diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 0000000000000000000000000000000000000000..7ae685c1c4a18ce95fe5eef9f6466b9b5fbfd050 --- /dev/null +++ b/.gitmodules @@ -0,0 +1,3 @@ +[submodule "tilt.rs"] + path = tilt.rs + url = https://gitlab.com/pseudowalls/tilt.rs.git diff --git a/content.tex b/content.tex index 53138be78437c0ebe762ad453b2f7b110d3563cb..086980e4d17cc1a858bdd67f08dc895c72262060 100644 --- a/content.tex +++ b/content.tex @@ -1912,8 +1912,44 @@ Given a Chern character $v$, the domain of the problem are first verified: that $v$ has positive rank, that it satisfies $\Delta(v) \geq 0$, and that $\beta_{-}(v)$ is rational. +\begin{figure} + \inputminted[ + frame=lines, + framesep=2mm, + baselinestretch=1.2, + fontsize=\scriptsize, + linenos, + firstline=24, + lastline=36 + ]{rust}{tilt.rs/src/tilt_stability/left_pseudo_semistabilizers.rs} + \caption{\raggedleft\texttt{tilt_stability::left_pseudo_semistabilizers\\::considered_b_for_beta}} + \label{fig:code:consideredb} +\end{figure} + Take $\beta_{-}(v)=\frac{a_v}{n}$ in simplest terms. -Iterate over $q \in [0,\chern_1^{\beta_{-}}(v)]\cap\frac{1}{n}\ZZ$. +Iterate over $q = \frac{b}{n} \in [0,\chern_1^{\beta_{-}}(v)]\cap\frac{1}{n}\ZZ$. +The code used to generate the corresponding values for $b$ is shown in figure +\ref{fig:code:consideredb}. + +\begin{figure} + \inputminted[ + frame=lines, + framesep=2mm, + baselinestretch=1.2, + fontsize=\scriptsize, + linenos, + firstline=79, + lastline=99 + ]{rust}{tilt.rs/src/tilt_stability/left_pseudo_semistabilizers.rs} + \caption{\raggedleft\texttt{tilt_stability::left_pseudo_semistabilizers\\::find_all}} + \label{fig:code:reducingtoeachb} +\end{figure} + +We can therefore reduce the problem of finding solutions to the problem to +finding the solutions $u$ with each fixed possible $\chern_1^\beta(u)$ +(i.e. choice of $b$). +The code representing this appears in figure +\ref{fig:code:reducingtoeachb} For any $u = (r,c\ell,\frac{e}{2}\ell^2)$, satisfying $\chern_1^{\beta_{-}}(u)=q$ for one of the $q$ considered is equivalent to diff --git a/main.tex b/main.tex index 2a58257e638fab33eb83b0e4bafaad9f1fc71ab5..00b82f303796b7a5d7bb28b8aedefaf1d2394428 100644 --- a/main.tex +++ b/main.tex @@ -3,6 +3,7 @@ \input{packages.tex} \input{newcommands.tex} \input{theoremstyles.tex} +\input{newunicodes.tex} \usepackage{sagetex} diff --git a/newunicodes.tex b/newunicodes.tex new file mode 100644 index 0000000000000000000000000000000000000000..68c60dba7a844e8a5aacaf3a578fd306893587cf --- /dev/null +++ b/newunicodes.tex @@ -0,0 +1,4 @@ +\newunicodechar{ᵇ}{b} +\newunicodechar{ₙ}{n} +\newunicodechar{∈}{\in} +\newunicodechar{ℤ}{{$\mathbb{Z}$}} \ No newline at end of file diff --git a/packages.tex b/packages.tex index 828da3632481371b498146151d3ed837f27b09c3..5f7b966f5920cfacdb7fd65e451058652bbdd954 100644 --- a/packages.tex +++ b/packages.tex @@ -8,4 +8,7 @@ \usepackage{cancel} \usepackage{mathtools} \usepackage[]{breqn} +\usepackage[nomap]{FiraMono} +\usepackage[cache=false]{minted} +\usepackage{newunicodechar} diff --git a/tilt.rs b/tilt.rs new file mode 160000 index 0000000000000000000000000000000000000000..10545bb4a862646b57b71e0a0af3e2d304a9ff37 --- /dev/null +++ b/tilt.rs @@ -0,0 +1 @@ +Subproject commit 10545bb4a862646b57b71e0a0af3e2d304a9ff37