gtsam/doc/macros.lyx

#LyX 2.0 created this file. For more info see http://www.lyx.org/
\lyxformat 413
\begin_document
\begin_header
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\cite_engine basic
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\index Index
\shortcut idx
\color #008000
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\end_header

\begin_body

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
Derivatives
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\deriv}[2]{\frac{\partial#1}{\partial#2}}
{\frac{\partial#1}{\partial#2}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\at}[1]{#1\biggr\vert_{\#2}}
{#1\biggr\vert_{\#2}}
\end_inset

 
\begin_inset FormulaMacro
\newcommand{\Jac}[3]{ \at{\deriv{#1}{#2}} {#3} }
{\at{\deriv{#1}{#2}}#3}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
Lie Groups
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\xhat}{\hat{x}}
{\hat{x}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\yhat}{\hat{y}}
{\hat{y}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\Ad}[1]{Ad_{#1}}
{Ad_{#1}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\AAdd}[1]{\mathbf{\mathop{Ad}}{}_{#1}}
{\mathbf{\mathop{Ad}}{}_{#1}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\define}{\stackrel{\Delta}{=}}
{\stackrel{\Delta}{=}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\gg}{\mathfrak{g}}
{\mathfrak{g}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\Rn}{\mathbb{R}^{n}}
{\mathbb{R}^{n}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
SO(2)
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\Rone}{\mathfrak{\mathbb{R}}}
{\mathfrak{\mathbb{R}}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\Rtwo}{\mathfrak{\mathbb{R}^{2}}}
{\mathfrak{\mathbb{R}^{2}}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\SOtwo}{SO(2)}
{SO(2)}
\end_inset


\begin_inset FormulaMacro
\newcommand{\sotwo}{\mathfrak{so(2)}}
{\mathfrak{so(2)}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\that}{\hat{\theta}}
{\hat{\theta}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\skew}[1]{[#1]_{+}}
{[#1]_{+}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
SE(2)
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\SEtwo}{SE(2)}
{SE(2)}
\end_inset


\begin_inset FormulaMacro
\newcommand{\setwo}{\mathfrak{se(2)}}
{\mathfrak{se(2)}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\Skew}[1]{[#1]_{\times}}
{[#1]_{\times}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
SO(3)
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\Rthree}{\mathfrak{\mathbb{R}^{3}}}
{\mathfrak{\mathbb{R}^{3}}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\SOthree}{SO(3)}
{SO(3)}
\end_inset


\begin_inset FormulaMacro
\newcommand{\sothree}{\mathfrak{so(3)}}
{\mathfrak{so(3)}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\what}{\hat{\omega}}
{\hat{\omega}}
\end_inset


\begin_inset FormulaMacro
\renewcommand{\Skew}[1]{[#1]_{\times}}
{[#1]_{\times}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
SE(3)
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\Rsix}{\mathfrak{\mathbb{R}^{6}}}
{\mathfrak{\mathbb{R}^{6}}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\SEthree}{SE(3)}
{SE(3)}
\end_inset


\begin_inset FormulaMacro
\newcommand{\sethree}{\mathfrak{se(3)}}
{\mathfrak{se(3)}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\xihat}{\hat{\xi}}
{\hat{\xi}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status open

\begin_layout Plain Layout
Aff(2),6
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\Afftwo}{Aff(2)}
{Aff(2)}
\end_inset


\begin_inset FormulaMacro
\newcommand{\afftwo}{\mathfrak{aff(2)}}
{\mathfrak{aff(2)}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\aa}{a}
{a}
\end_inset


\begin_inset FormulaMacro
\newcommand{\ahat}{\hat{a}}
{\hat{a}}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Comment
status collapsed

\begin_layout Plain Layout
SL(3),8
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\SLthree}{SL(3)}
{SL(3)}
\end_inset


\begin_inset FormulaMacro
\newcommand{\slthree}{\mathfrak{sl(3)}}
{\mathfrak{sl(3)}}
\end_inset


\begin_inset FormulaMacro
\newcommand{\hh}{h}
{h}
\end_inset


\begin_inset FormulaMacro
\newcommand{\hhat}{\hat{h}}
{\hat{h}}
\end_inset


\end_layout

\end_body
\end_document