From 2ba976b06ff8c59f0eec2151c5afb7671a35671e Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Tue, 14 Mar 2023 03:01:36 +0000 Subject: CTAN sync 202303140301 --- FILES.byname | 97 +- FILES.byname.gz | Bin 2516341 -> 2516655 bytes FILES.last07days | 158 +-- biblio/ctan-bibdata/ctan.bib | 22 +- biblio/ctan-bibdata/ctan.pdf | Bin 3653053 -> 3652252 bytes fonts/prodint/.DS_Store | Bin 8196 -> 0 bytes .../biblatex-contrib/biblatex-dw/latex/.DS_Store | Bin 6148 -> 0 bytes macros/latex/contrib/microtype/README.md | 2 +- macros/latex/contrib/microtype/microtype-code.pdf | Bin 2138452 -> 2139911 bytes macros/latex/contrib/microtype/microtype-utf.dtx | 2 +- macros/latex/contrib/microtype/microtype.dtx | 43 +- macros/latex/contrib/microtype/microtype.pdf | Bin 670263 -> 670821 bytes macros/latex/contrib/photobook/Makefile | 24 +- macros/latex/contrib/photobook/photobook.cls | 17 +- macros/latex/contrib/photobook/photobook.pdf | Bin 140737 -> 141191 bytes 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macros/luatex/generic/minim-pdf/README -2023/03/06 | 168316 | macros/latex/contrib/spacingtricks.zip -2023/03/06 | 1674 | language/lithuanian/doc/ChangeLog -2023/03/06 | 158960 | macros/luatex/generic/minim-math.zip -2023/03/06 | 1572 | systems/texlive/tlnet/archive/collection-pictures.r66377.tar.xz -2023/03/06 | 1528 | systems/texlive/tlnet/archive/opencolor.r66372.tar.xz -2023/03/06 | 150580 | systems/texlive/tlnet/archive/jlreq.r66374.tar.xz -2023/03/06 | 14329 | macros/luatex/generic/minim-pdf/minim-pdf.tex -2023/03/06 | 1397 | macros/luatex/latex/linebreaker/linebreaker.sty -2023/03/06 | 130186 | macros/luatex/generic/minim-pdf.zip -2023/03/06 | 12915 | macros/xetex/plain/unimath-plain-xetex/doc/unimath-plain-xetex-doc.tex -2023/03/06 | 1268380 | systems/texlive/tlnet/archive/siunitx.doc.r66370.tar.xz -2023/03/06 | 1259044 | systems/texlive/tlnet/archive/profcollege.r66371.tar.xz -2023/03/06 | 122160 | language/hyphenation/dehyph-exptl/dehyph-exptl.pdf -2023/03/06 | 117927 | biblio/biber/base/documentation/utf8-macro-map.html -2023/03/06 | 117796 | systems/texlive/tlnet/archive/siunitx.source.r66370.tar.xz -2023/03/06 | 116731 | macros/luatex/generic/minim-mp.zip -2023/03/06 | 11633 | language/hyphenation/dehyph-exptl/CHANGES -2023/03/06 | 111554 | macros/luatex/generic/minim-math/minim-math.pdf -2023/03/06 | 111274 | macros/luatex/generic/minim-pdf/minim-pdf.pdf -2023/03/06 | 1080481 | biblio/biber/base/source/biblatex-biber.tar.gz -2023/03/06 | 10755 | language/hyphenation/dehyph-exptl/INSTALL -2023/03/06 | 10656244 | systems/texlive/tlnet/archive/profcollege.doc.r66371.tar.xz -2023/03/06 | 1061236 | systems/texlive/tlnet/archive/bithesis.doc.r66369.tar.xz diff --git a/biblio/ctan-bibdata/ctan.bib b/biblio/ctan-bibdata/ctan.bib index 8b712f6c29..a04cfc007f 100644 --- a/biblio/ctan-bibdata/ctan.bib +++ b/biblio/ctan-bibdata/ctan.bib @@ -1,7 +1,7 @@ %% bib file of all CTAN packages %% (C) Herbert Voß %% -%% created at 13-03-2023, 02:01:16 +%% created at 14-03-2023, 02:00:16 %% %% This file is provided under the terms of the LPPL v1.3 or @@ -6773,8 +6773,8 @@ title = {The \texttt{biber-freebsd} package}, subtitle = {Biber binaries for FreeBSD}, author = {Philip Kime and Nikola Lečić}, - date = {2022-07-23}, - version = {2.18}, + date = {2023-03-13}, + version = {2.19}, license = {artistic2}, mirror = {https://mirror.ctan.org/biblio/biber/biber-freebsd}, url = {https://ctan.org/pkg/biber-freebsd}, @@ -44483,8 +44483,8 @@ title = {The \texttt{microtype} package}, subtitle = {Subliminal refinements towards typographical perfection}, author = {Robert Schlicht}, - date = {2023-03-07}, - version = {3.1}, + date = {2023-03-13}, + version = {3.1a}, license = {lppl1.3c}, mirror = {https://mirror.ctan.org/macros/latex/contrib/microtype}, url = {https://ctan.org/pkg/microtype}, @@ -52161,8 +52161,8 @@ title = {The \texttt{photobook} package}, subtitle = {A document class for typesetting photo books}, author = {Alex A. Naanou}, - date = {2023-03-11}, - version = {0.1.10}, + date = {2023-03-13}, + version = {0.1.13}, license = {bsd3}, mirror = {https://mirror.ctan.org/macros/latex/contrib/photobook}, url = {https://ctan.org/pkg/photobook}, @@ -53901,8 +53901,8 @@ title = {The \texttt{principia} package}, subtitle = {Notations for typesetting the “Principia Mathematica”}, author = {Landon D. C. Elkind}, - date = {2021-04-20}, - version = {1.3}, + date = {2023-03-13}, + version = {2.0}, license = {lppl1.3c}, mirror = {https://mirror.ctan.org/macros/latex/contrib/principia}, url = {https://ctan.org/pkg/principia}, @@ -59715,8 +59715,8 @@ title = {The \texttt{schulmathematik} package}, subtitle = {Commands and document classes for German-speaking teachers of mathematics and physics}, author = {Keno Wehr}, - date = {2022-08-12}, - version = {1.3}, + date = {2023-03-13}, + version = {1.4}, license = {lppl1.3}, mirror = {https://mirror.ctan.org/macros/latex/contrib/schulmathematik}, url = {https://ctan.org/pkg/schulmathematik}, diff --git a/biblio/ctan-bibdata/ctan.pdf b/biblio/ctan-bibdata/ctan.pdf index c3e315cfdb..95c4b946e6 100644 Binary files a/biblio/ctan-bibdata/ctan.pdf and b/biblio/ctan-bibdata/ctan.pdf differ diff --git a/fonts/prodint/.DS_Store b/fonts/prodint/.DS_Store deleted file mode 100644 index 7666056420..0000000000 Binary files a/fonts/prodint/.DS_Store and /dev/null differ diff --git a/macros/latex/contrib/biblatex-contrib/biblatex-dw/latex/.DS_Store b/macros/latex/contrib/biblatex-contrib/biblatex-dw/latex/.DS_Store deleted file mode 100644 index 83c57d053c..0000000000 Binary files a/macros/latex/contrib/biblatex-contrib/biblatex-dw/latex/.DS_Store and /dev/null differ diff --git a/macros/latex/contrib/microtype/README.md b/macros/latex/contrib/microtype/README.md index 251860143d..cc63892a47 100644 --- a/macros/latex/contrib/microtype/README.md +++ b/macros/latex/contrib/microtype/README.md @@ -4,7 +4,7 @@ The `microtype` package **Subliminal refinements towards typographical perfection** - (v3.1 -- 2023/03/06) + (v3.1a -- 2023/03/13) Overview diff --git a/macros/latex/contrib/microtype/microtype-code.pdf b/macros/latex/contrib/microtype/microtype-code.pdf index ec73da44e1..bba1009e7c 100644 Binary files a/macros/latex/contrib/microtype/microtype-code.pdf and b/macros/latex/contrib/microtype/microtype-code.pdf differ diff --git a/macros/latex/contrib/microtype/microtype-utf.dtx b/macros/latex/contrib/microtype/microtype-utf.dtx index 380619cf8c..02af4db500 100644 --- a/macros/latex/contrib/microtype/microtype-utf.dtx +++ b/macros/latex/contrib/microtype/microtype-utf.dtx @@ -27,7 +27,7 @@ \ProvidesFile % %<*driver> - {\jobname.dtx}[2023/03/06 v3.1] + {\jobname.dtx}[2023/03/13 v3.1a] % % {mt-CharisSIL.cfg}[2017/07/07 v1.1 microtype config. file: Charis SIL (RS)] % {mt-LatinModernRoman.cfg}[2021/02/21 v1.1 microtype config. file: Latin Modern Roman (RS)] diff --git a/macros/latex/contrib/microtype/microtype.dtx b/macros/latex/contrib/microtype/microtype.dtx index db89547894..cfa8994833 100644 --- a/macros/latex/contrib/microtype/microtype.dtx +++ b/macros/latex/contrib/microtype/microtype.dtx @@ -37,7 +37,7 @@ % {microtype-luatex.def} % {microtype-xetex.def} %<*package|letterspace|m-t|pdf-|lua-|xe-|show> - [2023/03/06 v3.1 + [2023/03/13 v3.1a % Micro-typographical refinements % Robust letterspacing % Visual debugging for the microtype package @@ -52,8 +52,8 @@ %local microtype = microtype %microtype.module = { % name = "microtype", -% version = "3.1", -% date = "2023/03/06", +% version = "3.1a", +% date = "2023/03/13", % description = "microtype module.", % author = "E. Roux, R. Schlicht and P. Gesang", % copyright = "E. Roux, R. Schlicht and P. Gesang", @@ -3086,7 +3086,7 @@ %\microtypesetup{nopatch={eqnum}} %\end{verbatim} % -%% \item +% \item %\begin{verbatim} %! Font csnameendcsname= not loadable: Metric (TFM) file not found. %\end{verbatim} @@ -3510,6 +3510,8 @@ %\begin{History} % %\Version{\expandafter\@gobble\fileversion}{\filedate} +% +%\Version{3.1}{2023/03/06} % \item New command \cs{DeclareMicrotypeFilePrefix} to change the prefix of the % configuration files \refsection{\ref{sub:config-file}} % \item New protrusion patch |verbatim| to switch off protrusion @@ -8553,6 +8555,7 @@ time will almost certainly lead to undesired results. Have your choice!}% % and which we trial-typeset without any contents. % \begin{macrocode} \def\MT@prot@check@E{% + \the\MT@toks \def\MT@temp*##1{\MT@prot@l{##1}}% } % \end{macrocode} @@ -8563,6 +8566,7 @@ time will almost certainly lead to undesired results. Have your choice!}% % Same for starred commands (the main candidate here is \pkg{csquotes}'s \cmd\enquote). % \begin{macrocode} \def\MT@prot@check@e{% + \the\MT@toks \def\MT@temp*##1{\@ifstar{\MT@prot@l{##1*}}{\MT@prot@l{##1}}}% } % \end{macrocode} @@ -8573,9 +8577,11 @@ time will almost certainly lead to undesired results. Have your choice!}% % Here we replace the `integrated interface' (\pkg{csquotes}) with the regular one. % \begin{macrocode} \def\MT@prot@check@eX#1{% + \the\MT@toks \def\MT@temp*##1{\@ifstar {\MT@get@prot{#1*}{left}##1*} - {\MT@get@prot{#1}{left}##1}}} + {\MT@get@prot{#1}{left}##1}}% +} % \end{macrocode} %\end{macro} % \item @@ -8587,8 +8593,12 @@ time will almost certainly lead to undesired results. Have your choice!}% % (the language) we also have to evaluate before trial typesetting. % \begin{macrocode} \def\MT@prot@check@l{% - \def\MT@temp*##1{\@ifstar{\MT@prot@check@l@{##1*}}{\MT@prot@check@l@{##1}}}} -\def\MT@prot@check@l@#1#2{\MT@prot@l{#1{#2}}} + \def\MT@temp*##1{\@ifstar{\MT@prot@check@l@{##1*}}{\MT@prot@check@l@{##1}}}% +} +\def\MT@prot@check@l@#1#2{% + \the\MT@toks + \MT@prot@l{#1{#2}}% +} % \end{macrocode} %\end{macro} %\end{macro} @@ -8602,19 +8612,27 @@ time will almost certainly lead to undesired results. Have your choice!}% \def\MT@prot@check@lX#1{% \def\MT@temp*##1{\@ifstar {\def\MT@temp{##1*}\MT@prot@check@lX@{#1*}} - {\def\MT@temp{##1}\MT@prot@check@lX@{#1}}}} + {\def\MT@temp{##1}\MT@prot@check@lX@{#1}}}% +} \def\MT@prot@check@lX@#1#2{% - \MT@get@prot{#1{#2}}{left}\MT@temp{#2}} + \the\MT@toks + \MT@get@prot{#1{#2}}{left}\MT@temp{#2}% +} % \end{macrocode} %\end{macro} %\end{macro} % \item %\begin{macro}{\MT@prot@check@F} %\changes{v3.1}{2022/03/06}{new macro: for text commands} +%\changes{v3.1a}{2022/03/12}{fix: execute (and empty) \cs{MT@toks} +% (reported by \contributor Artur A. Marczok )} +% ^^A private mail, 2023/03/12 % Here we deal with \textbf{F}ont switching commands (\ie, text commands, % which take an argument). % We (a) remember the text command, (b) save the full text, % and then (c) continue inspecting the contents of the argument. +% We also have to execute (and empty) \cs{MT@toks}, because it might +% already contain other commands. % Nested text commands still don't work. % \begin{macrocode} \def\MT@prot@check@F{% @@ -8624,8 +8642,11 @@ time will almost certainly lead to undesired results. Have your choice!}% \let\MT@prot@l\MT@prot@l@tc \def\MT@temp*##1##2{% \let\MT@maybe@textcmd##1% + \the\MT@toks + \MT@toks{}% \MT@prot@toks{##1{##2}}% - \MT@prot@get@firstgroup@tc##2\MT@nil}% + \MT@prot@get@firstgroup@tc##2\MT@nil + }% \fi } % \end{macrocode} @@ -20326,7 +20347,7 @@ This is the current font stretched by 5\%, normal, and shrunk by 5\%: % Grave accent \` Left brace \{ Vertical bar \| % Right brace \} Tilde \~} % -% \CheckSum{12962} +% \CheckSum{12975} % % \Finale % diff --git a/macros/latex/contrib/microtype/microtype.pdf b/macros/latex/contrib/microtype/microtype.pdf index 7fcb8a53af..51110edd6a 100644 Binary files a/macros/latex/contrib/microtype/microtype.pdf and b/macros/latex/contrib/microtype/microtype.pdf differ diff --git a/macros/latex/contrib/photobook/Makefile b/macros/latex/contrib/photobook/Makefile index 39b57fa353..ddbd047536 100644 --- a/macros/latex/contrib/photobook/Makefile +++ b/macros/latex/contrib/photobook/Makefile @@ -45,6 +45,8 @@ .EXPORT_ALL_VARIABLES: +#.ONESHELL: + # NOTE: this makes things run consistently on different systems including # things like Android... SHELL := bash @@ -287,7 +289,6 @@ ctan-dist: dist cp -f $(DIST_DIR)/$(DIST_NAME).zip $(DIST_DIR)/$(MODULE).zip - .PHONY: tag tag: @echo "Will create and publish git tag:" @@ -297,8 +298,25 @@ tag: | tail -n 5 \ | sed 's/^/ /' \ | tac - @echo "Note that this must be done after a commit." - @read -p "(press any key to continue or ctrl-c to cancel)" +# # check if we need to bug the user about committing and/or pushing stuff... + @\ + UNCOMITTED=$$(git status --porcelain=v1 2> /dev/null | grep -v '??' | wc -l) ;\ + UNPUSHED=$$(git log origin..HEAD | wc -l) ;\ + if ! [ $$UNCOMITTED = 0 ] ; then \ + echo ;\ + echo "WARNING: Uncommited changes found!" ;\ + fi ;\ + if ! [ $$UNPUSHED = 0 ] ; then \ + [ $$UNCOMITTED = 0 ] \ + && echo ;\ + echo "WARNING: Unpushed commits found!" ;\ + fi ;\ + if ! [ $$UNCOMITTED = 0 ] || ! [ $$UNPUSHED = 0 ] ; then \ + echo ;\ + echo "Note that this must be done after a commit and a push." ;\ + echo "(press any key to continue or ctrl-c to cancel)" ;\ + read ;\ + fi ;\ git tag "v$(VERSION)" git push origin "v$(VERSION)" diff --git a/macros/latex/contrib/photobook/photobook.cls b/macros/latex/contrib/photobook/photobook.cls index 8f9da6cf24..fc9a349c3a 100644 --- a/macros/latex/contrib/photobook/photobook.cls +++ b/macros/latex/contrib/photobook/photobook.cls @@ -76,8 +76,8 @@ %%% NOTE: \def\@[A-Z]+ macros will be visible to both the %%% code and the generated docs... -\edef\photobook@FILEVERSION{v0.1.10} -\edef\photobook@FILEDATE{2023-03-11} +\edef\photobook@FILEVERSION{v0.1.13} +\edef\photobook@FILEDATE{2023-03-13} %% \documentclass{ltxdoc} @@ -1156,6 +1156,19 @@ \InitPages% \ResetFoldMarks} +%% \DescribeMacro{\ChangeLayout} +% +%% Change document layout. +% +%% >> \ChangeLayout{} +% +%% This is a shorthand for |\def\layoutmode{}| and then +%% |\ReInitPages|, and as this is changing any other parameters that may +%% affect the layout, this should be done last. +%% +\newcommand\ChangeLayout[1]{% + \def\layoutmode{#1}% + \ReInitPages} %---------------------------------------------------------------------- diff --git a/macros/latex/contrib/photobook/photobook.pdf b/macros/latex/contrib/photobook/photobook.pdf index 64778bbbf3..59b9da74cd 100644 Binary files a/macros/latex/contrib/photobook/photobook.pdf and b/macros/latex/contrib/photobook/photobook.pdf differ diff --git a/macros/latex/contrib/photobook/scripts/README.md b/macros/latex/contrib/photobook/scripts/README.md index 5970cfbb72..223578f7bb 100644 --- a/macros/latex/contrib/photobook/scripts/README.md +++ b/macros/latex/contrib/photobook/scripts/README.md @@ -23,7 +23,7 @@ Support scripts `make-spreads.sh` ---------------- -Generate LaTeX block of pages from a directory tree. +Generate LaTeX block of pages/spreads from a directory tree. This was initially intended as a means to convert the exported directory tree from an image viewer where image/text sequencing was done, but it @@ -315,8 +315,7 @@ but with a .txt extension. All the configuration options can be given in a configuration file as well as environment variables. - +Environment variables take precedence over the configuration file. The default `make-images.cfg` would look something like: ```shell @@ -361,6 +360,11 @@ IMAGE_SPREAD=( ) ``` +An explicit configuration file can be manually specified: +```shell +$ make-spreads.sh -c .. +``` + --- diff --git a/macros/latex/contrib/photobook/scripts/make-spreads.cfg.example b/macros/latex/contrib/photobook/scripts/make-spreads.cfg.example new file mode 100644 index 0000000000..4627fee339 --- /dev/null +++ b/macros/latex/contrib/photobook/scripts/make-spreads.cfg.example @@ -0,0 +1,39 @@ +# if non-empty make-spreads.sh will add image paths to pdf notes... +ANOTATE_IMAGE_PATHS= + +# file extensions to treat as text (separated with "|") +TEXT_FORMATS=txt + +# file extensions to treat as images (separated with "|") +IMAGE_FORMATS=jpeg|jpg|png|pdf|svg|eps + +# default directory spread definitions are located in... +SPREADS_DIR=spreads/ + +# if non-empty link link images to matching ones from this directory... +IMAGE_HIRES_DIR= + +# directory where external captions are stored... +CAPTION_DIR=captions/ + +# root template directory... +TEMPLATE_DIR=templates/ + +# empty page template... +EMPTY_PAGE=emptypage + +# text page template... +TEXT_PAGE=textpage + +# image page template... +IMAGE_PAGE=imagepage + +# spread templates... +IMAGE_SPREAD=( + # + # +------- number of found images + # / +-- template name + # / / + [0]=text-spread + [2]=image-image +) diff --git a/macros/latex/contrib/photobook/scripts/make-spreads.sh b/macros/latex/contrib/photobook/scripts/make-spreads.sh index 57be2ff448..05979ae03d 100644 --- a/macros/latex/contrib/photobook/scripts/make-spreads.sh +++ b/macros/latex/contrib/photobook/scripts/make-spreads.sh @@ -18,12 +18,12 @@ shopt -s nullglob extglob # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # Template structure: -# templates/ +# $TEMPLATE_DIR/ # spread.tex # imagepage.tex # textpage.tex # ... -# captions/ +# $CAPTION_DIR/ # .txt # image caption. # this is separated to decouple caption writing from the @@ -131,29 +131,45 @@ shopt -s nullglob extglob # # #---------------------------------------------------------------------- - # load config... + CONFIG=${CONFIG:=$(basename ${0%.