Question 1: You have to "hide" the height of the title
\renewcommand\thechapter{\arabic{chapter}.0}
\titleformat{\chapter}[display]
{\normalfont\fontsize{25pt}{0pt}\bfseries\sffamily}
{\varhrulefill\enskip\thechapter\enskip\varhrulefill}
{12pt} % <--- modify this for lowering the title
{\center\ignoretitleheight}
\newcommand{\ignoretitleheight}[1]{\leavevmode\smash{\MakeUppercase{#1}}}
Question 2: You have to avoid inserting the \lineskip
when two lines are "too near" to each other
\newcommand{\trailthesubsection}[1]{\MakeUppercase{#1} (\thesubsection)}
\titleformat{\subsection}
{\normalfont\fontsize{15pt}{14pt}\bfseries\sffamily\lineskiplimit=-\maxdimen}
{}
{0pt}
{\filcenter\trailthesubsection}
\titleformat{\subsubsection}
{\normalfont\fontsize{12pt}{11pt}\bfseries\scshape\lineskiplimit=-\maxdimen}
{}
{0pt}
{\filcenter}
However the spacing won't be uniform if some character is higher than the stated baseline skip (an accented uppercase letter, for example).
If you want to use ntheorem
instead of amsthm
as the back-end, then you will have to resign to some of the formatting features that were available with amsthm
and some other changes will have to be made:
The commands \NAME
, \NUMBER
, and \NOTE
will no longer be available.
To simulate the desired head formatting, you can use the headformat=swapnumber
option instead, but then you loose the flexibility to change the head format.
The option qed=\text{\guillemotleft}
will have to be used in \declaretheoremstyle
instead of in \declaretheorem
(which, in any case, makes sense).
Your proof
environment will have to be defined separately.
Here's an example of how your definitions would look like using ntheorem
:
\documentclass[10pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath, amssymb}
\usepackage[thmmarks,amsmath]{ntheorem}
\usepackage{thmtools}
\numberwithin{equation}{section}
\declaretheoremstyle[headformat=swapnumber,bodyfont=\normalfont]{theorem}
\declaretheoremstyle[headformat=swapnumber,bodyfont=\normalfont
,qed=\text{\guillemotleft}]{mydefinition}
\declaretheorem[style=theorem,sibling=equation]{theorem}
\declaretheorem[style=theorem,sibling=equation]{proposition}
\declaretheorem[style=theorem,sibling=equation]{lemma}
\declaretheorem[style=mydefinition,sibling=equation]{definition}
\declaretheorem[style=mydefinition,sibling=equation]{exercise}
\declaretheorem[style=mydefinition,sibling=equation]{example}
\newtheorem*{proof}{Proof}
%% Math macro stuff to make this compile
\DeclareMathOperator{\Spec}{Spec} % Spectrum
\DeclareMathOperator{\M}{M}
\DeclareMathOperator{\Ga}{Ga}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Gm}{Gm}
\def\ol{\overline}
\begin{document}
\begin{definition}
A \emph{group variety over $k$} is an integral group scheme of finite type over $\Spec k$.
\end{definition}
\begin{proof}
Test
\end{proof}
\begin{example}
Let $k$ be a field and $R$ a commutative $k$-algebra.
\begin{itemize}
\item The varieties $\Ga_{k} = \Spec k[x]$ and $\Gm_{k} = \Spec k[x,y]/(xy - 1)$ are group varieties. Indeed, $\Ga_{k}(R)$ is the additive group underlying $R$, and $\Gm_{k}(R) = R^*$ is the group of units in $R$.
\item The variety $\M_{n,k} = \Spec k[(x_{ij})_{ij}]$ is a group variety. Also the closed sub variety $\GL_{n,k}$ defined by the polynomial $\det \left( (x_{ij})_{ij} \right) - 1$ is a group variety. The $R$-valued points are the $n \times n$-matrices $\M_{n,k}(R)$ with coefficients in $R$, and $\GL_{n,k}(R)$ consists of the invertible matrices respectively. Observe that $\Gm_{k} = \GL_{1,k}$.
\item The variety $\mu_{n,k} = \Spec k[x]/(x^n -1)$ is a group variety, and $\mu_{n,k}(R)$ consists of the group of $n$-th roots of unity in $R$.
\item An elliptic curve over $k$ is defined as a proper variety $E/k$ that is smooth of relative dimension $1$, of which the geometric fibre $E_{\ol{k}}$ has genus $1$, together with a given point $0 \in E(k)$. It can be shown that every elliptic curve is a group variety. Actually they form an important class of objects in the study of abelian varieties.
\end{itemize}
\end{example}
\end{document}
Best Answer
Using, for example,
\theoremprework
you can set those lengths for particular groups of theorem-like structures:Using the
thmtools
front-end, you can define custom styles with their own values forspaceabove
,spacebelow
: