<commit_before><commit_msg>- Reworked macros to fit our agreed notation<commit_after>%%% Defined here (in order): mathematical macros, theorem style, colour of hyperlinks, spaces for indention and between lines,
%%% tikz, reminder, fix for bigint package

%% Mathematical macros %%

% Logic
\newcommand{\eq}{\Leftrightarrow}
\newcommand{\imp}{\Rightarrow}
\newcommand{\To}{\longrightarrow}
\newcommand{\inj}{\hookrightarrow}
\newcommand{\surj}{\longrightarrow\!\!\!\!\to}
\newcommand{\isom}{\cong}


% Sets
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\K}{\mathbb{K}}
\renewcommand{\P}{\mathbb{P}}


% Operators
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\arctanh}{arctanh}
\DeclareMathOperator{\arcsinh}{arcsinh}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\Jac}{Jac}
\DeclareMathOperator{\GL}{GL}
\renewcommand{\Im}{\operatorname{Im}}
\renewcommand{\div}{\operatorname{div}}
\renewcommand{\deg}{\operatorname{deg}}


% Variables
\newcommand{\cu}{\mathcal{C}} % projective curve
\newcommand{\caff}{\mathcal{C}_{\text{aff}}} % affine model
\newcommand{\X}{\{ \, x_1,\dots,x_d \,\}} % branch points
\newcommand{\dx}{\mathrm d x}
\newcommand{\dy}{\mathrm d y}
\newcommand{\dt}{\mathrm d t}
\newcommand{\du}{\mathrm d u}
\newcommand{\w}{\omega} % differential
\newcommand{\wij}{\frac{\dx^i}{iy^j}} %w \in W
\newcommand{\W}{\mathcal{W}} % basis of holomorphic differentials
\newcommand{\WM}{\mathcal{W}^{\text{mer}}} % basis of meromorphic differentials
\newcommand{\hd}{\Omega^1_{\mathcal{C}}} % holomorphic differentials
\newcommand{\coho}{H^1_{\text{dR}}(\cu)} % holomorphic differentials in deRham
\newcommand{\homo}{H_1(\cu,\Z)} % first integral homology group
\newcommand{\cyab}{\gamma(a,b)}
\newcommand{\cycd}{\gamma(c,d)}
\newcommand{\cyt}{\tilde{gamma}}
\newcommand{\cytab}{\tilde{gamma}(a,b)}
\newcommand{\cytcd}{\tilde{gamma}(c,d)}
\newcommand{\OA}{\Omega_A} % A-periods
\newcommand{\OB}{\Omega_B} % B-periods
\newcommand{\OC}{\Omega_C} % C-periods
\newcommand{\AJ}{\mathcal{A}} % Abel-Jacobi map
\newcommand{\sab}{s(\alpha,\beta)} % shifting number
\newcommand{\sij}{s(\alpha^{(i)},\beta^{(j)})} % shifting number
\newcommand{\yab}{y_{a,b}}
\newcommand{\ycd}{y_{c,d}}
\newcommand{\mr}{^{\frac{1}{m}}}


%%  Theorem style %%
\theoremstyle{plain}
\newtheorem{thm}{Theorem}[section]
\newtheorem{prop}[thm]{Proposition}
\newtheorem{lemma}[thm]{Lemma}
\newtheorem{coro}[thm]{Corollary}

\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition}
\newtheorem{ex}[thm]{Example}
\newtheorem{alg}[thm]{Algorithm}

\theoremstyle{remark}
\newtheorem{rmk}[thm]{Remark}


%% Colour of hyperlinks %%
\hypersetup{linkbordercolor 	={1 1 1}}
\hypersetup{citebordercolor 	={1 1 1}}
\hypersetup{urlbordercolor 	={1 1 1}}


%% Set spaces for indention and between lines %%
\setlength{\parskip}{0.75\baselineskip}
\setlength{\parindent}{0em}
\newcommand{\abstand}{{\\[0.25\baselineskip]}}
\newcommand{\abstandl}{{\\[0.5\baselineskip]}}
\newcommand{\abstandll}{{\\[0.75\baselineskip]}}


%% Tikz %%
\usetikzlibrary{arrows}
\usetikzlibrary{shapes.misc}
\usetikzlibrary{decorations.markings}
\tikzset{cross/.style={cross out, draw=black, minimum size=2*(#1-\pgflinewidth), inner sep=0pt, outer sep=0pt},cross/.default={1pt}}
\tikzset{
    halfarrow1/.style={postaction={decorate},
        decoration={markings,mark=at position .5 with
        {\arrow[line width=0.4mm]{>}}}} }
\tikzset{
    halfarrow2/.style={postaction={decorate},
        decoration={markings,mark=at position .5 with
        {\arrow[line width=0.4mm]{<}}}} }


%% Reminder %%
\newcommand{\todo}{{\color{red}\textbf{TODO}}:\;}
        
        
%% Problem with lmodern and bitint packages %%
\DeclareFontFamily{OMX}{lmex}{}
\DeclareFontShape{OMX}{lmex}{m}{n}{<-> lmex10}{}
{'fraction_non_alphanumeric': 0.21313537996980372, 'fraction_numerical': 0.01031706089582285, 'mean_word_length': 5.841652323580035, 'pattern_counts': {'":': 0, '<': 5, '<?xml version=': 0, '>': 5, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '3915473', 'n_tokens_mistral': 1418, 'n_tokens_neox': 1335, 'n_words': 216}