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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-angg "LATEX/2009fractions.tex")
% (find-dn4ex "edrx08.sty")
% (find-angg ".emacs.templates" "s2008a")
% (defun c () (interactive) (find-zsh "cd ~/LATEX/ && ~/dednat4/dednat41 2009fractions.tex && latex 2009fractions.tex"))
% (defun c () (interactive) (find-zsh "cd ~/LATEX/ && ~/dednat4/dednat41 2009fractions.tex && pdflatex 2009fractions.tex"))
% (eev "cd ~/LATEX/ && Scp 2009fractions.{dvi,pdf} edrx@angg.twu.net:slow_html/LATEX/")
% (find-dvipage "~/LATEX/2009fractions.dvi")
% (find-pspage "~/LATEX/2009fractions.pdf")
% (find-zsh0 "cd ~/LATEX/ && dvips -D 300 -o 2009fractions.ps 2009fractions.dvi")
% (find-pspage "~/LATEX/2009fractions.ps")
% (find-zsh0 "cd ~/LATEX/ && dvips -D 300 -o tmp.ps tmp.dvi")
% (find-pspage "~/LATEX/tmp.ps")
% (ee-cp "~/LATEX/2009fractions.pdf" (ee-twupfile "LATEX/2009fractions.pdf") 'over)
% (ee-cp "~/LATEX/2009fractions.pdf" (ee-twusfile "LATEX/2009fractions.pdf") 'over)
% (find-angg ".emacs.papers" "fritz")
% (find-angg ".emacs.papers" "johnstone")
% (find-angg "books/__cats/__cats.el" "borceux")
% (find-angg "books/__cats/__cats.el" "gabriel-zisman")
\documentclass[oneside]{book}
\usepackage[latin1]{inputenc}
\usepackage{edrx08} % (find-dn4ex "edrx08.sty")
%L process "edrx08.sty" -- (find-dn4ex "edrx08.sty")
\input edrxheadfoot.tex % (find-dn4ex "edrxheadfoot.tex")
\begin{document}
\input 2009fractions.dnt
%*
% (eedn4-51-bounded)
Notes on categories of fractions.
\msk
Index of the slides:
\msk
% To update the list of slides uncomment this line:
%\makelos{tmp.los}
% then rerun LaTeX on this file, and insert the contents of "tmp.los"
% below, by hand (i.e., with "insert-file"):
% (find-fline "tmp.los")
% (insert-file "tmp.los")
\def\ptwo#1#2{\begin{pmatrix} #1 \\ #2 \end{pmatrix}}
\def\sm#1{\begin{smallmatrix}#1\end{smallmatrix}}
\def\scrE{{\mathscr{E}}}
\def\scrF{{\mathscr{F}}}
%D diagram filter-Phi
%D 2Dx 100 +15 +15 +20 +15 +15 +35 +20 +20 +28 +18 +18
%D 2D 100 U a
%D 2D v v
%D 2D | |
%D 2D v u L(u) v
%D 2D +30 1_\scrE --> Ø_\scrE 1 ---> L(Ø_\scrE) b ----> c d ----> e
%D 2D | |
%D 2D | |
%D 2D v v
%D 2D +30 Ø_\scrF f
%D 2D
%D 2D +20 \scrE ----------> \scrF E ---------> F
%D 2D L
%D 2D +20
%D 2D
%D (( U 1_\scrE Ø_\scrE
%D @ 0 @ 1 >-> @ 1 @ 2 -> .plabel= a u
%D ))
%D (( 1 L(Ø_\scrE) Ø_\scrF
%D @ 0 @ 1 -> .plabel= a L(u) @ 1 @ 2 -> .plabel= r \Phi
%D @ 0 @ 2 .> .plabel= l t
%D ))
%D (( \scrE \scrF -> .plabel= b L
%D ))
%D (( a .tex= \ptwo{m\N}{\N}
%D b .tex= \ptwo{\N}{\N}
%D c .tex= \ptwo{\N{×}Ø}{\N}
%D @ 0 @ 1 >-> @ 1 @ 2 -> .plabel= a \sm{ðn.\\nÝm\N}
%D ))
%D (( d .tex= 1
%D e .tex= (N{->}Ø)
%D f .tex= Ø
%D d e -> .plabel= a \sm{ð*.ðn.\\nÝm\N}
%D e f -> .plabel= r \sm{ðP.Îm.\\ýk.P(mk)}
%D d f .> .plabel= l {§}
%D ))
%D (( E .tex= \Set/\N
%D F .tex= \Set
%D @ 0 @ 1 -> sl__ .plabel= b å_\N
%D @ 0 @ 1 <- .plabel= m K
%D @ 0 @ 1 .> sl^^ .plabel= a Æ_\N
%D ))
%D enddiagram
%D
$$\diag{filter-Phi}$$
%D diagram ??
%D 2Dx 100 +30 +30 +55
%D 2D 100 U^*(X) <---| X a <------| b
%D 2D | | | |
%D 2D U^*(f)| |f | |
%D 2D v v v v
%D 2D +30 U^*(Y) <---| Y c <------| d
%D 2D
%D 2D +20 \scrE/\U <- \scrE \Set/m\N <-- \Set/\N
%D 2D
%D (( U^*(X) X U^*(Y) Y
%D @ 0 @ 1 <-|
%D @ 0 @ 2 -> .plabel= l U^*(f)
%D @ 1 @ 3 -> .plabel= r f
%D @ 2 @ 3 <-|
%D @ 0 @ 3 harrownodes nil 20 nil <-|
%D ))
%D (( \scrE/\U \scrE <-
%D ))
%D (( a .tex= \ptwo{Æk¨m\N.X_k}{m\N}
%D b .tex= \ptwo{Æn¨\N.X_n}{\N}
%D c .tex= \ptwo{Æk¨m\N.Y_k}{m\N}
%D d .tex= \ptwo{Æn¨\N.Y_n}{\N}
%D @ 0 @ 1 <-|
%D @ 0 @ 2 -> .plabel= l U^*(f)
%D @ 1 @ 3 -> .plabel= r f
%D @ 2 @ 3 <-|
%D @ 0 @ 3 harrownodes nil 20 nil <-|
%D ))
%D (( \Set/m\N \Set/\N <-
%D ))
%D enddiagram
%D
$$\diag{??}$$
%D diagram filter-Phi2
%D 2Dx 100 +15 +15 +20 +15 +15
%D 2D 100 U
%D 2D v
%D 2D |
%D 2D v u L(u)
%D 2D +30 1_\scrE --> Ø_\scrE 1 ---> L(Ø_\scrE)
%D 2D |
%D 2D |
%D 2D v
%D 2D +30 U^*(X) <-----| X Ø_\scrF
%D 2D | |
%D 2D U^*(f)| |f
%D 2D v v
%D 2D +30 U^*(Y) <-----| Y
%D 2D
%D 2D +20 \scrE/\U <--- \scrE ---------> \scrF
%D 2D U^* L
%D 2D +20
%D 2D
%D (( U 1_\scrE Ø_\scrE
%D @ 0 @ 1 >-> @ 1 @ 2 -> .plabel= a u
%D ))
%D (( 1 L(Ø_\scrE) Ø_\scrF
%D @ 0 @ 1 -> .plabel= a L(u) @ 1 @ 2 -> .plabel= r \Phi
%D @ 0 @ 2 .> .plabel= l t
%D ))
%D (( \scrE \scrF -> .plabel= b L
%D ))
%D enddiagram
%D
$$\diag{filter-Phi2}$$
%D diagram filter-Phi3
%D 2Dx 100 +30 +20 +20 +20 +15 +15
%D 2D 100 a
%D 2D v
%D 2D |
%D 2D v
%D 2D +30 b ----> c d ----> e
%D 2D |
%D 2D |
%D 2D v
%D 2D +30 g <-------| h f
%D 2D | |
%D 2D | |
%D 2D v v
%D 2D +30 i <-------| j
%D 2D
%D 2D +25 E/mN <------- E ---------> F
%D 2D U^* L
%D 2D +20
%D 2D
%D (( a .tex= \ptwo{m\N}{\N}
%D b .tex= \ptwo{\N}{\N}
%D c .tex= \ptwo{\N{×}Ø}{\N}
%D @ 0 @ 1 >-> @ 1 @ 2 -> .plabel= a \sm{ðn.\\nÝm\N}
%D ))
%D (( d .tex= 1
%D e .tex= (N{->}Ø)
%D f .tex= Ø
%D d e -> .plabel= a \sm{ð*.ðn.\\nÝm\N}
%D e f -> .plabel= r \sm{ðP.Îm.\\ýk.P(mk)}
%D d f .> .plabel= l {§}
%D ))
%D (( E/mN .tex= \Set/m\N
%D E .tex= \Set/\N
%D F .tex= \Set
%D @ 0 @ 1 <- .plabel= m U^*
%D @ 1 @ 2 -> sl__ .plabel= b å_\N
%D @ 1 @ 2 <- .plabel= m K
%D @ 1 @ 2 .> sl^^ .plabel= a Æ_\N
%D ))
%D (( g .tex= \ptwo{Æk¨m\N.X_k}{m\N}
%D h .tex= \ptwo{Æn¨\N.X_n}{\N}
%D i .tex= \ptwo{Æk¨m\N.Y_k}{m\N}
%D j .tex= \ptwo{Æn¨\N.Y_n}{\N}
%D @ 0 @ 1 <-|
%D @ 0 @ 2 -> .plabel= l U^*(f)
%D @ 1 @ 3 -> .plabel= r f
%D @ 2 @ 3 <-|
%D @ 0 @ 3 harrownodes nil 20 nil <-|
%D ))
%D enddiagram
%D
$$\diag{filter-Phi3}$$
%D diagram ??
%D 2Dx 100 +30 +30 +55
%D 2D 100 U^*(X) <---| X a <------| b
%D 2D | | | |
%D 2D U^*(f)| |f | |
%D 2D v v v v
%D 2D +30 U^*(Y) <---| Y c <------| d
%D 2D
%D 2D +20 \scrE/\U <- \scrE \Set/m\N <-- \Set/\N
%D 2D
%D (( U^*(X) X U^*(Y) Y
%D @ 0 @ 1 <-|
%D @ 0 @ 2 -> .plabel= l U^*(f)
%D @ 1 @ 3 -> .plabel= r f
%D @ 2 @ 3 <-|
%D @ 0 @ 3 harrownodes nil 20 nil <-|
%D ))
%D (( \scrE/\U \scrE <-
%D ))
%D (( a .tex= \ptwo{Æk¨m\N.X_k}{m\N}
%D b .tex= \ptwo{Æn¨\N.X_n}{\N}
%D c .tex= \ptwo{Æk¨m\N.Y_k}{m\N}
%D d .tex= \ptwo{Æn¨\N.Y_n}{\N}
%D @ 0 @ 1 <-|
%D @ 0 @ 2 -> .plabel= l U^*(f)
%D @ 1 @ 3 -> .plabel= r f
%D @ 2 @ 3 <-|
%D @ 0 @ 3 harrownodes nil 20 nil <-|
%D ))
%D (( \Set/m\N \Set/\N <-
%D ))
%D enddiagram
%D
$$\diag{??}$$
%*
\end{document}
% Local Variables:
% coding: raw-text-unix
% ee-anchor-format: "«%s»"
% End: