this is my first time posting on StackExchange so apologies for any formatting mistakes.
I have a raw .tex file from my professor of a set of lecture notes, I'm attempting to combine this with another set of notes that I have from throughout the course written through LyX. I would like to use LyX instead of combining in another TeX editor as I find it much more readable and easier to edit.
When importing from 'File -> Import -> LaTeX (Plain)' only a small portion (3/32 pages) show up in the LyX editor. I have modified the LyX Preamble to match the Preamble of my raw .tex and it is as follows:
\documentclass[12pt]{article}\topmargin -1mm % -10mm\oddsidemargin 0mm % 7mm\evensidemargin 0mm % 7mm\textwidth 15.5cm\textheight 22.5cm %\parindent 0pt\usepackage{amsmath}\usepackage{amscd}\usepackage{amsthm}\usepackage{amssymb}\usepackage{tikz}\usetikzlibrary{positioning, calc}\setlength{\parindent}{0pt}\setlength{\parskip}{0pt}\def\beginpf{\noindent {\bf Proof. }}\newcommand{\boite}{\mbox{} \hfill $\square$}\def\endpf{\boite\medskip}\newcommand{\ndiv}{\hspace{-4pt}\not{\hspace{3pt}|}\hspace{0pt}}\def\NN{{\mathbb N}}\def\N{{\mathbb N}}\def\QQ{{\mathbb Q}}\def\Q{{\mathbb Q}}\def\RR{{\mathbb R}}\def\R{{\mathbb R}}\def\CC{{\mathbb C}}\def\C{{\mathbb C}}\def\ZZ{{\mathbb Z}}\def\Z{{\mathbb Z}}\newcommand{\GL}{\mathrm{GL}}\newcommand{\SL}{\mathrm{SL}}\newcommand{\OO}{\mathrm{O}}\newcommand{\ima}{\mathrm{im}}\newcommand{\Ker}{\mathrm{ker}}\newcommand{\conj}{\mathrm{conj}}\def\a{{\bf a}}\def\e{{\bf e}}\def\u{{\bf u}}\def\v{{\bf v}}\def\w{{\bf w}}\def\x{{\bf x}}\def\y{{\bf y}}\def\z{{\bf z}}\def\0{{\bf 0}}\def\gcd{\mathop{\rm gcd}\nolimits}\def\hcf{\mathop{\rm hcf}\nolimits}\def\lcm{\mathop{\rm lcm}\nolimits}\def\mod{\mathop{\rm mod}\nolimits}\def\ds{\displaystyle}\def\bb{\begin{bit}}\def\eb{\end{bit}}\def\eps{\varepsilon}\def\LHS{{\rm LHS}}\def\RHS{{\rm RHS}}\def\ds{\displaystyle}\def\pl{\polter{1}}\swapnumbers\theoremstyle{plain}\newtheorem{theorem}{Theorem}[section]\newtheorem{prop}[theorem]{Proposition}\newtheorem{lemma}[theorem]{Lemma}\newtheorem{corollary}[theorem]{Corollary}\newtheorem{facts}[theorem]{Facts}\theoremstyle{definition}\newtheorem{definition}[theorem]{Definition}\newtheorem{remark}[theorem]{Remark}\newtheorem{remarks}[theorem]{Remarks}\newtheorem{example}[theorem]{Example}\newtheorem{examples}[theorem]{Examples}\newtheorem{notation}[theorem]{Notation}\newtheorem{bit}[theorem]{}\def\FF{{\mathbb F}}\providecommand{\abs}[1]{\lvert#1\rvert}\providecommand{\Norm}[1]{\lVert#1\rVert}\def\b{{\bf b}}\def\Span{\mathop{\rm span}\nolimits}\def\im{\mathop{\rm im}\nolimits}\def\tr{\mathop{\rm tr}\nolimits}\def\rank{\mathop{\rm rank}\nolimits}%\def\ds{\displaystyle}\def\bp{\begin{pmatrix}}\def\ep{\end{pmatrix}}\newcommand{\pile}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}And then for the body of the .tex file the following imports fine, but the following 3000+ lines do not appear to import correctly:
\begin{document}\centerline{\Large{\textbf{MATH 2022 Groups and Vector Spaces}}}\vspace{.1in}This outline is based on the previous lecturer's lectures notes, and is a useful resource, but not exactly the same as the course as now given (though I have tried to be consistent about notation). You should take your own notes in lectures, and may use these notes as back-up.\section{Definition and examples of groups; subgroups and order}${\mathbb N} = \{0, 1, 2, 3, \ldots\}$, the set of natural numbers (note that some authors omit 0, but I do not).$\mathbb Z$, $\Q$, $\R$, and $\C$ are the sets of integers, rational numbers, real numbers, and complex numbers respectively. All come with binary operations $+$ and $\times$.\begin{definition} Fix an integer $n \ge 1$. We let $\Z_n = \{ 0, 1, 2, \ldots, n-1\}$, and we add and multiply members of ${\mathbb Z}_n$ `modulo' $n$. That is, we add or multiply two given members of ${\mathbb Z}_n$ as usual, and then find the remainder of the answer on division by $n$. This is called the \emph{ring of integers modulo $n$}. \end{definition}\medskip\textbf{Example.}$\Z_4 = \{0, 1, 2, 3\}$ and $+$ and $\times$ are given by the tables\begin{center}\begin{tabular}{ c | c c c c}$+$ & $0$ & $1$ & $2$ & $3$ \\\hline\\[-10pt]$0$ & $0$ & $1$ & $2$ & $3$ \\$1$ & $1$ & $2$ & $3$ & $0$ \\ $2$ & $2$ & $3$ & $0$ & $1$ \\ $3$ & $3$ & $0$ & $1$ & $2$ \end{tabular}\qquad\begin{tabular}{ c | c c c c}$\times$ & $0$ & $1$ & $2$ & $3$ \\\hline\\[-10pt]$0$ & $0$ & $0$ & $0$ & $0$ \\$1$ & $0$ & $1$ & $2$ & $3$ \\ $2$ & $0$ & $2$ & $0$ & $2$ \\ $3$ & $0$ & $3$ & $2$ & $1$ \end{tabular}\end{center}\begin{definition} A \emph{group} is a non-empty set $G$ on which is defined an associative binary operation $\circ$ such that there is an identity $e$ ($e \circ x = x$ and $x \circ e = x$ for all $x \in G$), and each $x \in G$ has an inverse in $G$ (an element $y$ such that $x \circ y = e$ and $y \circ x = e$). \end{definition}The full notation is $(G, \circ)$, but if $\circ$ is understood, then we write $G$ for short. Thus to check that $G$ is a group, you have to check four things:\vspace{.1in}$G$ is closed under the operation, the operation is associativethere is an identityevery element has an inverse\vspace{.1in}(note that `$G$ is closed under the operation' means that if $x, y \in G$ then $x \circ y \in G$; this is not listed as an axiom, since it is part of what is meant by `$\circ$ is a binary operation on $G$'; also notice that you should avoid saying that $G$ is `closed', as that means something else - use the {\em whole phrase} `$G$ is closed under $\circ$').\begin{examples} (1) $(\Z_4, +)$ is a group. It is closed under the operation, since any remainder modulo 4 lies in the set $\{0, 1, 2, 3\}$. Associative. For example $(3 + 2) + 1 = 1 + 1 = 2$, while $3 + (2 + 1) = 3 + 3 = 2$. In fact it inherits associativity from $+$ for $\Z$.Identity element $0$.The inverses of $0,1,2,3$ are $0,3,2,1$ respectively.\medskip(2) More generally $(\Z_n, +)$ is a group for any $n$. \medskip(3) $(\Z_4, \times)$ is not a group. It is closed under the operation as before, and the operation is associative (it inherits it from $\Z$). The identity element is $1$. But $0$ has no inverse, since there is no $y$ with $0 \cdot y = 1$.\medskip(4) The subset $\{1,2,3\}$ of $\Z_4$ is not a group under $\times$, since it is not closed under the operation.\medskip(5) The subset $\{1, 3\}$ of $\Z_4$ {\em is} a group under $\times$. It is closed under the operation since $1 \times a = a$ and $3 \times 3 = 1$.It inherits associativity from $\times$ on $\Z_4$.The identity element is $1$.The inverses of $1, 3$ are $1, 3$ respectively.