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[diderot] Diff of /trunk/doc/diderot.tex
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Diff of /trunk/doc/diderot.tex

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revision 43, Fri Mar 12 04:28:29 2010 UTC revision 44, Tue Apr 6 15:36:27 2010 UTC
# Line 41  Line 41 
41             & \mid & \TYint & \text{integers} \\[1em]             & \mid & \TYint & \text{integers} \\[1em]
42        % \mu for memory, where images of rawtensors will live (or on disk)        % \mu for memory, where images of rawtensors will live (or on disk)
43        \mu & ::= & \TYrawten{\Seq{d}}{\rho} & \begin{minipage}[l]{3in}\begin{flushright}        \mu & ::= & \TYrawten{\Seq{d}}{\rho} & \begin{minipage}[l]{3in}\begin{flushright}
44            tensors of order $o$ and dimension $d$,\\with coefficients of type $\rho$            tensors of order $|\Seq{d}|$ and dimensions $\Seq{d}$,\\with coefficients of type $\rho$
45            \end{flushright}\end{minipage}\\[1em]            \end{flushright}\end{minipage}\\[1em]
46        \theta & ::= & \TYtensor{\Seq{d}} & \begin{minipage}[l]{3in}\begin{flushright}        \theta & ::= & \TYtensor{\Seq{d}} & \begin{minipage}[l]{3in}\begin{flushright}
47            tensors of order $o$ and dimension $d$,\\with real coefficients            tensors of order $|\Seq{d}|$ and dimensions $\Seq{d}$,\\with real coefficients
48            \end{flushright}\end{minipage}\\[1em]            \end{flushright}\end{minipage}\\[1em]
49        \tau & ::= & \iota \\        \tau & ::= & \iota \\
50             & \mid & \theta \\             & \mid & \theta \\
# Line 72  Line 72 
72  \begin{displaymath}  \begin{displaymath}
73    \begin{array}{cl}    \begin{array}{cl}
74      \BinopTy{{\odot}}{\tau}{\tau}{\tau}      \BinopTy{{\odot}}{\tau}{\tau}{\tau}
75      & \text{for $\odot\in\SET{{+},{-},{*},{/}}$ and $\tau\in\SET{\TYint,\TYreal}$} \\      & \text{for $\odot\in\SET{\OP{+},\OP{-},\OP{*},\OP{/}}$ and $\tau\in\SET{\TYint,\TYreal}$} \\
76      \UnopTy{{-}}{\tau}{\tau}      \UnopTy{\OP{-}}{\tau}{\tau}
77      & \text{for $\tau\in\SET{\TYint,\TYreal}$}      & \text{for $\tau\in\SET{\TYint,\TYreal}$}
78    \end{array}%    \end{array}%
79  \end{displaymath}%  \end{displaymath}%
# Line 81  Line 81 
81  \noindent{}\point Comparisons:  \noindent{}\point Comparisons:
82  \begin{displaymath}  \begin{displaymath}
83    \BinopTy{{\odot}}{\tau}{\tau}{\TYbool}    \BinopTy{{\odot}}{\tau}{\tau}{\TYbool}
84    \qquad\text{for $\odot\in\SET{{<},{\leq},{=},{\neq}{>},{\geq}}$ and $\tau\in\SET{\TYint,\TYreal}$}    \qquad\text{for $\odot\in\SET{\OP{<},{\leq},\OP{=},{\neq}\OP{>},{\geq}}$ and $\tau\in\SET{\TYint,\TYreal}$}
85  \end{displaymath}%  \end{displaymath}%
86    
87    
# Line 92  Line 92 
92  \noindent{}\point Addition:  \noindent{}\point Addition:
93  \begin{displaymath}  \begin{displaymath}
94    \BinopTy{{\odot}}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}}    \BinopTy{{\odot}}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}}
95    \qquad\text{for $\odot\in\SET{{+},{-}}$}    \qquad\text{for $\odot\in\SET{\OP{+},\OP{-}}$}
96  \end{displaymath}%  \end{displaymath}%
97    
98  \noindent{}\point Negation:  \noindent{}\point Negation:
99  \begin{displaymath}  \begin{displaymath}
100    \UnopTy{-}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}}    \UnopTy{\OP{-}}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}}
101  \end{displaymath}%  \end{displaymath}%
102    
103  \noindent{}\point Scalar division:  \noindent{}\point Scalar division:
104  \begin{displaymath}  \begin{displaymath}