*}).cfg} +# prepend CFG_ to settings in config... +# NOTE: this is done to prevent them overriding the environment... [ -e $CONFIG ] \ - && source "$CONFIG" + && eval $(cat "$CONFIG" \ + | sed -e 's/^\(\s*\)\([A-Z_]\+=\)/\1CFG_\2/') # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # defaults... +# # NOTE: all of these options can be either set in the $CONFIG file or # set in the script env. # NOTE: env takes priority over $CONFIG # if set add pdf annotations of paths to each image... +ANOTATE_IMAGE_PATHS=${ANOTATE_IMAGE_PATHS:=$CFG_ANOTATE_IMAGE_PATHS} ANOTATE_IMAGE_PATHS=${ANOTATE_IMAGE_PATHS:=} # supported formats/extensions... +TEXT_FORMATS=${TEXT_FORMATS:=$CFG_TEXT_FORMATS} TEXT_FORMATS=${TEXT_FORMATS:=txt} + +IMAGE_FORMATS=${IMAGE_FORMATS:=$CFG_IMAGE_FORMATS} IMAGE_FORMATS=${IMAGE_FORMATS:=jpeg|jpg|png|pdf|svg|eps} + +SPREADS_DIR=${SPREADS_DIR:=$CFG_SPREADS_DIR} SPREADS_DIR=${SPREADS_DIR:=spreads/} + +IMAGE_HIRES_DIR=${IMAGE_HIRES_DIR:=$CFG_IMAGE_HIRES_DIR} IMAGE_HIRES_DIR=${IMAGE_HIRES_DIR:=} + +CAPTION_DIR=${CAPTION_DIR:=$CFG_CAPTION_DIR} CAPTION_DIR=${CAPTION_DIR:=captions/} + +TEMPLATE_DIR=${TEMPLATE_DIR:=$CFG_TEMPLATE_DIR} TEMPLATE_DIR=${TEMPLATE_DIR:=templates/} # Default templates @@ -161,18 +177,30 @@ TEMPLATE_DIR=${TEMPLATE_DIR:=templates/} # page components... # page templates... +EMPTY_PAGE=${EMPTY_PAGE:=$CFG_EMPTY_PAGE} EMPTY_PAGE=${EMPTY_PAGE:=emptypage} + +TEXT_PAGE=${TEXT_PAGE:=$CFG_TEXT_PAGE} TEXT_PAGE=${TEXT_PAGE:=textpage} + +IMAGE_PAGE=${IMAGE_PAGE:=$CFG_IMAGE_PAGE} IMAGE_PAGE=${IMAGE_PAGE:=imagepage} # dynamic spread templates... # NOTE: the index here corresponds to the number of images found in a # spread directory... if [ ${#IMAGE_SPREAD[@]} = 0 ] ; then - IMAGE_SPREAD=( - [0]=text-spread - [2]=image-image - ) + if ! [ ${#CFG_IMAGE_SPREAD[@]} = 0 ] ; then + IMAGE_SPREAD=() + for i in ${!CFG_IMAGE_SPREAD[@]} ; do + IMAGE_SPREAD[$i]=${CFG_IMAGE_SPREAD[$i]} + done + else + IMAGE_SPREAD=( + [0]=text-spread + [2]=image-image + ) + fi fi @@ -188,17 +216,18 @@ printhelp(){ echo echo "Arguments:" echo " -h --help - print this help and exit." + echo " -c PATH - load configuration from PATH." echo " -a --annotate" echo " - add annotations with image paths to pages." - echo " --templates=PATH" + echo " --templates PATH" echo " - path to search for templates (default: $TEMPLATE_DIR)." - echo " --single-image-tpl=NAME" + echo " --single-image-tpl NAME" echo " - single image default template (default: ${IMAGE_SPREAD[1]})." - echo " --double-image-tpl=NAME" + echo " --double-image-tpl NAME" echo " - double image default template (default: ${IMAGE_SPREAD[2]})." - echo " --text-spread-tpl=NAME" + echo " --text-spread-tpl NAME" echo " - text spread default template (default: ${IMAGE_SPREAD[0]})." - echo " --captions=PATH" + echo " --captions PATH" echo " - path to search for captions (default: $CAPTION_DIR)." echo echo "Parameters:" @@ -248,31 +277,32 @@ while true ; do ANOTATE_IMAGE_PATHS=1 shift ;; + -c) + $CONFIG="$2" + [ -e "$CONFIG" ] \ + && source "$CONFIG" + shift 2 + ;; --templates) TEMPLATE_DIR=$2 - shift - shift + shift 2 ;; --single-image-tpl) IMAGE_SPREAD[1]=$2 - shift - shift + shift 2 ;; --double-image-tpl) IMAGE_SPREAD[2]=$2 - shift - shift + shift 2 ;; --text-spread-tpl) IMAGE_SPREAD[0]=$2 - shift - shift + shift 2 ;; --captions) CAPTION_DIR=$2 - shift - shift + shift 2 ;; # handle unknown options... @@ -289,7 +319,7 @@ done if [ -z $1 ] ; then - SPREADS_DIR=pages/ + SPREADS_DIR=spreads/ else SPREADS_DIR=$1/ fi diff --git a/macros/latex/contrib/principia/List_of_Definitions.pdf b/macros/latex/contrib/principia/List_of_Definitions.pdf new file mode 100644 index 0000000000..e80fc41955 Binary files /dev/null and b/macros/latex/contrib/principia/List_of_Definitions.pdf differ diff --git a/macros/latex/contrib/principia/List_of_Definitions.tex b/macros/latex/contrib/principia/List_of_Definitions.tex new file mode 100644 index 0000000000..7377911b3a --- /dev/null +++ b/macros/latex/contrib/principia/List_of_Definitions.tex @@ -0,0 +1,1197 @@ +\documentclass[12pt,openany,leqno,twocolumn]{book} +%Licensed under LaTeX Project Public License 1.3c. +%This is a list of definitions for use with the principia package, Version 2.0. +%Copyright Landon D. C. Elkind, 2021 (https://landonelkind.com/contact/). + +\usepackage{newtxtext} +%\usepackage{mathptmx} + +%Principia package requirements +\usepackage{pifont} %This loads the eight-pointed asterisk. +\usepackage{amssymb} %This loads the relation domain and converse domain limitation symbols. +\usepackage{graphicx} %This loads commands that flip iota for definite descriptions, Lambda for the universal class, and so on. The (superseded) graphics package should also work here, but is not recommended. +%\usepackage{amssymb} +\usepackage{amsmath} %This loads the circumflex, substitution into theorems, \text{}, \mathbf{}, \boldsymbol{}, \overleftarrow{}, \overrightarrow{}, etc. + +\usepackage{fullpage} +\usepackage{perpage} +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{mathrsfs} +\usepackage[hidelinks,pdfencoding=unicode]{hyperref} +\usepackage{enumitem} +\usepackage{moreenum} +\usepackage[normalem]{ulem} +\usepackage[perpage,symbol]{footmisc} +\usepackage{setspace} + +%Volume I +%Mathematical logic +%The theory of deduction +%Meta-logical symbols +\newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions. +\newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof. +\newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof. +\newcommand{\pmhp}{\text{Hp}} %This typesets Hp (short for antecedent), which occurs at the beginning of a proof. +\newcommand{\pmprop}{\text{Prop}} %This occurs at the end of a proof. +\newcommand{\pmithm}{\pmimp\;\pmthm} %This occurs when a meta-theoretic implication is asserted. +\newcommand{\pmbr}[1]{\bigg \lbrack \normalsize #1 \bigg \rbrack} %These are larger brackets for substitution. +\newcommand{\pmsub}[2]{\bigg \lbrack \small \begin{array}{c} #1 \\ \hline #2 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsubb}[4]{\bigg \lbrack \small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsubbb}[6]{\bigg \lbrack \small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsubbbb}[8]{\bigg \lbrack \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command. +\newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command. +\newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command. +\newcommand{\pmsUbbbb}[8]{\small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. +\newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command. +\newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command. +\newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command. +\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. +\newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign. +\newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number. +\newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol{\cdot}$}}} %This is a sign introducing a theorem sub-number. +\newcommand{\pmiddf}{\mathbin{=}} +\newcommand{\pmdf}{\quad \text{Df}} +\newcommand{\pmpp}{\quad \text{Pp}} + +%Square dots for scope, defined for up to six dots +\newcommand{\pmdot}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}} +\newcommand{\pmdott}{\mathrel{\overset{\pmdot}{\pmdot}}} +\newcommand{\pmdottt}{\pmdott\hspace{.1em}\pmdot} +\newcommand{\pmdotttt}{\pmdott\hspace{.1em}\pmdott} +\newcommand{\pmdottttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdot} +\newcommand{\pmdotttttt}{\pmdott\hspace{.1em}\pmdott\hspace{.1em}\pmdott} + +%Logical connectives +\newcommand{\pmnot}{\mathord{\ooalign{$\boldsymbol{\sim}\mkern.5mu$\hidewidth\cr$\boldsymbol{\sim}$\cr\hidewidth$\mkern.5mu\boldsymbol{\sim}$}}} +\newcommand{\pmor}{\mathbin{\ooalign{$\boldsymbol{\vee}\mkern.5mu$\hidewidth\cr$\boldsymbol{\vee}$\cr\hidewidth$\mkern.5mu\boldsymbol{\vee}$}}} +\newcommand{\pmimp}{\mathbin{\ooalign{$\boldsymbol{\supset}\mkern.5mu$\hidewidth\cr$\boldsymbol{\supset}$\cr\hidewidth$\mkern.5mu\boldsymbol{\supset}$}}} %1.01 +\newcommand{\pmand}{\mathrel{\hbox{\rule{.3ex}{.3ex}}}} %3.01 +\newcommand{\pmandd}{\overset{\pmand}{\pmand}} +\newcommand{\pmanddd}{\pmandd\hspace{.1em}\pmand} +\newcommand{\pmandddd}{\pmandd\hspace{.1em}\pmandd} +\newcommand{\pmanddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmand} +\newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd} +\newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction. +\newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01 + +%The theory of apparent variables +\newcommand{\pmall}[1]{(#1)} +\newcommand{\pmsome}[1]{(\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}#1)} %10.01 +\newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}} + +%Additional defined logic signs +\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}} +\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}} +\newcommand{\pmcirc}[1]{\mathbf{\dot{\text{$#1$}}}} +\newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable +\newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables +\newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables +\newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions +\newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable +\newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables +\newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables +\newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02 +\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions +\newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01 +\newcommand{\pmDsc}{\pmiota} +\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02 + +%Classes and relations +%Class signs +\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01 +\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02 +\newcommand{\pmCls}{\text{Cls}} %20.03 +\newcommand{\pmClsn}[1]{\text{Cls}^{#1}} +\newcommand{\pmcinn}{\pmnot\pmcin} %20.06 +\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01 +\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02 +\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03 +\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04 +\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05 +\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01 +\newcommand{\pmcnull}{\mathrm{\Lambda}} %24.02 +\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03 + +%Relation signs +\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01 +\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02 +\newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc. +\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccmp}$}#1} %23.04 +\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccmp}$}}#2} %23.05 +\newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01 +\newcommand{\pmrnull}{\pmcirc{\mathrm{\Lambda}}} %25.02 +\newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03 +\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\mathbf{\pmcinc}$}}} %23.01 +\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccap}$}}} %23.02 +\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\mathbf{\pmccup}$}}} %23.03 + +%Logic of Relations +\newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01 +\newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01 +\newcommand{\pmCnv}{\text{Cnv}} +\newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02 +\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} %32.01 +\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}} +\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} %32.02 +\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}} +\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03 +\newcommand{\pmSg}{\text{sg}} +\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04 +\newcommand{\pmGs}{\text{gs}} +\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01 +\newcommand{\pmDm}{\text{D}} +\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02 +\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}} +\newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03 +\newcommand{\pmCmp}{C} +\newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04 +\newcommand{\pmFld}{F} +\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01 +\newcommand{\pmRprd}{\mathop{|}} +\newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc. +\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01 +\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02 +\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03 +\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04 +\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01 +\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01 +\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02 +\newcommand{\pmdscfR}[1]{#1_{\pmcin}} +\newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03 +\newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}} +\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04 +\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05 +\newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package +\newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02 +\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03 + +%Products and sums of classes of classes or relations +\newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01 +\newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02 +\newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01 +\newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02 +\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01 +\newcommand{\pmRprdd}{\mathop{||}} + +%Prolegomena to Cardinal Arithmetic +%Unit Classes and Couples +%Identity and Diversity +\newcommand{\pmrid}{I} %50.01 +\newcommand{\pmrdiv}{J} %50.02 +\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01 +\newcommand{\pmcUnit}{\iota} +\newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01 + +%Cardinal numbers +\newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc. + +%Ordinal numbers +\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc. +\newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01 +\newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc. + +%Sub-classes, Sub-relations, and Relative Types +%Sub-classes +\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01 +\newcommand{\pmsCl}{\text{Cl}} +\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02 +\newcommand{\pmsCle}{\text{Cl ex}} +\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03 +\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01 +\newcommand{\pmsRl}{\text{Rl}} +\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02 +\newcommand{\pmsRle}{\text{Rl ex}} +\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03 +\newcommand{\pmRel}{\text{Rel}} +\newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04 +\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01 + +%Relative type symbols +\newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01 +\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011 +\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc. +\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04 +\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc. +\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc. +\newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc. +\newcommand{\pmrtdi}[2]{#1_{#2}} %65.01 +\newcommand{\pmrtdc}[2]{#1(#2)} %65.02 +\newcommand{\pmrtdri}[2]{#1_{#2}} %65.03 +\newcommand{\pmrtdrc}[2]{#1(#2)} %65.04 + +%One-many, Many-one, and One-one relations +%Similarity relation signs +\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01 +\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01 +\newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02 +\newcommand{\pmSM}{\text{sm}} +\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}} +\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls} +\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1} +\newcommand{\pmoneone}{1\boldsymbol{\to}1} + +%Selections +\newcommand{\pmselp}[1]{P_{\small\Delta}\mathbf{`}#1} %80.01 +\newcommand{\pmSelp}{P_{\Delta}} +\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\mathbf{`}#1} +\newcommand{\pmSele}{\pmcin_{\Delta}} +\newcommand{\pmself}[1]{F_{\small\Delta}\mathbf{`}#1} +\newcommand{\pmSelf}{F_{\Delta}} +\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01 +\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02 +\newcommand{\pmex}{\text{Cls excl}} +\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03 +\newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\mathbf{\mapsto}$}}} #2} +\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01 +\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02 +\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03 + + %Inductive relations +\newcommand{\pmanc}[1]{#1_\pmast} %90.01 +\newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02 +\newcommand{\pmrst}[1]{#1_\text{st}} %91.01 +\newcommand{\pmrts}[1]{#1_\text{ts}} %91.02 +\newcommand{\pmpot}[1]{\text{Pot}\mathbf{`}#1} %91.03 +\newcommand{\pmpotid}[1]{\text{Potid}\mathbf{`}#1} %91.04 +\newcommand{\pmpo}[1]{#1_\text{po}} %91.05 +\newcommand{\pmB}{B} %93.01 +\newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02 +\newcommand{\pmMin}{\text{min}} +\newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021 +\newcommand{\pmMax}{\text{max}} +\newcommand{\pmgen}[1]{\text{gen}\mathbf{`}#1} %93.03 +\newcommand{\pmGen}{\text{gen}} +\newcommand{\pmefr}[2]{#1\pmast#2} %95.05 +\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01 +\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02 +\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01 + + %Volume II + %Cardinal arithmetic + %Definition and Logical Properties of Cardinal Numbers +\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01 +\newcommand{\pmNc}{\text{Nc}} +\newcommand{\pmNC}{\text{NC}} %100.02 +\newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01 +\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01 +\newcommand{\pmNoc}{\text{N}_0\text{c}} +\newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02 +\newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc. +\newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc. +\newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc. +\newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01 +\newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc. +\newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc. +\newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc. +\newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011 +\newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02 +\newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021 +\newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03 +\newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}} +\newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04 +\newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041 +\newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01 + + %Addition, Multiplication, Exponentiation +\newcommand{\pmarsumc}{\mathrel{+}} %110.01 +\newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02 +\newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01 +\newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02 +\newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03 +\newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01 +\newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02 +\newcommand{\pmarprodc}{\times} %113.02 +\newcommand{\pmarprodnc}{\times_\text{c}} %113.03 +\newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01 +\newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01 +\newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02 +\newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01 +\newcommand{\pmArexp}{\text{exp}} +\newcommand{\pmarncexp}[2]{#1^{#2}} %116.02 +\newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01 +\newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04 +\newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05 +\newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06 + + %Finite and infinite +\newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01 +\newcommand{\pmArsubt}{{-}_\text{c}} +\newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01 +\newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011 +\newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02 +\newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021 +\newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03 +\newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04 +\newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43 +\newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01 +\newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011 +\newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012 +\newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013 +\newcommand{\pmintnc}[1]{P_{#1}} %121.02 +\newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03 +\newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031 +\newcommand{\pmintt}[2]{#1_{#2}} %121.04 +\newcommand{\pmprog}{\text{Prog}} %122.01 +\newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01 +\newcommand{\pmsucc}{\text{N}} %123.02 +\newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01 +\newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02 +\newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03 +\newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01 +\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1} +\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}} + + %Relation-arithmetic + %Ordinal similarity and relation-numbers +\newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01 +\newcommand{\pmrnsmd}[2]{#1 \mathop{\mathbf{\dagger}} #2} %150.02 +\newcommand{\pmrnsmdf}[1]{#1\mathbf{\dagger}} +\newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03 +\newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01 +\newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01 +\newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02 +\newcommand{\pmSmor}{\text{smor}} +\newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01 +\newcommand{\pmNr}{\text{Nr}} +\newcommand{\pmNR}{\text{NR}} %152.02 +\newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01 +\newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01 +\newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01 +\newcommand{\pmNor}{\text{N}_0\text{r}} +\newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02 + + %Addition of Relations, and the Product of Two Relations +\newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01 +\newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}} +\newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01 +\newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} } +\newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02 +\newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}} +\newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01 +\newcommand{\pmRsumr}{\Sigma} +\newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01 +\newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01 +\newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}} +\newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02 +\newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor} +\newcommand{\pmrprod}[2]{#1 \times #2} %166.01 + + %First differences and the multiplication and exponentiation of relations + %On the relation of first differences among the sub-classes of a given class +\newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01 +\newcommand{\pmRfdcl}[1]{#1_{\text{cl}}} +\newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02 +\newcommand{\pmRfdlc}[1]{#1_{\text{lc}}} +\newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01 +\newcommand{\pmRfddf}[1]{#1_{\text{df}}} +\newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02 +\newcommand{\pmRfdfd}[1]{#1_{\text{fd}}} +\newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01 +\newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01 +\newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01 +\newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01 +\newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02 +\newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01 +\newcommand{\pmRnsum}{+} +\newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02 +\newcommand{\pmRndsum}{\pmcirc{+}} +\newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01 +\newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}} +\newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011 +\newcommand{\pmRnsumur}{\pmcirc{\pmRsume}} +\newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02 +\newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01 +\newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01 +\newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01 +\newcommand{\pmRnprod}{\pmcirc{\times}} +\newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01 +\newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01 +\newcommand{\pmRnexp}[1]{\pmArexp_{#1}} + +%Series +%General theory of series +\newcommand{\pmtrans}{\text{trans}} %201.01 +\newcommand{\pmconnex}{\text{connex}} %202.01 +\newcommand{\pmser}{\text{Ser}} %204.01 +\newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01 +\newcommand{\pmSeq}[1]{\text{seq}_{#1}} +\newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02 +\newcommand{\pmPrec}[1]{\text{prec}_{#1}} +\newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01 +\newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01 +\newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03 +\newcommand{\pmLimax}[1]{\text{limax}_{#1}} +\newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04 +\newcommand{\pmLimin}[1]{\text{limin}_{#1}} +\newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}} +\newcommand{\pmCr}{\text{cr}} +\newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01 +\newcommand{\pmCror}{\text{cror}} + +%On sections, segments, stretches, and derivatives +\newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01 +\newcommand{\pmSect}{\text{sect}} +\newcommand{\pmseg}[1]{\mathbf{\varsigma}\textbf{`}{#1}} %212.01 +\newcommand{\pmSeg}{\mathbf{\varsigma}} +\newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02 +\newcommand{\pmSym}{\text{sym}} +\newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01 +\newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01 +\newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02 +\newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01 +\newcommand{\pmStr}{\text{str}} +\newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01 +\newcommand{\pmDer}[1]{\delta_{#1}} +\newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3} +\newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02 +\newcommand{\pmDen}{\text{dense}} +\newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03 +\newcommand{\pmClsd}{\text{closed}} +\newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04 +\newcommand{\pmPerf}{\text{perf}} +\newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05 +\newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}} + +%On convergence, and the limits of functions +\newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01 +\newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02 +\newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3} +\newcommand{\pmConvg}[1]{{#1}_{\text{cng}}} +\newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01 +\newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02 +\newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01 +\newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02 +\newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01 +\newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}} +\newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02 +\newcommand{\pmLimf}[3]{#1(#2#3)} +\newcommand{\pmscf}[3]{\text{sc}(#1, #2)\mathbf{`}#3} %234.01 +\newcommand{\pmosf}[3]{\text{os}(#1, #2)\mathbf{`}#3} %234.02 +\newcommand{\pmctf}[3]{\text{ct}(#1#2)\mathbf{`}#3} %234.03 +\newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\mathbf{`}#3} %234.04 +\newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05 +\newcommand{\pmContin}{\text{contin}} + +%Volume III +%Well-Ordered Series +\newcommand{\pmbord}{\text{Bord}} %250.01 +\newcommand{\pmword}{\Omega} %250.02 +\newcommand{\pmordn}{\text{NO}} %251.01 +\newcommand{\pmless}{\mathrel{\text{less}}} %254.01 +\newcommand{\pmLess}{\text{less}} +\newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02 +\newcommand{\pmPsc}{P_{\text{sm}}} +\newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01 +\newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02 +\newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03 +\newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04 +\newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05 +\newcommand{\pmm}{\emph{M}} %256.01 +\newcommand{\pmn}{\emph{N}} %256.02, 263.02 +\newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01 +\newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01 +\newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02 +\newcommand{\pma}{\emph{A}} %259.01 +\newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02 +\newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03 + +%Finite and Infinite Series and Ordinals +\newcommand{\pmintf}{P_{\text{fn}}} %260.01 +\newcommand{\pmserinf}{\text{Ser infin}} %261.01 +\newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02 +\newcommand{\pmserfin}{\text{Ser fin}} %261.03 +\newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04 +\newcommand{\pmwordind}{\pmword\text{ induct}} %261.04 +\newcommand{\pmordnfin}{\text{NO fin}} %262.01 +\newcommand{\pmordninf}{\text{NO infin}} %262.02 +\newcommand{\pmfinord}[1]{#1_r} %262.03 +\newcommand{\pmom}{\boldsymbol{\omega}} %263.01 +\newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01 +\newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc. +\newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc. + +%Compact series, rational series, and continuous series +\newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01 +\newcommand{\pmComp}{\text{Comp}} +\newcommand{\pmmed}{\mathrel{\text{med}}} %271.01 +\newcommand{\pmMed}{\text{med}} +\newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01 +\newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02 +\newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03 +\newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04 +\newcommand{\pmrats}{\eta} %273.01 +\newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01 +\newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02 +\newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03 +\newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04 +\newcommand{\pmcser}{\theta} %275.01 +\newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01 +\newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04 +\newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05 +%Skipped some temprary definitions as repetitious + +%Quantity +%Generalization of Number +\newcommand{\pmu}{\textit{U}} %300.01 +\newcommand{\pmrnum}{\text{Rel num}} %300.02 +\newcommand{\pmrnumid}{\text{Rel num id}} %300.03 +\newcommand{\pmrpwr}[2]{#1^#2} %301.03 +\newcommand{\pmPrm}{\text{Prm}} %302.01 +\newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02 +\newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03 +\newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04 +\newcommand{\pmHcf}{\text{hcf}} +\newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05 +\newcommand{\pmLcm}{\text{lcm}} +\newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01 +\newcommand{\pmqn}[1]{#1_q} %303.02 +\newcommand{\pmqnil}{\infty_q} %303.03 +\newcommand{\pmRat}{\text{Rat}} %303.04 +\newcommand{\pmRatdef}{\text{Rat def}} %303.05 +\newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01 +\newcommand{\pmQnle}{\boldsymbol{<}_r} +\newcommand{\pmqnLe}{H} %304.02 +\newcommand{\pmqnlez}{H'} %304.03 +\newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01 +\newcommand{\pmProdsr}{\times_s} +\newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01 +\newcommand{\pmSumsr}{+_s} +\newcommand{\pmratn}{\text{Rat}_n} %307.01 +\newcommand{\pmratg}{\text{Rat}_g} %307.011 +\newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02 +\newcommand{\pmRatnle}{\boldsymbol{<}_n} +\newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021 +\newcommand{\pmRatngr}{\boldsymbol{>}_n} +\newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03 +\newcommand{\pmRatgle}{\boldsymbol{<}_g} +\newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031 +\newcommand{\pmRatggr}{\boldsymbol{>}_g} +\newcommand{\pmratnLe}{H_n} %307.04 +\newcommand{\pmratgLe}{H_g} %307.05 +\newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01 +\newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02 +\newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01 +\newcommand{\pmrenp}{\Theta} %310.01 +\newcommand{\pmrenpz}{\Theta'} %310.011 +\newcommand{\pmrenn}{\Theta_n} %310.02 +\newcommand{\pmrennz}{\Theta_n'} %310.021 +\newcommand{\pmreng}{\Theta_g} %310.03 +\newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01 +\newcommand{\pmConc}{\text{concord}} +\newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02 +\newcommand{\pmrensub}[2]{#1 -_p #2} %312.01 +\newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02 +\newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01 +\newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01 +\newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02 +\newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package +\newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03 +\newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04 +\newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05 + +%Vector Families +\newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01 +\newcommand{\pmabel}{\text{Abel}} %330.02 +\newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03 +\newcommand{\pmVfm}{\text{fm}} +\newcommand{\pmvfmcl}{\textit{FM}} %330.04 +\newcommand{\pmvffb}[1]{#1_\iota} %330.05 +\newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01 +\newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02 +\newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01 +\newcommand{\pmfopen}[1]{#1_\partial} %333.01 +\newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011 +\newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02 +\newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03 +\newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01 +\newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02 +\newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03 +\newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02 +\newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05 +\newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01 +\newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02 +\newcommand{\pmvr}[1]{\textit{V}_#1} %336.01 +\newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011 +\newcommand{\pmarvs}[1]{A_{#1}} %336.02 + +%Measurement +\newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01 +\newcommand{\pmvrm}[2]{#1_#2} %352.01 +\newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02 +\newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01 +\newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02 +\newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03 +\newcommand{\pmfmg}[1]{#1_g} %354.01 +\newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02 +\newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03 +\newcommand{\pmrems}[2]{#1_#2} %356.01 + +%Cyclic Families +\newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01 +\newcommand{\pmcycl}[2]{#1_#2} %370.02 +\newcommand{\pmcycli}[2]{#1_#2} %370.03 +\newcommand{\pmvser}[2]{#1_#2} %371.01 +\newcommand{\pmintsecvser}[2]{#1_#2} %372.01 +\newcommand{\pmprime}{\text{Prime}} %373.01 +\newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02 +\newcommand{\pmsmltid}[2]{(#1, #2)} %373.03 +\newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01 + +\begin{document} + +\chapter*{\centering LIST OF DEFINITIONS} +\onehalfspacing +\begin{tabular}{l l} + \text{ }$\pmast1\pmcdot01$. & $p \pmimp q$ \\ + \text{ }$\pmast2\pmcdot33$. & $p \pmor q \pmor r$ \\ + \text{ }$\pmast3\pmcdot01$. & $p \pmand q$ \\ + \text{ }$\pmast3\pmcdot02$. & $p \pmimp q \pmimp r$ \\ + \text{ }$\pmast4\pmcdot01$. & $p \pmiff q$ \\ + \text{ }$\pmast4\pmcdot02$. & $p \pmiff q \pmiff r$ \\ + \text{ }$\pmast4\pmcdot34$. & $p \pmand q \pmand r$ \\ + \text{ }$\pmast9\pmcdot01$. & $\pmnot\{\pmall{x}\pmdot \phi x\}$ \\ + \text{ }$\pmast9\pmcdot011$. & $\pmnot\pmall{x}\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot02$. & $\pmnot\{\pmsome{x}\pmdot \phi x\}$ \\ + \text{ }$\pmast9\pmcdot021$. & $\pmnot\pmsome{x}\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot03$. & $\pmall{x}\pmdot \phi x \pmdot \pmor \pmdot p$ \\ + \text{ }$\pmast9\pmcdot04$. & $p \pmdot \pmor \pmdot \pmall{x}\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot05$. & $\pmsome{x}\pmdot \phi x \pmdot \pmor \pmdot p$ \\ + \text{ }$\pmast9\pmcdot06$. & $p \pmdot \pmor \pmdot \pmsome{x}\pmdot \phi x$ \\ + \text{ }$\pmast9\pmcdot07$. & $\pmall{x}\pmdot \phi x \pmdot \pmor \pmdot \pmsome{y}\pmdot \psi y$ \\ + \text{ }$\pmast9\pmcdot08$. & $\pmsome{y}\pmdot \psi y \pmdot \pmor \pmdot \pmall{x}\pmdot \phi x$ \\ + $\pmast10\pmcdot01$. & $\pmsome{x}\pmdot \phi x$ \\ + $\pmast10\pmcdot02$. & $\phi x \pmimp_x \psi x$ \\ + $\pmast10\pmcdot03$. & $\phi x \pmiff_x \psi x$ \\ + $\pmast11\pmcdot01$. & $\pmall{x,y}\pmdot \phi(x, y)$ \\ + $\pmast11\pmcdot02$. & $\pmall{x,y,z}\pmdot \phi(x, y, z)$ \\ + $\pmast11\pmcdot03$. & $\pmsome{x,y}\pmdot \phi(x, y)$ \\ + $\pmast11\pmcdot04$. & $\pmsome{x,y,z}\pmdot \phi(x, y, z)$ \\ + $\pmast11\pmcdot05$. & $\phi(x, y) \pmdot\pmimp_{x, y}\pmdot \psi(x, y)$ \\ + $\pmast11\pmcdot06$. & $\phi(x, y) \pmdot\pmiff_{x, y}\pmdot \psi(x, y)$ \\ + $\pmast13\pmcdot01$. & $x = y$ \\ + $\pmast13\pmcdot02$. & $x \pmnid y$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast13\pmcdot03$. & $x = y = z$ \\ + $\pmast14\pmcdot01$. & $[\pmdsc{x}(\phi x)]\pmdot \psi\pmdsc{x}(\phi x)$ \\ + $\pmast14\pmcdot02$. & $\pmexists\pmdsc{x}(\phi x)$ \\ + $\pmast14\pmcdot03$. & $[\pmdsc{x}(\phi x), \pmdsc{x}(\psi x)]\pmdot f\{\pmdsc{x}(\phi x),$\\ + & \indent $\pmdsc{x}(\psi x)\}$ \\ + $\pmast14\pmcdot04$. & $[\pmdsc{x}(\psi x)]\pmdot f\{\pmdsc{x}(\phi x), \pmdsc{x}(\psi x)\}$ \\ + $\pmast20\pmcdot01$. & $f\{\pmcls{z}{\psi z}\}$ \\ + $\pmast20\pmcdot02$. & $x \mathrel{\pmcin} (\pmpred{\phi}{\pmhat{z}})$ \\ + $\pmast20\pmcdot03$. & $\pmCls$ \\ + $\pmast20\pmcdot04$. & $x, y \pmcin \alpha$ \\ + $\pmast20\pmcdot05$. & $x, y, z \pmcin \alpha$ \\ + $\pmast20\pmcdot06$. & $x \pmnot \pmcin \alpha$ \\ + $\pmast20\pmcdot07$. & $\pmall{\alpha}\pmdot f\alpha$ \\ + $\pmast20\pmcdot071$. & $\pmsome{\alpha}\pmdot f\alpha$ \\ + $\pmast20\pmcdot072$. & $[\pmdsc{\alpha}(\phi \alpha)]\pmdot f\pmdsc{\alpha}(\phi \alpha)$ \\ + $\pmast20\pmcdot08$. & $f\{\pmcls{\alpha}{\psi \alpha}\}$ \\ + $\pmast20\pmcdot081$. & $\alpha \pmcin \pmpred{\psi}{\alpha}$ \\ + $\pmast21\pmcdot01$. & $f\{\pmrel{x}{y}{\psi(x,y)}\}$ \\ + $\pmast21\pmcdot02$. & $\pmrelep{a}{\pmpredd{\phi}{\pmhat{x}}{\pmhat{y}}}{b}$ \\ + $\pmast21\pmcdot03$. & $\pmRel$ \\ + $\pmast21\pmcdot07$. & $\pmall{R}\pmdot fR$ \\ + $\pmast21\pmcdot071$. & $\pmsome{R}\pmdot fR$ \\ + $\pmast21\pmcdot072$. & $[\pmdsc{R}(\phi R)]\pmdot f\pmdsc{R}(\phi R)$ \\ + $\pmast21\pmcdot08$. & $f\{\pmrel{R}{S}{\psi(R, S)}\}$ \\ + $\pmast21\pmcdot081$. & $\pmrelep{P}{\pmpredd{\phi}{\pmhat{R}}{\pmhat{S}}}{Q}$ \\ + $\pmast21\pmcdot082$. & $f\{\pmcls{R}{\psi R}\}$ \\ + $\pmast21\pmcdot083$. & $R \pmcin \pmpred{\phi}{\pmhat{R}}$ \\ + $\pmast22\pmcdot01$. & $\alpha \pmcinc \beta$ \\ + $\pmast22\pmcdot02$. & $\alpha \pmccap \beta$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast22\pmcdot03$. & $\alpha \pmccup \beta$ \\ +$\pmast22\pmcdot04$. & $\pmccmp{\alpha}$ \\ +$\pmast22\pmcdot05$. & $\pmcmin{\alpha}{\beta}$ \\ +$\pmast22\pmcdot53$. & $\alpha \pmccap \beta \pmccap \gamma$ \\ +$\pmast22\pmcdot71$. & $\alpha \pmccup \beta \pmccup \gamma$ \\ +$\pmast23\pmcdot01$. & $R \pmrinc S$ \\ +$\pmast23\pmcdot02$. & $R \pmrcap S$ \\ +$\pmast23\pmcdot03$. & $R \pmrcup S$ \\ +$\pmast23\pmcdot04$. & $\pmrcmp{R}$ \\ +$\pmast23\pmcdot05$. & $\pmrmin{R}{S}$ \\ +$\pmast23\pmcdot53$. & $R \pmrcap S \pmrcap T$ \\ +$\pmast23\pmcdot71$. & $R \pmrcup S \pmrcup T$ \\ +$\pmast24\pmcdot01$. & $\pmcuni$ \\ +$\pmast24\pmcdot02$. & $\pmcnull$ \\ +$\pmast24\pmcdot03$. & $\pmcexists \alpha$ \\ +$\pmast25\pmcdot01$. & $\pmruni$ \\ +$\pmast25\pmcdot02$. & $\pmrnull$ \\ +$\pmast25\pmcdot03$. & $\pmrexists R$ \\ +$\pmast30\pmcdot01$. & $\pmdscf{R}{y}$ \\ +$\pmast30\pmcdot02$. & $\pmdscf{R}{\pmdscf{S}{y}}$ \\ +$\pmast31\pmcdot01$. & $\pmCnv$ \\ +$\pmast31\pmcdot02$. & $\pmcrel{P}$ \\ +$\pmast32\pmcdot01$. & $\pmRrf{R}$ \\ +$\pmast32\pmcdot02$. & $\pmRrl{R}$ \\ +$\pmast32\pmcdot03$. & $\pmSg$ \\ +$\pmast32\pmcdot04$. & $\pmGs$ \\ +$\pmast33\pmcdot01$. & $\pmDm$ \\ +$\pmast33\pmcdot02$. & $\pmCdm$ \\ +$\pmast33\pmcdot03$. & $\pmCmp$ \\ +$\pmast33\pmcdot04$. & $\pmFld$ \\ +$\pmast34\pmcdot01$. & $\pmrprd{R}{S}$ \\ +$\pmast34\pmcdot02$. & $\pmrprdn{R}{2}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast34\pmcdot03$. & $\pmrprdn{R}{3}$ \\ +$\pmast35\pmcdot01$. & $\pmrld{\alpha}{R}$ \\ +$\pmast35\pmcdot02$. & $\pmrlcd{R}{\beta}$ \\ +$\pmast35\pmcdot03$. & $\pmrlf{\alpha}{R}{\beta}$ \\ +$\pmast35\pmcdot04$. & $\pmrl{\alpha}{\beta}$ \\ +$\pmast35\pmcdot05$. & $\pmrl{\pmdscf{R}{x}}{\beta}$ \\ +$\pmast35\pmcdot24$. & $\pmrld{\alpha}{\pmrprd{R}{S}}$ \\ +$\pmast35\pmcdot25$. & $\pmrlcd{\pmrprd{S}{R}}{\alpha}$ \\ +$\pmast36\pmcdot01$. & $\pmrlF{P}{\alpha}$ \\ +$\pmast37\pmcdot01$. & $\pmdscff{R}{\beta}$ \\ +$\pmast37\pmcdot02$. & $\pmdscfR{R}$ \\ +$\pmast37\pmcdot03$. & ${\pmdscfR{\pmcrel{R}}}$\\ +$\pmast37\pmcdot04$. & $\pmdscfff{R}{\kappa}$ \\ +$\pmast37\pmcdot05$. & $\pmdscfe{R}{\beta}$ \\ +$\pmast38\pmcdot01$. & $x \pmop$ \\ +$\pmast38\pmcdot02$. & $\pmop y$ \\ +$\pmast38\pmcdot03$. & $\pmopc{\alpha}{y}$\\ +$\pmast40\pmcdot01$. & $\pmccsum{\kappa}$ \\ +$\pmast40\pmcdot02$. & $\pmccprd{\kappa}$ \\ +$\pmast41\pmcdot01$. & $\pmcrsum{\lambda}$ \\ +$\pmast41\pmcdot02$. & $\pmcrprd{\lambda}$ \\ +$\pmast43\pmcdot01$. & $\pmrprdd{R}{S}$ \\ +$\pmast50\pmcdot01$. & $\pmrid$ \\ +$\pmast50\pmcdot02$. & $\pmrdiv$ \\ +$\pmast51\pmcdot01$. & $\pmcUnit$ \\ +$\pmast52\pmcdot01$. & $\pmcn{1}$ \\ +$\pmast54\pmcdot01$. & $\pmcn{0}$ \\ +$\pmast54\pmcdot02$. & $\pmcn{2}$ \\ +$\pmast55\pmcdot01$. & $\pmoc{x}{y}$ \\ +$\pmast55\pmcdot02$. & $\pmoc{\pmdscf{R}{x}}{y}$ \\ +$\pmast56\pmcdot01$. & $\pmdn{2}$ \\ +$\pmast56\pmcdot02$. & $\pmorn{2}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast56\pmcdot03$. & $\pmorn{0}$ \\ +$\pmast60\pmcdot01$. & $\pmsCl$ \\ +$\pmast60\pmcdot02$. & $\pmsCle$ \\ +$\pmast60\pmcdot03$. & $\pmClsn{2}$ \\ +$\pmast60\pmcdot04$. & $\pmClsn{3}$ \\ +$\pmast61\pmcdot01$. & $\pmsRl$ \\ +$\pmast61\pmcdot02$. & $\pmsRle$ \\ +$\pmast61\pmcdot03$. & $\pmReln{2}$ \\ +$\pmast61\pmcdot04$. & $\pmReln{3}$ \\ +$\pmast62\pmcdot01$. & $\pmrin$ \\ +$\pmast63\pmcdot01$. & $\pmrt{x}$ \\ +$\pmast63\pmcdot011$. & $\pmrti{1}{x}$ \\ +$\pmast63\pmcdot02$. & $\pmrtc{0}{\alpha}$ \\ +$\pmast63\pmcdot03$. & $\pmrtc{1}{\kappa}$ \\ +$\pmast63\pmcdot04$. & $\pmrti{2}{\kappa}$ \\ +$\pmast63\pmcdot041$. & $\pmrti{3}{\kappa}$ \\ +$\pmast63\pmcdot05$. & $\pmrtc{2}{\kappa}$ \\ +$\pmast63\pmcdot051$. & $\pmrtc{3}{\kappa}$ \\ +$\pmast64\pmcdot01$. & $\pmrtrc{00}{\alpha}$ \\ +$\pmast64\pmcdot011$. & $\pmrtri{11}{x}$ \\ +$\pmast64\pmcdot012$. & $\pmrti{12}{x}$ \\ +$\pmast64\pmcdot013$. & $\pmrti{21}{x}$ \\ +$\pmast64\pmcdot014$. & $\pmrti{22}{x}$ \\ +$\pmast64\pmcdot02$. & $\pmrtc{01}{\alpha}$ \\ +$\pmast64\pmcdot021$. & $\pmrtc{10}{\alpha}$ \\ +$\pmast64\pmcdot022$. & $\pmrtc{11}{\alpha}$ \\ +$\pmast64\pmcdot03$. & $\pmrtrci{0}{1}{\alpha}$ \\ +$\pmast64\pmcdot031$. & $\pmrtrci{1}{1}{\alpha}$ \\ +$\pmast64\pmcdot04$. & $\pmrtric{1}{0}{\alpha}$ \\ +$\pmast64\pmcdot041$. & $\pmrtric{1}{1}{\alpha}$ \\ +$\pmast65\pmcdot01$. & $\pmrtdi{\alpha}{x}$ \\ +$\pmast65\pmcdot02$. & $\pmrtdc{\alpha}{x}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast65\pmcdot03$. & $\pmrtdri{R}{x}$ \\ +$\pmast65\pmcdot04$. & $\pmrtdrc{R}{x}$ \\ +$\pmast65\pmcdot1$. & $\pmrtdri{R}{(x,y)}$ \\ +$\pmast65\pmcdot11$. & $\pmrtdrc{R}{x_y}$\\ +$\pmast65\pmcdot12$. & $\pmrtdrc{R}{x, y}$ \\ +$\pmast70\pmcdot01$. & $\pmrdc{\alpha}{\beta}$ \\ +$\pmast73\pmcdot01$. & $\alpha \pmsmbar \beta$ \\ +$\pmast73\pmcdot02$. & $\pmsm$\\ +$\pmast80\pmcdot01$. & $\pmSelp$ \\ +$\pmast84\pmcdot01$. & $\pmexc$ \\ +$\pmast84\pmcdot02$. & $\pmexcc{\gamma}$ \\ +$\pmast84\pmcdot03$. & $\pmexcn$\\ +$\pmast85\pmcdot5$. & $\pmselc{P}{\,y}$ \\ +$\pmast88\pmcdot01$. & $\pmmultr$ \\ +$\pmast88\pmcdot02$. & $\pmmultc$ \\ +$\pmast88\pmcdot03$. & $\pmmultax$ \\ +$\pmast90\pmcdot01$. & $\pmanc{R}$ \\ +$\pmast90\pmcdot02$. & $\pmancc{R}$ \\ +$\pmast91\pmcdot01$. & $\pmrst{R}$ \\ +$\pmast91\pmcdot02$. & $\pmrts{R}$ \\ +$\pmast91\pmcdot03$. & $\pmpot{R}$ \\ +$\pmast91\pmcdot04$. & $\pmpotid{R}$ \\ +$\pmast91\pmcdot05$. & $\pmpo{R}$ \\ +$\pmast93\pmcdot01$. & $\pmB$ \\ +$\pmast93\pmcdot02$. & $\pmmin{P}$ \\ +$\pmast93\pmcdot021$. & $\pmmax{P}$ \\ +$\pmast93\pmcdot03$. & $\pmgen{P}$ \\ +$\pmast95\pmcdot01$. & $\pmefr{P}{Q}$ \hspace{.3cm} Dft [$\pmast95$] \\ +$\pmast96\pmcdot01$. & $\pmipr{R}{x}$ \hspace{.415cm} Dft [$\pmast96$] \\ +$\pmast96\pmcdot02$. & $\pmjpr{R}{x}$ \hspace{.375cm} Dft [$\pmast96$] \\ +$\pmast97\pmcdot01$. & $\pmfr{R}{x}$ \\ +$\pmast100\pmcdot01$. & $\pmNc$ +\end{tabular} + +\onehalfspacing +\begin{tabular}{l l} + $\pmast100\pmcdot02$. & $\pmNC$ \\ + $\pmast102\pmcdot01$. & $\pmNCat{\beta}{\alpha}$ \\ + $\pmast103\pmcdot01$. & $\pmnoc{\alpha}$ \\ + $\pmast103\pmcdot02$. & $\pmNoC$ \\ + $\pmast104\pmcdot01$. & $\pmnca{1}{\alpha}$ \\ + $\pmast104\pmcdot011$. & $\pmnca{2}{\alpha}$ \\ + $\pmast104\pmcdot02$. & $\pmNca{1}$ \\ + $\pmast104\pmcdot021$. & $\pmNca{2}$ \\ + $\pmast104\pmcdot03$. & $\pmch{\mu}{1}$ \\ + $\pmast104\pmcdot031$. & $\pmch{\mu}{2}$ \\ + $\pmast105\pmcdot01$. & $\pmncd{1}{\alpha}$ \\ + $\pmast105\pmcdot011$. & $\pmncd{2}{\alpha}$ \\ + $\pmast105\pmcdot02$. & $\pmNcd{1}$ \\ + $\pmast105\pmcdot021$. & $\pmNcd{2}$ \\ + $\pmast105\pmcdot03$. & $\pmcl{\mu}{1}$ \\ + $\pmast105\pmcdot031$. & $\pmcl{\mu}{2}$ \\ + $\pmast106\pmcdot01$. & $\pmncll{0}{0}{\alpha}$ \\ + $\pmast106\pmcdot011$. & $\pmnchh{1}{1}{\alpha}$ \\ + $\pmast106\pmcdot012$. & $\pmncll{0}{1}{\alpha}$ \\ + $\pmast106\pmcdot02$. & $\pmncaa{0}{1}{\alpha}$ \\ + $\pmast106\pmcdot021$. & $\pmncdd{1}{0}{\alpha}$ \\ + $\pmast106\pmcdot03$. & $\pmNCll{0}{0}$ \\ + $\pmast106\pmcdot04$. & $\pmcll{\mu}{0}{0}$ \\ + $\pmast106\pmcdot041$. & $\pmchh{\mu}{1}{1}$ \\ + $\pmast110\pmcdot01$. & $\alpha \pmarsumc \beta$ \\ + $\pmast110\pmcdot02$. & $\mu \pmarsumnc \nu$ \\ + $\pmast110\pmcdot03$. & $\pmnc{\alpha} \pmarsumnc \mu$ \\ + $\pmast110\pmcdot04$. & $\mu \pmarsumnc \pmnc{\alpha}$ \\ + $\pmast110\pmcdot0561$. & $\mu \pmarsumnc \nu \pmarsumnc \varpi$ \\ + $\pmast111\pmcdot01$. & $\kappa \pmsmsmb \lambda$ \\ + $\pmast111\pmcdot02$. & $\pmcrp{S}{\beta}$ \\ + $\pmast111\pmcdot03$. & $\pmsmsm$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast112\pmcdot01$. & $\pmarsumcc{\kappa}$ \\ + $\pmast112\pmcdot02$. & $\pmarsumcnc{\kappa}$ \\ + $\pmast113\pmcdot02$. & $\beta \pmarprodc \alpha$ \\ + $\pmast113\pmcdot03$. & $\mu \pmarprodnc \nu$ \\ + $\pmast113\pmcdot04$. & $\pmnc{\beta} \pmarprodnc \mu$ \\ + $\pmast113\pmcdot05$. & $\mu \pmarprodnc \pmnc{\alpha}$ \\ + $\pmast113\pmcdot511$. & $\alpha \pmarprodc \beta \pmarprodc \gamma$ \\ + $\pmast113\pmcdot541$. & $\mu \pmarprodnc \nu \pmarprodnc \varpi$ \\ + $\pmast114\pmcdot01$. & $\pmarprodcnc{\kappa}$ \\ + $\pmast115\pmcdot01$. & $\pmarprodcc{\kappa}$ \\ + $\pmast115\pmcdot02$. & $\pmarcls$ \\ + $\pmast116\pmcdot01$. & $\pmarexp{\alpha}{\beta}$ \\ + $\pmast116\pmcdot02$. & $\pmarncexp{\mu}{\nu}$ \\ + $\pmast116\pmcdot03$. & $\pmarncexp{(\pmnc{\alpha})}{\nu}$ \\ + $\pmast116\pmcdot04$. & $\pmarncexp{\mu}{\pmnc{\beta}}$ \\ + $\pmast117\pmcdot01$. & $\mu \pmarg \nu$ \\ + $\pmast117\pmcdot02$. & $\mu \pmarg \pmnc{\alpha}$ \\ + $\pmast117\pmcdot03$. & $\pmnc{\alpha} \pmarg \nu$ \\ + $\pmast117\pmcdot04$. & $\mu \pmarl \nu$ \\ + $\pmast117\pmcdot05$. & $\mu \pmargeq \nu$ \\ + $\pmast117\pmcdot06$. & $\mu \pmarleq \nu$ \\ + $\pmast119\pmcdot01$. & $\pmarsubt{\gamma}{\nu}$ \\ + $\pmast119\pmcdot02$. & $\pmarsubt{\pmnc{\alpha}}{\nu}$ \\ + $\pmast119\pmcdot03$. & $\pmarsubt{\gamma}{\pmnc{\beta}}$ \\ + $\pmast120\pmcdot01$. & $\pmNCinduct$ \\ + $\pmast120\pmcdot011$. & $\pmncinduct{\xi}$ \\ + $\pmast120\pmcdot02$. & $\pmClsinduct$ \\ + $\pmast120\pmcdot021$. & $\pmclsinduct{\xi}$ \\ + $\pmast120\pmcdot03$. & $\pmInfinax$ \\ + $\pmast120\pmcdot04$. & $\pminfinax{x}$ \\ + $\pmast120\pmcdot43$. & $\pmspec{\beta}$ \\ + $\pmast121\pmcdot01$. & $\pmintoo{x}{y}$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast121\pmcdot011$. & $\pmintoc{x}{y}$ \\ + $\pmast121\pmcdot012$. & $\pmintco{x}{y}$ \\ + $\pmast121\pmcdot013$. & $\pmintcc{x}{y}$ \\ + $\pmast121\pmcdot02$. & $\pmintnc{\nu}$ \\ + $\pmast121\pmcdot03$. & $\pmfinid{P}$ \\ + $\pmast121\pmcdot031$. & $\pmfin{P}$ \\ + $\pmast121\pmcdot04$. & $\pmintt{\nu}{P}$ \\ + $\pmast122\pmcdot01$. & $\pmprog$ \\ + $\pmast123\pmcdot01$. & $\pmalephn{0}$ \\ + $\pmast123\pmcdot02$. & $\pmsucc$ Dft [$\pmast123\textbf{---}4$] \\ + $\pmast124\pmcdot01$. & $\pmclsrefl$ \\ + $\pmast124\pmcdot02$. & $\pmncrefl$ \\ + $\pmast124\pmcdot021$. & $\pmnc{\rho}\pmcin \pmncrefl$ \\ + $\pmast124\pmcdot03$. & $\pmncmult$ \\ + $\pmast126\pmcdot01$. & $\pmncind$ \\ + $\pmast150\pmcdot01$. & $\pmrnsm{S}{Q}$ \\ + $\pmast150\pmcdot02$. & $\pmrnsmd{S}{Q}$ \\ + $\pmast150\pmcdot03$. & $\pmopsc{Q}{y}$ \\ + $\pmast150\pmcdot04$. & $\pmdscf{R}{\pmrnsm{S}{Q}}$ \\ + $\pmast150\pmcdot05$. & $\pmrnsm{R}{\pmrnsm{S}{Q}}$ \\ + $\pmast151\pmcdot01$. & $\pmsmorb{P}{Q}$ \\ + $\pmast151\pmcdot02$. & $\pmSmor$ \\ + $\pmast152\pmcdot01$. & $\pmNr$ \\ + $\pmast152\pmcdot02$. & $\pmNR$ \\ + $\pmast153\pmcdot01$. & $\pmsrrn{1}$ \\ + $\pmast154\pmcdot01$. & $\pmNRat{\gamma}{X}$ \\ + $\pmast155\pmcdot01$. & $\pmnor{P}$ \\ + $\pmast155\pmcdot02$. & $\pmNoR$ \\ + $\pmast160\pmcdot01$. & $\pmrsum{P}{Q}$ \\ + $\pmast161\pmcdot01$. & $\pmrsumb{P}{x}$ \\ + $\pmast161\pmcdot02$. & $\pmrsume{x}{P}$ \\ + $\pmast161\pmcdot212$. & $\pmrsumb{P}{\pmrsumb{x}{y}}$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast161\pmcdot213$. & $\pmrsume{\pmrsume{x}{y}}{P}$ \\ + $\pmast162\pmcdot01$. & $\pmrsumr{P}$ \\ + $\pmast163\pmcdot01$. & $\pmrsumrex{2}$ \\ + $\pmast164\pmcdot01$. & $\pmsmorsmorb{P}{Q}$ \\ + $\pmast164\pmcdot02$. & $\pmSmorsmor$ \\ + $\pmast166\pmcdot01$. & $\pmrprod{Q}{P}$ \\ + $\pmast166\pmcdot421$. & $\pmrprod{P}{\pmrprod{Q}{R}}$ \\ + $\pmast170\pmcdot01$. & $\pmRfdcl{P}$ \\ + $\pmast170\pmcdot02$. & $\pmRfdlc{P}$ \\ + $\pmast171\pmcdot01$. & $\pmRfddf{P}$ \\ + $\pmast171\pmcdot02$. & $\pmRfdfd{P}$ \\ + $\pmast172\pmcdot01$. & $\pmrfprod{P}$ \\ + $\pmast173\pmcdot01$. & $\pmRfprod{P}$ \\ + $\pmast174\pmcdot01$. & $\pmrarrel{3}$ \\ + $\pmast176\pmcdot01$. & $P \pmrexp Q$ \\ + $\pmast176\pmcdot02$. & $\pmRexp{P}{Q}$ \\ + $\pmast180\pmcdot01$. & $\pmrnsum{P}{Q}$ \\ + $\pmast180\pmcdot02$. & $\pmrndsum{\mu}{\nu}$ \\ + $\pmast180\pmcdot03$. & $\pmrndsum{\pmnr{P}}{\nu}$ \\ + $\pmast180\pmcdot04$. & $\pmrndsum{\mu}{\pmnr{Q}}$ \\ + $\pmast180\pmcdot561$. & $\pmrndsum{\mu}{\pmrndsum{\nu}{\varpi}}$ \\ + $\pmast181\pmcdot01$. & $\pmrnsumru{P}{x}$ \\ + $\pmast181\pmcdot011$. & $\pmrnsumur{x}{P}$ \\ + $\pmast181\pmcdot02$. & $\pmrndsum{\mu}{\pmrn{1}}$ \\ + $\pmast181\pmcdot021$. & $\pmrndsum{\pmrn{1}}{\mu}$ \\ + $\pmast181\pmcdot03$. & $\pmrndsum{\pmnr{P}}{\pmrn{1}}$ \\ + $\pmast181\pmcdot031$. & $\pmrndsum{\pmrn{1}}{\pmnr{P}}$ \\ + $\pmast181\pmcdot04$. & $\pmrndsum{\pmrn{1}}{\pmrn{1}}$ \\ + $\pmast181\pmcdot561$. & $\pmrndsum{\mu}{\pmrndsum{\pmrn{1}}{\pmrn{1}}}$ \\ + $\pmast181\pmcdot571$. & $\pmrndsum{\pmrn{1}}{\pmrndsum{\pmrn{1}}{\mu}}$ \\ + $\pmast182\pmcdot01$. & $\pmrsep{\pmop}$ \\ + $\pmast183\pmcdot01$. & $\pmrnsumf{P}$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast184\pmcdot01$. & $\pmrnprod{\mu}{\nu}$ \\ + $\pmast184\pmcdot02$. & $\pmrnprod{\pmnr{P}}{\nu}$ \\ + $\pmast184\pmcdot03$. & $\pmrnprod{\mu}{\pmnr{Q}}$ \\ + $\pmast184\pmcdot32$. & $\pmrnprod{\mu}{\pmrnprod{\nu}{\varpi}}$ \\ + $\pmast185\pmcdot01$. & $\pmrnprodf{P}$ \\ + $\pmast186\pmcdot01$. & $\pmrnexp{r}{\mu}{\nu}$ \\ + $\pmast186\pmcdot02$. & $\pmrnexp{r}{(\pmnr{P})}{\nu}$ \\ + $\pmast186\pmcdot03$. & $\pmrnexp{r}{\mu}{(\pmnr{Q})}$ \\ + $\pmast201\pmcdot01$. & $\pmtrans$ \\ + $\pmast202\pmcdot01$. & $\pmconnex$ \\ + $\pmast204\pmcdot01$. & $\pmser$ \\ + $\pmast206\pmcdot01$. & $\pmSeq{P}$ \\ + $\pmast206\pmcdot02$. & $\pmPrec{P}$ \\ + $\pmast207\pmcdot01$. & $\pmlt{P}$ \\ + $\pmast207\pmcdot02$. & $\pmtl{P}$ \\ + $\pmast207\pmcdot03$. & $\pmLimax{P}$ \\ + $\pmast207\pmcdot04$. & $\pmLimin{P}$ \\ + $\pmast208\pmcdot01$. & $\pmcror{P}$ \\ + $\pmast211\pmcdot01$. & $\pmsect{P}$ \\ + $\pmast212\pmcdot01$. & $\pmseg{P}$ \\ + $\pmast212\pmcdot02$. & $\pmsym{P}$ \\ + $\pmast213\pmcdot01$. & $\pmsectr{P}$ \\ + $\pmast214\pmcdot01$. & $\pmded$ \\ + $\pmast214\pmcdot02$. & $\pmsded$ \\ + $\pmast215\pmcdot01$. & $\pmstr{P}$ \\ + $\pmast216\pmcdot01$. & $\pmDer{P}$ \\ + $\pmast216\pmcdot02$. & $\pmden{P}$ \\ + $\pmast216\pmcdot03$. & $\pmclsd{P}$ \\ + $\pmast216\pmcdot04$. & $\pmperf{P}$ \\ + $\pmast216\pmcdot05$. & $\pmders{P}$ \\ + $\pmast230\pmcdot01$. & $\pmconv{R}{Q}{\alpha}$ \\ + $\pmast230\pmcdot02$. & $\pmConv{Q}$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast231\pmcdot01$. & $\pmlsc{P}{R}{Q}$ \\ + $\pmast231\pmcdot02$. & $\pmosc{P}{R}{Q}$ \\ + $\pmast232\pmcdot01$. & $\pmlscl{P}{R}{Q}{\alpha}$ \\ + $\pmast232\pmcdot02$. & $\pmoscl{P}{R}{Q}{\alpha}$ \\ + $\pmast233\pmcdot01$. & $\pmLmx{P}{R}{Q}$ \\ + $\pmast233\pmcdot02$. & $\pmLimf{R}{P}{Q}$ \\ + $\pmast234\pmcdot01$. & $\pmscf{P}{Q}{R}$ \\ + $\pmast234\pmcdot02$. & $\pmosf{P}{Q}{R}$ \\ + $\pmast234\pmcdot03$. & $\pmctf{P}{Q}{R}$ \\ + $\pmast234\pmcdot04$. & $\pmcontinf{P}{Q}{R}$ \\ + $\pmast234\pmcdot05$. & $\pmcontin{P}{Q}$ \\ + $\pmast250\pmcdot01$. & $\pmbord$ \\ + $\pmast250\pmcdot02$. & $\pmword$ \\ + $\pmast251\pmcdot01$. & $\pmordn$ \\ + $\pmast254\pmcdot01$. & $\pmLess$ \\ + $\pmast254\pmcdot02$. & $\pmPsc$ \\ + $\pmast255\pmcdot01$. & $\pmorle$ \\ + $\pmast255\pmcdot02$. & $\pmorgr$ \\ + $\pmast255\pmcdot03$. & $\pmnoo$ \\ + $\pmast255\pmcdot04$. & $\pmorleq$ \\ + $\pmast255\pmcdot05$. & $\pmorgrq$ \\ + $\pmast255\pmcdot06$. & $\mu \pmorle \pmnr{P}$ \\ + $\pmast255\pmcdot07$. & $\pmnr{P} \pmorle \mu$ \\ + $\pmast256\pmcdot01$. & $\pmm$ \hspace{2ex} Dft [\(\pmast256\)] \\ + $\pmast256\pmcdot02$. & $\pmn \,$ \hspace{2ex} Dft [\(\pmast256\)] \\ + $\pmast257\pmcdot01$. & $\pmtranc{R}{Q}{x}$ \\ + $\pmast257\pmcdot02$. & $\pmtrpot{Q}{R}{x}$ \\ + $\pmast259\pmcdot01$. & $\pma$ \hspace{2.75ex} Dft [\(\pmast256\)] \\ + $\pmast259\pmcdot02$. & $\pmaw$ \hspace{1.2ex} Dft [\(\pmast256\)] \\ + $\pmast259\pmcdot03$. & $\pmwa$ \\ + $\pmast260\pmcdot01$. & $\pmintf$ \\ + $\pmast261\pmcdot01$. & $\pmserinf$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast261\pmcdot02$. & $\pmwordinf$ \\ + $\pmast261\pmcdot03$. & $\pmserfin$ \\ + $\pmast261\pmcdot04$. & $\pmwordfin$ \\ + $\pmast261\pmcdot05$. & $\pmwordind$ \\ + $\pmast262\pmcdot01$. & $\pmordnfin$ \\ + $\pmast262\pmcdot02$. & $\pmordninf$ \\ + $\pmast262\pmcdot03$. & $\pmfinord{\mu}$ \\ + $\pmast263\pmcdot01$. & $\pmom$ \\ + $\pmast263\pmcdot02$. & $\pmn$ \hspace{3.4ex} Dft [\(\pmast263\)] \\ + $\pmast264\pmcdot01$. & $\pmpr{P}$ \hspace{2ex} Dft [\(\pmast263\)] \\ + $\pmast264\pmcdot429$. & $\pmrnprod{\pmrn{1}}{\alpha}$ \\ + $\pmast265\pmcdot01$. & $\pmomn{1}$ \\ + $\pmast265\pmcdot02$. & $\pmalephn{1}$ \\ + $\pmast265\pmcdot03$. & $\pmomn{2}$ \\ + $\pmast265\pmcdot04$. & $\pmalephn{2}$ \\ + $\pmast265\pmcdot05$. & $\pmm$ \hspace{3.2ex} Dft [\(\pmast265\)] \\ + $\pmast265\pmcdot06$. & $\pmn$ \hspace{3.5ex} Dft [\(\pmast265\)] \\ + $\pmast270\pmcdot01$. & $\pmComp$ \\ + $\pmast271\pmcdot01$. & $\pmmed$ \\ + $\pmast272\pmcdot01$. & $\pmsimp{T}{P}{Q}$ \\ + $\pmast273\pmcdot01$. & $\pmrats$ \\ + $\pmast273\pmcdot02$. & $\pmsimps{R}{SPQ}{T}$ \hspace{3.4ex} Dft [\(\pmast273\)] \\ + $\pmast273\pmcdot03$. & $\pmSimp{R}{S}{PQ}$ \hspace{3.5ex} Dft [\(\pmast273\)] \\ + $\pmast273\pmcdot04$. & $\pmSimps{T}{RSPQ}$ \hspace{4.9ex} Dft [\(\pmast273\)] \\ + $\pmast274\pmcdot01$. & $\pmsfcls{P}$ \\ + $\pmast274\pmcdot02$. & $\pmsfclsm{P}{\kappa}$ \hspace{3.4ex} Dft [\(\pmast274\)] \\ + $\pmast274\pmcdot03$. & $\pmsfclsp{T}{\kappa}$ \hspace{3.7ex} Dft [\(\pmast274\)] \\ + $\pmast274\pmcdot04$. & $\pmsfclsmp{\kappa}$ \hspace{3ex} Dft [\(\pmast274\)] \\ + $\pmast275\pmcdot01$. & $\pmcser$ \\ + $\pmast276\pmcdot01$. & $\pmcsercl{P}$ \\ + $\pmast276\pmcdot02$. & $\pma$ \hspace{7.3ex} Dft [\(\pmast276\)] \\ + $\pmast276\pmcdot03$. & $\pmsfclsm{P}{\lambda}$ \hspace{4ex} Dft [\(\pmast276\)] +\end{tabular} + +\begin{tabular}{l l} +$\pmast276\pmcdot04$. & $\pmcsercls{T}{P}$ \hspace{8.2ex} Dft [\(\pmast276\)] \\ +$\pmast276\pmcdot05$. & $\pmCsercls{P}{\kappa}$ \hspace{6.25ex} Dft [\(\pmast276\)] \\ +$\pmast300\pmcdot01$. & $\pmu$ \\ +$\pmast300\pmcdot02$. & $\pmrnum$ \\ +$\pmast300\pmcdot03$. & $\pmrnumid$ \\ +$\pmast301\pmcdot01$. & $R_p$ \hspace{8.2ex} Dft [\(\pmast301\)] \\ +$\pmast301\pmcdot02$. & $\text{num}(R)$ \hspace{3ex} Dft [\(\pmast301\)] \\ +$\pmast301\pmcdot03$. & $\pmrpwr{R}{\sigma}$ \\ +$\pmast302\pmcdot01$. & $\pmPrm$ \\ +$\pmast302\pmcdot02$. & $\pmrprm{\rho}{\sigma}{\mu}{\nu}$ \\ +$\pmast302\pmcdot03$. & $\pmprm{\rho}{\sigma}{\mu}{\nu}$ \\ +$\pmast302\pmcdot04$. & $\pmhcf{\mu}{\nu}$ \\ +$\pmast302\pmcdot05$. & $\pmlcm{\mu}{\nu}$ \\ +$\pmast303\pmcdot01$. & $\pmrat{\mu}{\nu}$ \\ +$\pmast303\pmcdot02$. & $\pmqn{0}$ \\ +$\pmast303\pmcdot03$. & $\pmqnil$ \\ +$\pmast303\pmcdot04$. & $\pmRat$ \\ +$\pmast303\pmcdot05$. & $\pmRatdef$ \\ +$\pmast304\pmcdot01$. & $\pmqnle{X}{Y}$ \\ +$\pmast304\pmcdot02$. & $\pmqnLe$ \\ +$\pmast304\pmcdot03$. & $\pmqnlez$ \\ +$\pmast305\pmcdot01$. & $\pmprodsr{X}{Y}$ \\ +$\pmast306\pmcdot01$. & $\pmsumsr{X}{Y}$ \\ +$\pmast307\pmcdot01$. & $\pmratn$ \\ +$\pmast307\pmcdot011$. & $\pmratg$ \\ +$\pmast307\pmcdot02$. & $\pmRatnle$ \\ +$\pmast307\pmcdot021$. & $\pmRatngr$ \\ +$\pmast307\pmcdot03$. & $\pmRatgle$ \\ +$\pmast307\pmcdot031$. & $\pmRatggr$ \\ +$\pmast307\pmcdot04$. & $\pmratnLe$ \\ +$\pmast307\pmcdot05$. & $\pmratgLe$ \\ +$\pmast308\pmcdot01$. & $\pmratssub{X}{Y}$ +\end{tabular} + +\begin{tabular}{l l} +$\pmast308\pmcdot02$. & $\pmsumgr{X}{Y}$ \\ +$\pmast309\pmcdot01$. & $\pmprodgr{X}{Y}$ \\ +$\pmast310\pmcdot01$. & $\pmrenp$ \\ +$\pmast310\pmcdot011$. & $\pmrenpz$ \\ +$\pmast310\pmcdot02$. & $\pmrenn$ \\ +$\pmast310\pmcdot021$. & $\pmrennz$ \\ +$\pmast310\pmcdot03$. & $\pmreng$ \\ +$\pmast311\pmcdot01$. & $\pmconc{\mu,\nu,...}$ \\ +$\pmast311\pmcdot02$. & $\pmrensumc{\mu}{\nu}$ \\ +$\pmast312\pmcdot01$. & $\pmrensub{\mu}{\nu}$ \\ +$\pmast312\pmcdot02$. & $\pmrensuma{\mu}{\nu}$ \\ +$\pmast313\pmcdot01$. & $\pmrenproda{\mu}{\nu}$ \\ +$\pmast314\pmcdot01$. & $\pmrenrsum{X}{Y}$ \\ +$\pmast314\pmcdot02$. & $\pmrenrprod{X}{Y}$ \\ +$\pmast314\pmcdot03$. & $\pmrenr$ \\ +$\pmast314\pmcdot04$. & $\pmrenrssum{M}{N}$ \\ +$\pmast314\pmcdot05$. & $\pmrenrsprod{M}{N}$ \\ +$\pmast330\pmcdot01$. & $\pmcr{\alpha}$ \\ +$\pmast330\pmcdot02$. & $\pmabel$ \\ +$\pmast330\pmcdot03$. & $\pmvfm{\alpha}$ \\ +$\pmast330\pmcdot04$. & $\pmvfmcl$ \\ +$\pmast330\pmcdot05$. & $\pmvffb{\kappa}$ \\ +$\pmast331\pmcdot01$. & $\pmconx{\kappa}$ \\ +$\pmast331\pmcdot02$. & $\pmconxfm$ \\ +$\pmast332\pmcdot01$. & $\pmfrep{\kappa}{P}$ \\ +$\pmast333\pmcdot01$. & $\pmfopen{\kappa}$ \\ +$\pmast333\pmcdot011$. & $\pmfopennid{\kappa}$ \\ +$\pmast333\pmcdot02$. & $\pmfmap$ \\ +$\pmast333\pmcdot03$. & $\pmfmapconx$ +\end{tabular} + +\begin{tabular}{l l} + $\pmast334\pmcdot01$. & $\pmtrsp{\kappa}$ \\ + $\pmast334\pmcdot02$. & $\pmfmtrs$ \\ + $\pmast334\pmcdot03$. & $\pmfmconnex$ \\ + $\pmast334\pmcdot04$. & $\pmfmsr$ \\ + $\pmast334\pmcdot05$. & $\pmfmasym$ \\ + $\pmast335\pmcdot01$. & $\pminit{\kappa}$ \\ + $\pmast335\pmcdot02$. & $\pmfminit$ \\ + $\pmast336\pmcdot01$. & $\pmvr{\kappa}$ \\ + $\pmast336\pmcdot011$. & $\pmvrnid{\kappa}$ \\ + $\pmast336\pmcdot02$. & $\pmarvs{a}$ \\ + $\pmast351\pmcdot01$. & $\pmfmsubm$ \\ + $\pmast352\pmcdot01$. & $\pmvrm{T}{\kappa}$ \\ + $\pmast352\pmcdot02$. & $\pmvrmg{T}{\kappa}$ \\ + $\pmast353\pmcdot01$. & $\pmfmrt$ \\ + $\pmast353\pmcdot02$. & $\pmfmcx$ \\ + $\pmast353\pmcdot03$. & $\pmfmrtcx$ \\ + $\pmast354\pmcdot01$. & $\pmfmg{\kappa}$ \\ + $\pmast354\pmcdot02$. & $\pmrtnet{a}{\lambda}$ \\ + $\pmast354\pmcdot03$. & $\pmfmgrp$ \\ + $\pmast356\pmcdot01$. & $\pmrems{X}{\kappa}$ \\ + $\pmast370\pmcdot01$. & $\pmfmcycl$ \\ + $\pmast370\pmcdot02$. & $\pmcycl{K}{\kappa}$ \\ + $\pmast370\pmcdot03$. & $\pmcycli{I}{\kappa}$ \\ + $\pmast371\pmcdot01$. & $\pmvser{W}{\kappa}$ \\ + $\pmast372\pmcdot01$. & $\pmintsecvser{\nu}{\kappa}$ \\ + $\pmast373\pmcdot01$. & $\pmsfmid{M}{\nu}{\kappa}$ \hspace{2ex} Dft [\(\pmast373\text{---}5\)]\\ + $\pmast373\pmcdot02$. & $\pmprime$ \\ + $\pmast373\pmcdot03$. & $\pmsmltid{S}{\nu}$ \hspace{0.75ex} Dft [\(\pmast373\text{---}5\)]\\ + $\pmast375\pmcdot01$. & $\pmprrt{\mu}{\nu}{\kappa}$ +\end{tabular} +\end{document} \ No newline at end of file diff --git a/macros/latex/contrib/principia/README b/macros/latex/contrib/principia/README index 83b78ebc29..505f8978fd 100644 --- a/macros/latex/contrib/principia/README +++ b/macros/latex/contrib/principia/README @@ -1,12 +1,12 @@ principia.sty - a LaTeX2e package for typesetting the "Peanese" notation of Whitehead and Russell's 1910 "Principia Mathematica". -The file principia.sty is the original work of Landon D. C. Elkind (Copyright (c) 2021). It is released under the LaTeX Project Public License 1.3c. +The file principia.sty is the original work of Landon D. C. Elkind (Copyright (c) 2023). It is released under the LaTeX Project Public License 1.3c. -This is principia package Version 1.3 (2021/04/19). This version covers typesetting the notations through Sections A and B in Volume I of "Principia Mathematica". See the file principia.pdf for information on these changes and for further information on how to typeset Peanese symbols in LaTeX with the principia package. +This is principia package Version 2.0 (2023/03/13). This version covers typesetting the notations through Volumes I-III of "Principia Mathematica". See the file principia.pdf for information on these changes and for further information on how to typeset Peanese symbols in LaTeX with the principia package. Changes between version updates can be found at https://logicalatomist.github.io/principia/ Comments and suggestions are welcomed by the package maintainer, signed below. Landon D. C. Elkind -University of Alberta +Western Kentucky University diff --git a/macros/latex/contrib/principia/principia.pdf b/macros/latex/contrib/principia/principia.pdf index b0c8da5020..87c69193ba 100644 Binary files a/macros/latex/contrib/principia/principia.pdf and b/macros/latex/contrib/principia/principia.pdf differ diff --git a/macros/latex/contrib/principia/principia.sty b/macros/latex/contrib/principia/principia.sty index 421a0b65ab..29591fc070 100644 --- a/macros/latex/contrib/principia/principia.sty +++ b/macros/latex/contrib/principia/principia.sty @@ -1,13 +1,13 @@ %Package Identification \NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{principia}[2021/04/19 principia package version 1.3] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original. +\ProvidesPackage{principia}[2023/03/13 principia package version 2.0] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original. %Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24 %Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25 %Licensed under LaTeX Project Public License 1.3c. -%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25 -%Version 1.3 (minor update): removes package dependency on marvosym; updates Section A notation; removes other notations (corrected extension pending). 2021/04/19 +%Version 1.2 (superseded by Version 2.0) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25 +%Version 2.0 (major update): extends the package to cover typesetting of all notations in Volumes II and III; removes package dependency on marvosym. 2022/09/04 %Licensed under LaTeX Project Public License 1.3c. -%Copyright Landon D. C. Elkind, 2021 (https://landondcelkind.com/contact/). +%Copyright Landon D. C. Elkind, 2023 (https://landonelkind.com/contact/). %Principia package requirements \RequirePackage{amssymb} %This loads the relation domain and converse domain limitation symbols. @@ -20,6 +20,26 @@ %Mathematical logic %The theory of deduction %Meta-logical symbols +\newcommand{\ie}{\textit{i}.