\medskip(6) $(\R,+)$ is a group. The identity element is 0, and the inverse of $x$ is $-x$.\medskip(7) $(\R,\times)$ is not a group. It is closed under $\times$, $\times$ is associative, the identity is 1, but 0 has no inverse.\medskip(8) We define $\R^* = \{ x\in \R : x\neq 0\} = \R \setminus \{0\}$. Then $(\R^*,\times)$ is a group. The identity is 1, and the inverse of $x$ is $1/x$.\medskip(9) $(\R,-)$ is not a group. The operation is not associative, e.g.\ $(1-2)-3 = -4$ but $1-(2-3) = 2$. \end{examples}\begin{definition} We say that a group $(G,\circ)$ is \emph{abelian} if the operation $\circ$ is commutative, that is, $x \circ y = y \circ x$ for all $x, y \in G$. \end{definition}\medskip\textbf{Examples.} $(\Z_4,+)$, $(\R,+)$, $(\R^*,\times)$ are abelian groups. This next example is not.\begin{example} (The dihedral group $D_3$)Consider an equilateral triangle $XYZ$ with centroid $O$.\[\begin{tikzpicture}[scale=0.8] \coordinate[label=above left:$Y$] (Y) at (0,0); \coordinate[label=above right:$Z$] (Z) at (4,0); \coordinate[label=above:$X$] (X) at (2,3.464); \coordinate[label=$O$] (O) at (2,1.1547); \coordinate[label=below:A] (A) at (2, -0.6); \coordinate[label=right:B] (B) at (3.8,2.1939); \coordinate[label=left:C] (C) at (0.2,2.1939); \draw [dashed] (-0.3, -0.1732) -- (B); \draw [dashed] (4.3, -0.1732) -- (C); \draw [dashed] (A) -- (2,3.5); \draw [line width=1.5pt] (X) -- (Y) -- (Z) -- cycle; \end{tikzpicture}\]The isometries of the plane preserving the triangle are\[\begin{array}{c|l}I & \text{do nothing}\\R & \text{rotate about $O$ by angle $2\pi/3$ (clockwise)}\\S & \text{rotate about $O$ by angle $2\pi/3$ (anticlockwise)}\\A & \text{reflect in line $XO$}\\B & \text{reflect in line $YO$}\\C & \text{reflect in line $ZO$.}\end{array}\]The \emph{dihedral group} $D_3$ is given by the set $D_3 = \{ I, R, S, A, B, C\}$ with the operation $\circ$ given by composition. Specifically, $P \circ Q$ means `do $Q$ first, then $P$'.For example $A \circ R = C$, $R \circ A = B$, $A \circ B = S$. Then $\circ$ gives the following group table (where we write $P \circ Q$ in row $P$, column $Q$).\begin{center}\begin{tabular}{ c | c c c c c c }$\circ$ & $I$ & $R$ & $S$ & $A$ & $B$ & $C$ \\\hline\\[-10pt]$I$ & $I$ & $R$ & $S$ & $A$ & $B$ & $C$ \\$R$ & $R$ & $S$ & $I$ & $B$ & $C$ & $A$ \\$S$ & $S$ & $I$ & $R$ & $C$ & $A$ & $B$ \\$A$ & $A$ & $C$ & $B$ & $I$ & $S$ & $R$ \\$B$ & $B$ & $A$ & $C$ & $R$ & $I$ & $S$ \\$C$ & $C$ & $B$ & $A$ & $S$ & $R$ & $I$ \end{tabular}\end{center}The identity element is $I$. The inverses of $I, R, S, A, B, C$ are $I, S, R, A, B, C$ respectively.\end{example}When attempting to remove the
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the whole body does import, but then a large amount of errors prevents the document from being rendered, what would you suggest as the simplest fix for this. Additionally (although this is a minor problem in the long run) when imported there is still a large amount of LaTeX code environments present, what is the simplest way of cleaning these up. Thanks in advance and again, apologies for any formatting errors/unnecessary parts.