby_step_giant_step}
\section{Gauss和とJacobi和}
\subsection{Gauss和}
\input{tex/gauss_sum}
\section{篩}
\subsection{Eratosthenesの篩}
\input{tex/sieve}
\subsection{2次篩法}
\input{tex/quadratic_sieve_algorithm}
\subsection{2次体と整数環}
\input{tex/ring_of_integer}
\subsection{数体篩法}
\input{tex/number_field_sieve}
\section{さまざまな素数}
\subsection{定理の拡張}
\input{tex/expand_theorem}
\section{楕円曲線}
\subsection{楕円曲線の定義と構造}
\input{tex/elliptic_curve_def}
\subsection{楕円曲線を用いた素因数分解}
\input{tex/implementation_elliptic_curve_test}
\subsection{群の位数}
\input{tex/elliptic_curve_order}
\section{その他の方法}
\subsection{Pollardの$\rho$法}
\input{tex/rho_method}
\subsection{Baillie-PSWテスト}
\input{tex/baillie_psw_test}
\subsection{連分数}
\input{tex/continued_fraction}
\subsection{SQUFOF}
\input{tex/squfof}
\subsection{多項式評価法}
\input{tex/pollard_strassen_algorithm}
\subsection{格子}
\input{tex/lattice}
\subsection{AKSテスト}
\input{tex/aks_test}
\subsection{Aurifeuille分解}
\input{tex/aurifeuillean_factorization}
\subsection{$p^2q$型の素因数分解}
\input{tex/p2q}
\section{補遺 : 証明}
\subsection{数論}
\input{tex/proof_number}
\subsection{群論}
\input{tex/proof_group}
\section{補遺 : 補助関数}
\input{tex/submodule}
\newpage
\printindex
\bibliographystyle{jplain}
\bibliography{ref}
\end{document}