\textit{e}.\ } +\newcommand{\Ie}{\textit{I}.\textit{e}.\ } +\newcommand{\eg}{\textit{e}.\textit{g}.\ } +\newcommand{\Eg}{\textit{E}.\textit{g}.\ } +\newcommand{\pmsch}[1]{\pmast#1} %Starred chapter +\newcommand{\pmschs}[2]{\pmast#1\text{---}\pmast#2} %Starred chapter +\newcommand{\pmsns}[3]{\pmast#1\pmcdot#2\text{---}\pmcdot#3}%Starred number +\newcommand{\pmpsn}[2]{(\pmast#1\pmcdot#2)} +\newcommand{\pmpsnn}[3]{(\pmast#1\pmcdot#2\pmcdot#3)} +\newcommand{\pmsn}[2]{\pmast#1\pmcdot#2} +\newcommand{\pmnsn}[1]{\text{#1}} +\newcommand{\pmsnn}[3]{\pmast#1\pmcdot#2\pmcdot#3} +\newcommand{\pmsnnn}[4]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4} +\newcommand{\pmsnnnn}[5]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5} +\newcommand{\pmsnnnnn}[6]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6} +\newcommand{\pmsnb}[2]{\boldsymbol{\pmast#1\pmcdot#2}} %Starred number boldface +\newcommand{\pmsnnb}[3]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3}} +\newcommand{\pmsnnnb}[4]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}} +\newcommand{\pmsnnnnb}[5]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}} +\newcommand{\pmsnnnnnb}[6]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}} \newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions. \newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof. \newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof. @@ -34,7 +54,7 @@ \newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. -\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command. \newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command. \newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command. @@ -42,12 +62,13 @@ \newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command. \newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command. \newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command. -\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. +\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array}} %This is the substitution command. \newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign. \newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number. \newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number. \newcommand{\pmiddf}{\mathbin{=}} \newcommand{\pmdf}{\quad \text{Df}} +\newcommand{\pmDf}{\text{Df}} \newcommand{\pmpp}{\quad \text{Pp}} %Square dots for scope, defined for up to six dots @@ -70,6 +91,7 @@ \newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd} \newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction. \newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01 +\newcommand{\pminc}{\mathbin{|}} %8.01 %The theory of apparent variables \newcommand{\pmall}[1]{(#1)} @@ -77,18 +99,568 @@ \newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}} %Additional defined logic signs -\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}} -\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}} -\newcommand{\pmcirc}[1]{\mathbf{\dot{\text{$#1$}}}} +\newcommand{\pmhat}[1]{\boldsymbol{\hat{\text{$#1$}}}} +\newcommand{\pmbreve}[1]{\boldsymbol{\breve{\text{$#1$}}}} +\newcommand{\pmcirc}[1]{\boldsymbol{\dot{\text{$#1$}}}} \newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable \newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables \newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables +\newcommand{\pmpffff}[5]{#1(#2, #3, #4, #5)} %for propositional functions of four variables (including ellipses) +\newcommand{\pmppf}[2]{#1\pmshr#2} %for propositional predicative functions of one variable +\newcommand{\pmppff}[3]{#1\pmshr(#2, #3)} %for propositional predicative functions of two variables \newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions \newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable \newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables \newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables +\newcommand{\pmpredddd}[5]{#1\pmshr(#2, #3, #4, #5)} %for predicates (``predicative functions'') of four variables +\newcommand{\pmpreddddd}[6]{#1\pmshr(#2, #3, #4, #5, #6)} %for predicates (``predicative functions'') of five variables +\newcommand{\pmpredddddd}[7]{#1\pmshr(#2, #3, #4, #5, #6, #7)} %for predicates (``predicative functions'') of six variables +\newcommand{\pmid}{\mathbin{=}} \newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02 -\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions +\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}}} %the rotated Greek iota used in definite descriptions \newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01 +\newcommand{\pmthe}[2]{(\pmiota#1)(#2 #1)} %*14.01 +\newcommand{\pmtheb}[2]{[(\pmiota#1)(#2 #1)]} %*14.01 \newcommand{\pmDsc}{\pmiota} -\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02 \ No newline at end of file +\newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02 + +%Classes and relations +%Class signs +\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01 +\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02 +\newcommand{\pmCls}{\text{Cls}} %20.03 +\newcommand{\pmClsn}[1]{\text{Cls}^{#1}} +\newcommand{\pmcinn}{\pmnot\pmcin} %20.06 +\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01 +\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02 +\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03 +\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04 +\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05 +\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01 +\newcommand{\pmcnull}{\Lambda} %24.02 +\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03 + +%Relation signs +\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01 +\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02 +\newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc. +\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}#1} %23.04 +\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}}#2} %23.05 +\newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01 +\newcommand{\pmrnull}{\pmcirc{\Lambda}} %25.02 +\newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03 +\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\boldsymbol{\pmcinc}$}}} %23.01 +\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccap}$}}} %23.02 +\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccup}$}}} %23.03 + +%Logic of Relations +\newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01 +\newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01 +\newcommand{\pmCnv}{\text{Cnv}} +\newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02 +\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} %32.01 +\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}} +\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} %32.02 +\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}} +\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03 +\newcommand{\pmSg}{\text{sg}} +\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04 +\newcommand{\pmGs}{\text{gs}} +\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01 +\newcommand{\pmDm}{\text{D}} +\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02 +\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}} +\newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03 +\newcommand{\pmCmp}{C} +\newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04 +\newcommand{\pmFld}{F} +\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01 +\newcommand{\pmRprd}{\mathop{|}} +\newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc. +\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01 +\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02 +\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03 +\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04 +\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01 +\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01 +\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02 +\newcommand{\pmdscfR}[1]{#1_{\pmcin}} +\newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03 +\newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}} +\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04 +\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05 +\newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package +\newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02 +\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03 + +%Products and sums of classes of classes or relations +\newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01 +\newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02 +\newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01 +\newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02 +\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01 +\newcommand{\pmRprdd}{\mathop{||}} + +%Prolegomena to Cardinal Arithmetic +%Unit Classes and Couples +%Identity and Diversity +\newcommand{\pmrid}{I} %50.01 +\newcommand{\pmrdiv}{J} %50.02 +\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01 +\newcommand{\pmcUnit}{\iota} +\newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01 + +%Cardinal numbers +\newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc. + +%Ordinal numbers +\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc. +\newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01 +\newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc. + +%Sub-classes, Sub-relations, and Relative Types +%Sub-classes +\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01 +\newcommand{\pmsCl}{\text{Cl}} +\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02 +\newcommand{\pmsCle}{\text{Cl ex}} +\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03 +\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01 +\newcommand{\pmsRl}{\text{Rl}} +\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02 +\newcommand{\pmsRle}{\text{Rl ex}} +\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03 +\newcommand{\pmRel}{\text{Rel}} +\newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04 +\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01 + +%Relative type symbols +\newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01 +\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011 +\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc. +\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04 +\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc. +\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc. +\newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc. +\newcommand{\pmrtdi}[2]{#1_{#2}} %65.01 +\newcommand{\pmrtdc}[2]{#1(#2)} %65.02 +\newcommand{\pmrtdri}[2]{#1_{#2}} %65.03 +\newcommand{\pmrtdrc}[2]{#1(#2)} %65.04 + +%One-many, Many-one, and One-one relations +%Similarity relation signs +\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01 +\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01 +\newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02 +\newcommand{\pmSM}{\text{sm}} +\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}} +\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls} +\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1} +\newcommand{\pmoneone}{1\boldsymbol{\to}1} + +%Selections +\newcommand{\pmselp}[1]{P_{\small\Delta}\boldsymbol{`}#1} %80.01 +\newcommand{\pmSelp}{P_{\Delta}} +\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\boldsymbol{`}#1} +\newcommand{\pmSele}{\pmcin_{\Delta}} +\newcommand{\pmself}[1]{F_{\small\Delta}\boldsymbol{`}#1} +\newcommand{\pmSelf}{F_{\Delta}} +\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01 +\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02 +\newcommand{\pmex}{\text{Cls excl}} +\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03 +\newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}}} #2} +\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01 +\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02 +\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03 + +%Inductive relations +\newcommand{\pmanc}[1]{#1_\pmast} %90.01 +\newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02 +\newcommand{\pmrst}[1]{#1_\text{st}} %91.01 +\newcommand{\pmrts}[1]{#1_\text{ts}} %91.02 +\newcommand{\pmpot}[1]{\text{Pot}\boldsymbol{`}#1} %91.03 +\newcommand{\pmpotid}[1]{\text{Potid}\boldsymbol{`}#1} %91.04 +\newcommand{\pmpo}[1]{#1_\text{po}} %91.05 +\newcommand{\pmB}{B} %93.01 +\newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02 +\newcommand{\pmMin}{\text{min}} +\newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021 +\newcommand{\pmMax}{\text{max}} +\newcommand{\pmgen}[1]{\text{gen}\boldsymbol{`}#1} %93.03 +\newcommand{\pmGen}{\text{gen}} +\newcommand{\pmefr}[2]{#1\pmast#2} %95.05 +\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01 +\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02 +\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01 + +%Volume II +%Cardinal arithmetic +%Definition and Logical Properties of Cardinal Numbers +\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01 +\newcommand{\pmNc}{\text{Nc}} +\newcommand{\pmNC}{\text{NC}} %100.02 +\newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01 +\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01 +\newcommand{\pmNoc}{\text{N}_0\text{c}} +\newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02 +\newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc. +\newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc. +\newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc. +\newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01 +\newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc. +\newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc. +\newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc. +\newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011 +\newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02 +\newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021 +\newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03 +\newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}} +\newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04 +\newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041 +\newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01 + +%Addition, Multiplication, Exponentiation +\newcommand{\pmarsumc}{\mathrel{+}} %110.01 +\newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02 +\newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01 +\newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02 +\newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03 +\newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01 +\newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02 +\newcommand{\pmarprodc}{\times} %113.02 +\newcommand{\pmarprodnc}{\times_\text{c}} %113.03 +\newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01 +\newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01 +\newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02 +\newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01 +\newcommand{\pmArexp}{\text{exp}} +\newcommand{\pmarncexp}[2]{#1^{#2}} %116.02 +\newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01 +\newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04 +\newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05 +\newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06 + +%Finite and infinite +\newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01 +\newcommand{\pmArsubt}{{-}_\text{c}} +\newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01 +\newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011 +\newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02 +\newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021 +\newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03 +\newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04 +\newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43 +\newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01 +\newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011 +\newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012 +\newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013 +\newcommand{\pmintnc}[1]{P_{#1}} %121.02 +\newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03 +\newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031 +\newcommand{\pmintt}[2]{#1_{#2}} %121.04 +\newcommand{\pmprog}{\text{Prog}} %122.01 +\newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01 +\newcommand{\pmsucc}{\text{N}} %123.02 +\newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01 +\newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02 +\newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03 +\newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01 +\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1} +\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}} + +%Relation-arithmetic +%Ordinal similarity and relation-numbers +\newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01 +\newcommand{\pmrnsmd}[2]{#1 \mathop{\boldsymbol{\dagger}} #2} %150.02 +\newcommand{\pmrnsmdf}[1]{#1\boldsymbol{\dagger}} +\newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03 +\newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01 +\newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01 +\newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02 +\newcommand{\pmSmor}{\text{smor}} +\newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01 +\newcommand{\pmNr}{\text{Nr}} +\newcommand{\pmNR}{\text{NR}} %152.02 +\newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01 +\newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01 +\newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01 +\newcommand{\pmNor}{\text{N}_0\text{r}} +\newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02 + +%Addition of Relations, and the Product of Two Relations +\newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01 +\newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}} +\newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01 +\newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} } +\newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02 +\newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}} +\newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01 +\newcommand{\pmRsumr}{\Sigma} +\newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01 +\newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01 +\newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}} +\newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02 +\newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor} +\newcommand{\pmrprod}[2]{#1 \times #2} %166.01 + +%First differences and the multiplication and exponentiation of relations +%On the relation of first differences among the sub-classes of a given class +\newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01 +\newcommand{\pmRfdcl}[1]{#1_{\text{cl}}} +\newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02 +\newcommand{\pmRfdlc}[1]{#1_{\text{lc}}} +\newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01 +\newcommand{\pmRfddf}[1]{#1_{\text{df}}} +\newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02 +\newcommand{\pmRfdfd}[1]{#1_{\text{fd}}} +\newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01 +\newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01 +\newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01 +\newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01 +\newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02 +\newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01 +\newcommand{\pmRnsum}{+} +\newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02 +\newcommand{\pmRndsum}{\pmcirc{+}} +\newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01 +\newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}} +\newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011 +\newcommand{\pmRnsumur}{\pmcirc{\pmRsume}} +\newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02 +\newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01 +\newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01 +\newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01 +\newcommand{\pmRnprod}{\pmcirc{\times}} +\newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01 +\newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01 +\newcommand{\pmRnexp}[1]{\pmArexp_{#1}} + +%Series +%General theory of series +\newcommand{\pmtrans}{\text{trans}} %201.01 +\newcommand{\pmconnex}{\text{connex}} %202.01 +\newcommand{\pmser}{\text{Ser}} %204.01 +\newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01 +\newcommand{\pmSeq}[1]{\text{seq}_{#1}} +\newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02 +\newcommand{\pmPrec}[1]{\text{prec}_{#1}} +\newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01 +\newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01 +\newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03 +\newcommand{\pmLimax}[1]{\text{limax}_{#1}} +\newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04 +\newcommand{\pmLimin}[1]{\text{limin}_{#1}} +\newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}} +\newcommand{\pmCr}{\text{cr}} +\newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01 +\newcommand{\pmCror}{\text{cror}} + +%On sections, segments, stretches, and derivatives +\newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01 +\newcommand{\pmSect}{\text{sect}} +\newcommand{\pmseg}[1]{\boldsymbol{\varsigma}\textbf{`}{#1}} %212.01 +\newcommand{\pmSeg}{\boldsymbol{\varsigma}} +\newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02 +\newcommand{\pmSym}{\text{sym}} +\newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01 +\newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01 +\newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02 +\newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01 +\newcommand{\pmStr}{\text{str}} +\newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01 +\newcommand{\pmDer}[1]{\delta_{#1}} +\newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3} +\newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02 +\newcommand{\pmDen}{\text{dense}} +\newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03 +\newcommand{\pmClsd}{\text{closed}} +\newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04 +\newcommand{\pmPerf}{\text{perf}} +\newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05 +\newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}} + +%On convergence, and the limits of functions +\newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01 +\newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02 +\newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3} +\newcommand{\pmConvg}[1]{{#1}_{\text{cng}}} +\newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01 +\newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02 +\newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01 +\newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02 +\newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01 +\newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}} +\newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02 +\newcommand{\pmLimf}[3]{#1(#2#3)} +\newcommand{\pmscf}[3]{\text{sc}(#1, #2)\boldsymbol{`}#3} %234.01 +\newcommand{\pmosf}[3]{\text{os}(#1, #2)\boldsymbol{`}#3} %234.02 +\newcommand{\pmctf}[3]{\text{ct}(#1#2)\boldsymbol{`}#3} %234.03 +\newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\boldsymbol{`}#3} %234.04 +\newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05 +\newcommand{\pmContin}{\text{contin}} + +%Volume III +%Well-Ordered Series +\newcommand{\pmbord}{\text{Bord}} %250.01 +\newcommand{\pmword}{\Omega} %250.02 +\newcommand{\pmordn}{\text{NO}} %251.01 +\newcommand{\pmless}{\mathrel{\text{less}}} %254.01 +\newcommand{\pmLess}{\text{less}} +\newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02 +\newcommand{\pmPsc}{P_{\text{sm}}} +\newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01 +\newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02 +\newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03 +\newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04 +\newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05 +\newcommand{\pmm}{\emph{M}} %256.01 +\newcommand{\pmn}{\emph{N}} %256.02, 263.02 +\newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01 +\newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01 +\newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02 +\newcommand{\pma}{\emph{A}} %259.01 +\newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02 +\newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03 + +%Finite and Infinite Series and Ordinals +\newcommand{\pmintf}{P_{\text{fn}}} %260.01 +\newcommand{\pmserinf}{\text{Ser infin}} %261.01 +\newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02 +\newcommand{\pmserfin}{\text{Ser fin}} %261.03 +\newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04 +\newcommand{\pmwordind}{\pmword\text{ induct}} %261.04 +\newcommand{\pmordnfin}{\text{NO fin}} %262.01 +\newcommand{\pmordninf}{\text{NO infin}} %262.02 +\newcommand{\pmfinord}[1]{#1_r} %262.03 +\newcommand{\pmom}{\boldsymbol{\omega}} %263.01 +\newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01 +\newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc. +\newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc. + +%Compact series, rational series, and continuous series +\newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01 +\newcommand{\pmComp}{\text{Comp}} +\newcommand{\pmmed}{\mathrel{\text{med}}} %271.01 +\newcommand{\pmMed}{\text{med}} +\newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01 +\newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02 +\newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03 +\newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04 +\newcommand{\pmrats}{\eta} %273.01 +\newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01 +\newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02 +\newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03 +\newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04 +\newcommand{\pmcser}{\theta} %275.01 +\newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01 +\newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04 +\newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05 +%Skipped some temprary definitions as repetitious + +%Quantity +%Generalization of Number +\newcommand{\pmu}{\textit{U}} %300.01 +\newcommand{\pmrnum}{\text{Rel num}} %300.02 +\newcommand{\pmrnumid}{\text{Rel num id}} %300.03 +\newcommand{\pmrpwr}[2]{#1^#2} %301.03 +\newcommand{\pmPrm}{\text{Prm}} %302.01 +\newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02 +\newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03 +\newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04 +\newcommand{\pmHcf}{\text{hcf}} +\newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05 +\newcommand{\pmLcm}{\text{lcm}} +\newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01 +\newcommand{\pmqn}[1]{#1_q} %303.02 +\newcommand{\pmqnil}{\infty_q} %303.03 +\newcommand{\pmRat}{\text{Rat}} %303.04 +\newcommand{\pmRatdef}{\text{Rat def}} %303.05 +\newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01 +\newcommand{\pmQnle}{\boldsymbol{<}_r} +\newcommand{\pmqnLe}{H} %304.02 +\newcommand{\pmqnlez}{H'} %304.03 +\newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01 +\newcommand{\pmProdsr}{\times_s} +\newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01 +\newcommand{\pmSumsr}{+_s} +\newcommand{\pmratn}{\text{Rat}_n} %307.01 +\newcommand{\pmratg}{\text{Rat}_g} %307.011 +\newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02 +\newcommand{\pmRatnle}{\boldsymbol{<}_n} +\newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021 +\newcommand{\pmRatngr}{\boldsymbol{>}_n} +\newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03 +\newcommand{\pmRatgle}{\boldsymbol{<}_g} +\newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031 +\newcommand{\pmRatggr}{\boldsymbol{>}_g} +\newcommand{\pmratnLe}{H_n} %307.04 +\newcommand{\pmratgLe}{H_g} %307.05 +\newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01 +\newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02 +\newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01 +\newcommand{\pmrenp}{\Theta} %310.01 +\newcommand{\pmrenpz}{\Theta'} %310.011 +\newcommand{\pmrenn}{\Theta_n} %310.02 +\newcommand{\pmrennz}{\Theta_n'} %310.021 +\newcommand{\pmreng}{\Theta_g} %310.03 +\newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01 +\newcommand{\pmConc}{\text{concord}} +\newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02 +\newcommand{\pmrensub}[2]{#1 -_p #2} %312.01 +\newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02 +\newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01 +\newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01 +\newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02 +\newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package +\newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03 +\newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04 +\newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05 + +%Vector Families +\newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01 +\newcommand{\pmabel}{\text{Abel}} %330.02 +\newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03 +\newcommand{\pmVfm}{\text{fm}} +\newcommand{\pmvfmcl}{\textit{FM}} %330.04 +\newcommand{\pmvffb}[1]{#1_\iota} %330.05 +\newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01 +\newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02 +\newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01 +\newcommand{\pmfopen}[1]{#1_\partial} %333.01 +\newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011 +\newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02 +\newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03 +\newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01 +\newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02 +\newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03 +\newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02 +\newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05 +\newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01 +\newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02 +\newcommand{\pmvr}[1]{\textit{V}_#1} %336.01 +\newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011 +\newcommand{\pmarvs}[1]{A_{#1}} %336.02 + +%Measurement +\newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01 +\newcommand{\pmvrm}[2]{#1_#2} %352.01 +\newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02 +\newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01 +\newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02 +\newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03 +\newcommand{\pmfmg}[1]{#1_g} %354.01 +\newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02 +\newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03 +\newcommand{\pmrems}[2]{#1_#2} %356.01 + +%Cyclic Families +\newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01 +\newcommand{\pmcycl}[2]{#1_#2} %370.02 +\newcommand{\pmcycli}[2]{#1_#2} %370.03 +\newcommand{\pmvser}[2]{#1_#2} %371.01 +\newcommand{\pmintsecvser}[2]{#1_#2} %372.01 +\newcommand{\pmprime}{\text{Prime}} %373.01 +\newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02 +\newcommand{\pmsmltid}[2]{(#1, #2)} %373.03 +\newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01 \ No newline at end of file diff --git a/macros/latex/contrib/principia/principia.tex b/macros/latex/contrib/principia/principia.tex index 86d5ce3a22..8c5eb4e7bf 100644 --- a/macros/latex/contrib/principia/principia.tex +++ b/macros/latex/contrib/principia/principia.tex @@ -1,13 +1,13 @@ \documentclass[12pt]{article} \NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{principia}[2021/04/19 principia package version 1.3] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original. +\ProvidesPackage{principia}[2023/03/13 principia package version 2.0] %This is the principia package is for representing notations in Whitehead and Russell's ``Principia Mathematica" close to their appearance in the original. %Version 1.0 (superseded by Version 1.1): Covers typesetting of notation through Volume I. 2020/10/24 %Version 1.1 (superseded by Version 1.2) minor updates: fixed the spacing of scope dots around parentheses; fixed spacing of theorem sign; fixed spacing around primitive proposition and definition signs. 2020/10/25 %Licensed under LaTeX Project Public License 1.3c. -%Version 1.2 (superseded by Version 1.3) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25 -%Version 1.3 (minor update): removes package dependency on marvosym; updates Section A and Section B notations. 