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[diderot] View of /trunk/doc/defs.tex
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View of /trunk/doc/defs.tex

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Revision 21 - (download) (as text) (annotate)
Sat Jan 16 18:16:32 2010 UTC (9 years, 6 months ago) by glk
File size: 3950 byte(s)
* addition of a "rawten" type, also parameterized by \rho, which represents the type of tensors as they are stored in an image on disk or in memory.  As it was, images were only of type \rho, with no indication of the tensor structure.  The only annoyance now is that this allows one to store on disk or in memory tensors with int coefficients, which is probably nonsense, but its harmless.

* renamed the mapping of image to field from "sample" to "convolve".  However, its not clear to me if the definition as I wrote it is sufficiently clear that the mapping is from an image of rawten<o,d,\rho> to an field of tensor<o,d>, where the "o"s and "d"s must match up.

* added negation of fields

* moved what was in "tensor arithmatic" to the "addition" section.
\usepackage{times}
%-------------------------
% the following magic makes the tt font in math mode be the same as the
% normal tt font (i.e., Courier)
%
\SetMathAlphabet{\mathtt}{normal}{OT1}{pcr}{n}{n}
\SetMathAlphabet{\mathtt}{bold}{OT1}{pcr}{bx}{n}
%-------------------------

\usepackage{amsmath}

\newcommand{\NOTE}[1]{%
  \par\leavevmode\noindent\textbf{[[ #1 ]]}\par\leavevmode\noindent}
\newcommand{\CUT}[1]{}
\newcommand{\SIDENOTE}[1]{%
  \marginpar{\tiny\raggedright{#1}}}

\newcommand{\appref}[1]{Appendix~\ref{#1}}
\newcommand{\chapref}[1]{Chapter~\ref{#1}}
\newcommand{\secref}[1]{Section~\ref{#1}}
\newcommand{\tblref}[1]{Table~\ref{#1}}
\newcommand{\figref}[1]{Figure~\ref{#1}}
\newcommand{\listingref}[1]{Listing~\ref{#1}}
\newcommand{\pref}[1]{{page~\pageref{#1}}}
\newcommand{\defref}[1]{Definition~\ref{#1}}
\newcommand{\ruleref}[1]{Rule~\ref{#1}}

\newcommand{\eg}{{\em e.g.}}
\newcommand{\cf}{{\em cf.}}
\newcommand{\ie}{{\em i.e.}}
\newcommand{\etc}{{\em etc.\/}}
\newcommand{\naive}{na\"{\i}ve}
\newcommand{\ala}{{\em \`{a} la\/}}
\newcommand{\etal}{{\em et al.\/}}
\newcommand{\role}{r\^{o}le}
\newcommand{\vs}{{\em vs.}}
\newcommand{\forte}{{fort\'{e}\/}}

%
% font commands
\providecommand{\bftt}[1]{{\ttfamily\bfseries{}#1}}
\providecommand{\ittt}[1]{{\ttfamily\itshape{}#1}}
\providecommand{\kw}[1]{\bftt{#1}}
\providecommand{\nt}[1]{{\rmfamily\itshape{#1}}}
\providecommand{\term}[1]{{\sffamily{#1}}}
\providecommand{\tyvar}[1]{\ittt{#1}}
%
% math-mode versions
\providecommand{\mkw}[1]{\ensuremath{\text{\kw{#1}}}}
\providecommand{\mnt}[1]{\ensuremath{\text{\nt{#1}}}}
\providecommand{\mterm}[1]{\ensuremath{\text{\term{#1}}}}
\providecommand{\mtyvar}[1]{\ensuremath{\text{\tyvar{#1}}}}

% braces (in math mode)
\newcommand{\LCB}{\mkw{\{}}
\newcommand{\RCB}{\mkw{\}}}

% underscore
\newcommand{\US}{\char`\_}

%%%%%
% Some common math notation
%

% double brackets
\newcommand{\LDB}{\ensuremath{[\mskip -3mu [}}
\newcommand{\RDB}{\ensuremath{]\mskip -3mu ]}}

\newcommand{\dom}{\ensuremath{\mathrm{dom}}}
\newcommand{\rng}{\ensuremath{\mathrm{rng}}}

% sets
\newcommand{\SET}[1]{\ensuremath{\{#1\}}}
\newcommand{\Fin}{\textrm{Fin}}     % finite power set
\newcommand{\DISJOINT}[2]{\ensuremath{#1 \pitchfork #2}}
\newcommand{\finsubset}{\mathrel{\stackrel{\textrm{fin}}{\subset}}}

% finite maps
\newcommand{\finmap}{\mathrel{\stackrel{\textrm{fin}}{\rightarrow}}}
\newcommand{\MAP}[2]{\SET{#1 \mapsto #2}}
\newcommand{\EXTEND}[2]{\ensuremath{#1{\pm}#2}}
\newcommand{\EXTENDone}[3]{\EXTEND{#1}{\MAP{#2}{#3}}}
\newcommand{\SUBST}[3]{\ensuremath{#1[#2\mapsto{}#3]}}
\newcommand{\SUBSTTWO}[5]{\ensuremath{#1[#2\mapsto{}#3,#4\mapsto{}#5]}}

% inference rules
\newcommand{\infer}[2]{\frac{\;{#2}\;}{\;{#1}\;}}
%
% labeled inference rule:
%   \INFER{name}{label}{conclusion}{assumption}
%
\newcommand{\INFER}[2]{%                                                      
  \begin{equation*}
    \infer{#1}{#2}                                                            
  \end{equation*}}                                                               

% natural numbers
%
\newcommand{\Nat}{\mathcal{N}}

% Diderot types
%
\newcommand{\TYbool}{\mathbf{bool}}
\newcommand{\TYint}{\mathbf{int}}
\newcommand{\TYreal}{\mathbf{real}}
\newcommand{\TYrawten}[3]{\mathbf{rawten}\langle{}#1,#2,#3\rangle{}}
\newcommand{\TYtensor}[2]{\mathbf{tensor}\langle{}#1,#2\rangle{}}
\newcommand{\TYmatrix}[2]{\mathbf{matrix}\langle{}#1,#2\rangle{}}
\newcommand{\TYimage}[2]{\mathbf{image}_{#1}\langle{}#2\rangle{}}
\newcommand{\TYkern}[1]{\mathbf{kern}^{#1}}
\newcommand{\TYfield}[3]{\mathbf{field}^{#1}_{#2}\langle{}#3\rangle{}}
\newcommand{\TYvec}[1]{\mathbf{vec}_{#1}}

% Diderot operators
%
\newcommand{\OPdiff}{\mathbf{D}}
\newcommand{\OPconvolve}{\mathbf{convolve}}

% typing judgments
%
\newcommand{\HasTy}[2]{#1 : #2}
\newcommand{\UnopTy}[3]{\HasTy{#1}{#2 \rightarrow #3}}
\newcommand{\BinopTy}[4]{\HasTy{#1}{#2 \times #3 \rightarrow #4}}


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