105    \BinopTy{{/}}{\TYtensor{\Seq{d}}}{\TYreal}{\TYtensor{\Seq{d}}}    \BinopTy{\OP{/}}{\TYtensor{\Seq{d}}}{\TYreal}{\TYtensor{\Seq{d}}}
106  \end{displaymath}%  \end{displaymath}%
107    
108  \noindent{}\point Scalar multiplication (scalar times order-N):  \noindent{}\point Scalar multiplication (scalar times order-N):
109  \begin{displaymath}  \begin{displaymath}
110    \begin{array}{c}    \begin{array}{c}
111      \BinopTy{{?}}{\TYreal}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}} \\      \BinopTy{\OP{*}}{\TYreal}{\TYtensor{\Seq{d}}}{\TYtensor{\Seq{d}}} \\
112      \BinopTy{{?}}{\TYtensor{\Seq{d}}}{\TYreal}{\TYtensor{\Seq{d}}}      \BinopTy{\OP{*}}{\TYtensor{\Seq{d}}}{\TYreal}{\TYtensor{\Seq{d}}}
113    \end{array}%    \end{array}%
114  \end{displaymath}%  \end{displaymath}%
 Possible direct notation syntax (TBD): ~~ {\tt *} ~~ `` '' (space)  
115    
116  \noindent{}\point Tensor scalar multiplication (contraction of two order-N  \noindent{}\point Tensor scalar multiplication (contraction of two order-N
117  tensors down to a scalar, \eg{} dot product of vectors, double dot  tensors down to a scalar, \eg{} dot product of vectors, double dot
# Line 181  Line 180 
180  \noindent{}\point Scalar multiplication:  \noindent{}\point Scalar multiplication:
181  \begin{displaymath}  \begin{displaymath}
182    \begin{array}{c}    \begin{array}{c}
183      \BinopTy{{*}}{\TYreal}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} \\      \BinopTy{\OP{*}}{\TYreal}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} \\
184      \BinopTy{{*}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}}      \BinopTy{\OP{*}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}}
185    \end{array}%    \end{array}%
186  \end{displaymath}%  \end{displaymath}%
187    
188  \noindent{}\point Scalar division:  \noindent{}\point Scalar division:
189  \begin{displaymath}  \begin{displaymath}
190    \BinopTy{{/}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}}    \BinopTy{\OP{/}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}}
191  \end{displaymath}%  \end{displaymath}%
192    
193  \noindent{}\point Negation:  \noindent{}\point Negation:
194  \begin{displaymath}  \begin{displaymath}
195    \UnopTy{-}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}}    \UnopTy{\OP{-}}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}}
196  \end{displaymath}%  \end{displaymath}%
197    
198  \noindent{}\point Addition:  \noindent{}\point Addition:
# Line 203  Line 202 
202    \BinopTy{{\odot}}{\theta}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} \\    \BinopTy{{\odot}}{\theta}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} \\
203    \BinopTy{{\odot}}{\TYfield{k_1}{d}{\theta}}{\TYfield{k_2}{d}{\theta}}{\TYfield{\min(k_1,k_2)}{d}{\theta}}    \BinopTy{{\odot}}{\TYfield{k_1}{d}{\theta}}{\TYfield{k_2}{d}{\theta}}{\TYfield{\min(k_1,k_2)}{d}{\theta}}
204    \end{array}%    \end{array}%
205    \qquad\text{for $\odot\in\SET{{+},{-}}$}    \qquad\text{for $\odot\in\SET{\OP{+},\OP{-}}$}
206  \end{displaymath}%  \end{displaymath}%
207    
208  \noindent{}\point Differentiation:  \noindent{}\point Differentiation:
# Line 214  Line 213 
213    
214  \noindent{}\point Probing:  \noindent{}\point Probing:
215  \begin{displaymath}  \begin{displaymath}
216    \BinopTy{@}{\TYfield{k}{d}{\theta}}{\TYvec{d}}{\theta}    \BinopTy{\OP{@}}{\TYfield{k}{d}{\theta}}{\TYvec{d}}{\theta}
217  \end{displaymath}%  \end{displaymath}%
218    
219  \end{document}  \end{document}

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