2021/04/19 +%Version 1.2 (superseded by Version 2.0) (minor updates): boldfaced (`thickened') the truth-functional connectives, existential quantifier, set and relation symbols; added numerous commands for typesetting brackets and substitutions into theorems. 2021/02/25 +%Version 2.0 (major update): extends the package to cover typesetting of all notations in Volume II; removes package dependency on marvosym. 2023/03/13 %Licensed under LaTeX Project Public License 1.3c. -%Copyright Landon D. C. Elkind, 2021. (https://landondcelkind.com/contact/). +%Copyright Landon D. C. Elkind, 2022. (https://landonelkind.com/contact/). \usepackage{fullpage} \usepackage[T1]{fontenc} @@ -24,6 +24,26 @@ %Mathematical logic %The theory of deduction %Meta-logical symbols +\newcommand{\ie}{\textit{i}.\textit{e}.\ } +\newcommand{\Ie}{\textit{I}.\textit{e}.\ } +\newcommand{\eg}{\textit{e}.\textit{g}.\ } +\newcommand{\Eg}{\textit{E}.\textit{g}.\ } +\newcommand{\pmsch}[1]{\pmast#1} %Starred chapter +\newcommand{\pmschs}[2]{\pmast#1\text{---}\pmast#2} %Starred chapter +\newcommand{\pmsns}[3]{\pmast#1\pmcdot#2\text{---}\pmcdot#3}%Starred number +\newcommand{\pmpsn}[2]{(\pmast#1\pmcdot#2)} +\newcommand{\pmpsnn}[3]{(\pmast#1\pmcdot#2\pmcdot#3)} +\newcommand{\pmsn}[2]{\pmast#1\pmcdot#2} +\newcommand{\pmnsn}[1]{\text{#1}} +\newcommand{\pmsnn}[3]{\pmast#1\pmcdot#2\pmcdot#3} +\newcommand{\pmsnnn}[4]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4} +\newcommand{\pmsnnnn}[5]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5} +\newcommand{\pmsnnnnn}[6]{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6} +\newcommand{\pmsnb}[2]{\boldsymbol{\pmast#1\pmcdot#2}} %Starred number boldface +\newcommand{\pmsnnb}[3]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3}} +\newcommand{\pmsnnnb}[4]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4}} +\newcommand{\pmsnnnnb}[5]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5}} +\newcommand{\pmsnnnnnb}[6]{\boldsymbol{\pmast#1\pmcdot#2\pmcdot#3\pmcdot#4\pmcdot#5\pmcdot#6}} \newcommand{\pmfd}{\begin{center} \rule{5cm}{.5pt} \end{center}} %Dividing line between introductory remarks in a starred number and the formal deductions. \newcommand{\pmdem}{\textit{Dem}.} %This notation begins a proof. \newcommand{\pmdemi}{\indent \pmdem} %This idents the notation that begins a proof. @@ -38,7 +58,7 @@ \newcommand{\pmSub}[3]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubb}[5]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmSubbb}[7]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array} \bigg \rbrack} %This is the substitution command. -\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array} \bigg \rbrack} %This is the substitution command. +\newcommand{\pmSubbbb}[9]{\bigg \lbrack \normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array} \bigg \rbrack} %This is the substitution command. \newcommand{\pmsUb}[2]{\small \begin{array}{c} #1 \\ \hline #2 \end{array}} %This is the substitution command. \newcommand{\pmsUbb}[4]{\small \begin{array}{c c} #1, & #3 \\ \hline #2, & #4 \end{array}} %This is the substitution command. \newcommand{\pmsUbbb}[6]{\small \begin{array}{c c c} #1, & #3, & #5 \\ \hline #2, & #4, & #6 \end{array}} %This is the substitution command. @@ -46,12 +66,13 @@ \newcommand{\pmSUb}[3]{\normalsize #1 \text{ } \small \begin{array}{c} #2 \\ \hline #3 \end{array}} %This is the substitution command. \newcommand{\pmSUbb}[5]{\normalsize #1 \text{ } \small \begin{array}{c c} #2, & #4 \\ \hline #3, & #5 \end{array}} %This is the substitution command. \newcommand{\pmSUbbb}[7]{\normalsize #1 \text{ } \small \begin{array}{c c c} #2, & #4, & #6 \\ \hline #3, & #5, & #7 \end{array}} %This is the substitution command. -\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #1, & #3, & #5, & #7 \\ \hline #2, & #4, & #6, & #8 \end{array}} %This is the substitution command. +\newcommand{\pmSUbbbb}[9]{\normalsize #1 \text{ } \small \begin{array}{c c c c} #2, & #4, & #6, & #8 \\ \hline #3, & #5, & #7, & #9 \end{array}} %This is the substitution command. \newcommand{\pmthm}{\mathpunct{\text{\scalebox{.5}[1]{$\boldsymbol\vdash$}}}} %This is the theorem sign. \newcommand{\pmast}{\text{\resizebox{!}{.75\height}{\ding{107}}}} %This is the sign introducing a theorem number. \newcommand{\pmcdot}{\text{\raisebox{.05cm}{$\boldsymbol\cdot$}}} %This is a sign introducing a theorem sub-number. \newcommand{\pmiddf}{\mathbin{=}} \newcommand{\pmdf}{\quad \text{Df}} +\newcommand{\pmDf}{\text{Df}} \newcommand{\pmpp}{\quad \text{Pp}} %Square dots for scope, defined for up to six dots @@ -74,6 +95,7 @@ \newcommand{\pmandddddd}{\pmandd\hspace{.1em}\pmandd\hspace{.1em}\pmandd} \newcommand{\pmprod}{\mathbin{\ooalign{$\boldsymbol{\wedge}\mkern.5mu$\hidewidth\cr$\boldsymbol{\wedge}$\cr\hidewidth$\mkern.5mu\boldsymbol{\wedge}$}}} %Not in Principia, but added here as a dual of its symbol for disjunction. \newcommand{\pmiff}{\mathbin{\ooalign{$\boldsymbol{\equiv}\mkern.5mu$\hidewidth\cr$\boldsymbol{\equiv}$\cr\hidewidth$\mkern.5mu\boldsymbol{\equiv}$}}} %4.01 +\newcommand{\pminc}{\mathbin{|}} %8.01 %The theory of apparent variables \newcommand{\pmall}[1]{(#1)} @@ -81,24 +103,574 @@ \newcommand{\pmSome}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}} %Additional defined logic signs -\newcommand{\pmhat}[1]{\mathbf{\hat{\text{$#1$}}}} -\newcommand{\pmbreve}[1]{\mathbf{\breve{\text{$#1$}}}} -\newcommand{\pmcirc}[1]{\mathbf{\dot{\text{$#1$}}}} +\newcommand{\pmhat}[1]{\boldsymbol{\hat{\text{$#1$}}}} +\newcommand{\pmbreve}[1]{\boldsymbol{\breve{\text{$#1$}}}} +\newcommand{\pmcirc}[1]{\boldsymbol{\dot{\text{$#1$}}}} \newcommand{\pmpf}[2]{#1#2} %for propositional functions of one variable \newcommand{\pmpff}[3]{#1(#2, #3)} %for propositional functions of two variables \newcommand{\pmpfff}[4]{#1(#2, #3, #4)} %for propositional functions of three variables +\newcommand{\pmpffff}[5]{#1(#2, #3, #4, #5)} %for propositional functions of four variables (including ellipses) +\newcommand{\pmppf}[2]{#1\pmshr#2} %for propositional predicative functions of one variable +\newcommand{\pmppff}[3]{#1\pmshr(#2, #3)} %for propositional predicative functions of two variables \newcommand{\pmshr}{\textbf{!}} %*12.1 and *12.11, used for predicative propositional functions \newcommand{\pmpred}[2]{#1\pmshr#2} %for predicates (``predicative functions'') of one variable \newcommand{\pmpredd}[3]{#1\pmshr(#2, #3)} %for predicates (``predicative functions'') of two variables \newcommand{\pmpreddd}[4]{#1\pmshr(#2, #3, #4)} %for predicates (``predicative functions'') of three variables +\newcommand{\pmpredddd}[5]{#1\pmshr(#2, #3, #4, #5)} %for predicates (``predicative functions'') of four variables +\newcommand{\pmpreddddd}[6]{#1\pmshr(#2, #3, #4, #5, #6)} %for predicates (``predicative functions'') of five variables +\newcommand{\pmpredddddd}[7]{#1\pmshr(#2, #3, #4, #5, #6, #7)} %for predicates (``predicative functions'') of six variables +\newcommand{\pmid}{\mathbin{=}} \newcommand{\pmnid}{\mathrel{\ooalign{$=$\cr\hidewidth\footnotesize\rotatebox[origin=c]{210}{\textbf{/}}\hidewidth\cr}}} %*13.02 -\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\mathbf{\iota}$}}}} %the rotated Greek iota used in definite descriptions +\newcommand{\pmiota}{\ooalign{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}\cr\hidewidth\raisebox{.0125em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.025em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.0375em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}\cr\hidewidth\raisebox{.05em}{\rotatebox[origin=c]{180}{$\boldsymbol{\iota}$}}}} %the rotated Greek iota used in definite descriptions \newcommand{\pmdsc}[1]{(\pmiota#1)} %*14.01 +\newcommand{\pmthe}[2]{(\pmiota#1)(#2 #1)} %*14.01 +\newcommand{\pmtheb}[2]{[(\pmiota#1)(#2 #1)]} %*14.01 \newcommand{\pmDsc}{\pmiota} \newcommand{\pmexists}{\textbf{E}\hspace{.1em}\pmshr} %*14.02 -\title{\texttt{principia.sty}\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 1.3)} -\author{Landon D. C. Elkind \texttt{elkind@ualberta.ca}} +%Classes and relations +%Class signs +\newcommand{\pmcls}[2]{\pmhat{#1}(#2)} %20.01 +\newcommand{\pmcin}{\mathop{\boldsymbol{\epsilon}}} %20.02 +\newcommand{\pmCls}{\text{Cls}} %20.03 +\newcommand{\pmClsn}[1]{\text{Cls}^{#1}} +\newcommand{\pmcinn}{\pmnot\pmcin} %20.06 +\newcommand{\pmcinc}{\mathop{\ooalign{$\boldsymbol{\subset}$\cr\hidewidth$\hspace{.1em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.15em}\boldsymbol{\subset}$\cr\hidewidth$\hspace{.2em}\boldsymbol{\subset}$}}} %22.01 +\newcommand{\pmccap}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2){\oval(4,1)[t]}\phantom{\circ}$}}}} %22.02 +\newcommand{\pmccup}{\mathop{\ooalign{\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.1em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.2em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.3em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.4em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.5em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}\cr\hidewidth\hspace{.6em}\scalebox{1.3}[1.75]{$\put(3, 2.5){\oval(4,4)[b]}\phantom{\circ}$}}}} %22.03 +\newcommand{\pmccmp}[1]{\boldsymbol{-}#1} %22.04 +\newcommand{\pmcmin}[2]{#1\boldsymbol{-}#2} %22.05 +\newcommand{\pmcuni}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}} %24.01 +\newcommand{\pmcnull}{\Lambda} %24.02 +\newcommand{\pmcexists}{\text{\raisebox{.5em}{\rotatebox{180}{\textbf{E}}}}\hspace{-.1em}\mathop{\pmshr}} %24.03 + +%Relation signs +\newcommand{\pmrel}[3]{\pmhat{#1}\pmhat{#2}#3} %21.01 +\newcommand{\pmrele}[5]{#1\{\pmhat{#2}\pmhat{#3}#4(#2, #3)\}#5} %21.02 +\newcommand{\pmrelep}[3]{#1\{#2\}#3} %21.08, 21.081, 21.082, etc. +\newcommand{\pmrcmp}[1]{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}#1} %23.04 +\newcommand{\pmrmin}[2]{#1\mathrel{\ooalign{$\hidewidth\raisebox{.25em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccmp}$}}#2} %23.05 +\newcommand{\pmruni}{\pmcirc{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}} %25.01 +\newcommand{\pmrnull}{\pmcirc{\Lambda}} %25.02 +\newcommand{\pmrexists}{\pmcirc{\mathop{\text{\raisebox{.5em}{\rotatebox{180}{E}}}}}\mathop{\pmshr}} %25.03 +\newcommand{\pmrinc}{\mathrel{\ooalign{$\hidewidth\boldsymbol{\cdot}\hidewidth$\cr$\boldsymbol{\pmcinc}$}}} %23.01 +\newcommand{\pmrcap}{\mathrel{\ooalign{$\hidewidth\raisebox{.3em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccap}$}}} %23.02 +\newcommand{\pmrcup}{\mathrel{\ooalign{$\hidewidth\raisebox{.1em}{$\boldsymbol{\cdot}$}\hidewidth$\cr$\boldsymbol{\pmccup}$}}} %23.03 + +%Logic of Relations +\newcommand{\pmdscf}[2]{#1\textbf{`}#2} %30.01 +\newcommand{\pmcnv}[1]{\text{Cnv}\textbf{`}#1} %31.01 +\newcommand{\pmCnv}{\text{Cnv}} +\newcommand{\pmcrel}[1]{\pmbreve{#1}} %31.02 +\newcommand{\pmrrf}[2]{\overset{\boldsymbol{\rightarrow}}{#1\textbf{`}}#2} %32.01 +\newcommand{\pmRrf}[1]{\overset{\boldsymbol{\rightarrow}}{#1}} +\newcommand{\pmrrl}[2]{\overset{\boldsymbol{\leftarrow}}{#1\textbf{`}}#2} %32.02 +\newcommand{\pmRrl}[1]{\overset{\boldsymbol{\leftarrow}}{#1}} +\newcommand{\pmsg}[1]{\text{sg}\textbf{`}#1} %32.03 +\newcommand{\pmSg}{\text{sg}} +\newcommand{\pmgs}[1]{\text{gs}\textbf{`}#1} %32.04 +\newcommand{\pmGs}{\text{gs}} +\newcommand{\pmdm}[1]{\text{D}\textbf{`}#1} %33.01 +\newcommand{\pmDm}{\text{D}} +\newcommand{\pmcdm}[1]{\text{\rotatebox[origin=c]{180}{D}}\textbf{`}#1} %33.02 +\newcommand{\pmCdm}{\text{\rotatebox[origin=c]{180}{D}}} +\newcommand{\pmcmp}[1]{C\textbf{`}#1} %33.03 +\newcommand{\pmCmp}{C} +\newcommand{\pmfld}[1]{F\textbf{`}#1} %33.04 +\newcommand{\pmFld}{F} +\newcommand{\pmrprd}[2]{{#1}\mathop{|}{#2}} %34.01 +\newcommand{\pmRprd}{\mathop{|}} +\newcommand{\pmrprdn}[2]{#1^{#2}} %34.02, 34.03, etc. +\newcommand{\pmrld}[2]{#1 \boldsymbol{\upharpoonleft} #2} %35.01 +\newcommand{\pmrlcd}[2]{#1 \boldsymbol{\upharpoonright} #2} %35.02 +\newcommand{\pmrlf}[3]{#1 \boldsymbol{\upharpoonleft} #2 \boldsymbol{\upharpoonright} #3} %35.03 +\newcommand{\pmrl}[2]{#1 \boldsymbol{\uparrow} #2} %35.04 +\newcommand{\pmrlF}[2]{#1 \mathbin{\ooalign{$\upharpoonright$\cr\hidewidth\rotatebox[origin=c]{180}{\text{$\upharpoonleft$}}\hidewidth\cr}} #2} %36.01 +\newcommand{\pmdscff}[2]{#1\textbf{`}\textbf{`}#2} %37.01 +\newcommand{\pmdscfr}[2]{#1_{\pmcin}\textbf{`}#2} %37.02 +\newcommand{\pmdscfR}[1]{#1_{\pmcin}} +\newcommand{\pmdscfcr}[2]{\pmbreve{#1}_{\pmcin}\textbf{`}#2} %37.03 +\newcommand{\pmdscfcR}[1]{\pmbreve{#1}_{\pmcin}} +\newcommand{\pmdscfff}[2]{#1\textbf{`}\textbf{`}\textbf{`}#2} %37.04 +\newcommand{\pmdscfe}[2]{\mathop{\text{E}}\mathop{\pmshr\pmshr}\pmdscff{#1}{#2}} %37.05 +\newcommand{\Female}{{\usefont{U}{mvs}{m}{n}\symbol{126}}} %from the Marvosym package +\newcommand{\pmop}{\mathop{\text{\Female}}} %38.01, 38.02 +\newcommand{\pmopc}[2]{#1 \mathop{\underset{\textbf{''}}{\text{\Female}}} #2} %38.03 + +%Products and sums of classes of classes or relations +\newcommand{\pmccsum}[1]{p\textbf{`}#1} %40.01 +\newcommand{\pmccprd}[1]{s\textbf{`}#1} %40.02 +\newcommand{\pmcrsum}[1]{\pmcirc{p}\textbf{`}#1} %41.01 +\newcommand{\pmcrprd}[1]{\pmcirc{s}\textbf{`}#1} %41.02 +\newcommand{\pmrprdd}[2]{{#1}\mathop{||}{#2}} %43.01 +\newcommand{\pmRprdd}{\mathop{||}} + +%Prolegomena to Cardinal Arithmetic +%Unit Classes and Couples +%Identity and Diversity +\newcommand{\pmrid}{I} %50.01 +\newcommand{\pmrdiv}{J} %50.02 +\newcommand{\pmcunit}[1]{\iota\textbf{`}#1} %51.01 +\newcommand{\pmcUnit}{\iota} +\newcommand{\pmcunits}[1]{\pmbreve{\iota}\textbf{`}#1} %52.01 + +%Cardinal numbers +\newcommand{\pmcn}[1]{#1} %52.01, 54.01, 54.02, etc. + +%Ordinal numbers +\newcommand{\pmoc}[2]{#1 \boldsymbol{\downarrow} #2} %55.01, 55.02, etc. +\newcommand{\pmdn}[1]{\pmcirc{#1}} %56.01 +\newcommand{\pmorn}[1]{#1_r} %56.02, 56.03, etc. + +%Sub-classes, Sub-relations, and Relative Types +%Sub-classes +\newcommand{\pmscl}[1]{\text{Cl}\textbf{`}#1} %60.01 +\newcommand{\pmsCl}{\text{Cl}} +\newcommand{\pmscle}[1]{\text{Cl ex}\textbf{`}#1} %60.02 +\newcommand{\pmsCle}{\text{Cl ex}} +\newcommand{\pmscls}[1]{\text{Cls}\textbf{`}#1} %60.03 +\newcommand{\pmsrl}[1]{\text{Rl}\textbf{`}#1} %61.01 +\newcommand{\pmsRl}{\text{Rl}} +\newcommand{\pmsrle}[1]{\text{Rl ex}\textbf{`}#1} %61.02 +\newcommand{\pmsRle}{\text{Rl ex}} +\newcommand{\pmsrel}[1]{\text{Rel}\textbf{`}#1} %61.03 +\newcommand{\pmRel}{\text{Rel}} +\newcommand{\pmReln}[1]{\text{Rel}^{#1}} %61.04 +\newcommand{\pmrin}{\mathop{\boldsymbol{\epsilon}}} %62.01 + +%Relative type symbols +\newcommand{\pmrt}[1]{t\textbf{`}#1} %63.01 +\newcommand{\pmrti}[2]{t^{#1}\textbf{`}#2} %63.011 +\newcommand{\pmrtc}[2]{t_{#1}\textbf{`}#2} %63.02, 63.03, etc. +\newcommand{\pmrtri}[2]{t^{#1}\textbf{`}#2} %63.04 +\newcommand{\pmrtrc}[2]{t_{#1}\textbf{`}#2} %64.02, 64.021, 64.022, etc. +\newcommand{\pmrtrci}[3]{t_{#1}^{\text{ }#2}\textbf{`}#3} %64.03, 64.031, etc. +\newcommand{\pmrtric}[3]{{}^{#1}t_{#2}\textbf{`}#3} %64.04, 64.041, etc. +\newcommand{\pmrtdi}[2]{#1_{#2}} %65.01 +\newcommand{\pmrtdc}[2]{#1(#2)} %65.02 +\newcommand{\pmrtdri}[2]{#1_{#2}} %65.03 +\newcommand{\pmrtdrc}[2]{#1(#2)} %65.04 + +%One-many, Many-one, and One-one relations +%Similarity relation signs +\newcommand{\pmrdc}[2]{#1\boldsymbol{\to}#2} %70.01 +\newcommand{\pmsmbar}{\mathrel{\overline{\text{sm}}}} %73.01 +\newcommand{\pmsm}{\mathrel{\text{sm}}} %73.02 +\newcommand{\pmSM}{\text{sm}} +\newcommand{\pmsmarr}{\overrightarrow{{\pmsm}}} +\newcommand{\pmonemany}{1\boldsymbol{\to}\pmCls} +\newcommand{\pmmanyone}{\pmCls\boldsymbol{\to}1} +\newcommand{\pmoneone}{1\boldsymbol{\to}1} + +%Selections +\newcommand{\pmselp}[1]{P_{\small\Delta}\boldsymbol{`}#1} %80.01 +\newcommand{\pmSelp}{P_{\Delta}} +\newcommand{\pmsele}[1]{\pmcin_{\small\Delta}\boldsymbol{`}#1} +\newcommand{\pmSele}{\pmcin_{\Delta}} +\newcommand{\pmself}[1]{F_{\small\Delta}\boldsymbol{`}#1} +\newcommand{\pmSelf}{F_{\Delta}} +\newcommand{\pmexc}{\text{Cls}^2 \mathop{\text{excl}}} %84.01 +\newcommand{\pmexcc}[1]{\text{Cl} \mathop{\text{excl}}\textbf{`}#1} %84.02 +\newcommand{\pmex}{\text{Cls excl}} +\newcommand{\pmexcn}{\text{Cls} \mathop{\text{ex}^2} \mathop{\text{excl}}} %84.03 +\newcommand{\pmselc}[2]{#1 \mathrel{\ooalign{\rotatebox[origin=c]{270}{$\boldsymbol{\mapsto}$}}} #2} +\newcommand{\pmmultr}{\mathop{\text{Rel}} \mathop{\text{Mult}}} %88.01 +\newcommand{\pmmultc}{\mathop{\text{Cls}^2} \mathop{\text{Mult}}} %88.02 +\newcommand{\pmmultax}{\mathop{\text{Mult}} \mathop{\text{ax}}} %88.03 + +%Inductive relations +\newcommand{\pmanc}[1]{#1_\pmast} %90.01 +\newcommand{\pmancc}[1]{\pmcrel{#1}_\pmast} %90.02 +\newcommand{\pmrst}[1]{#1_\text{st}} %91.01 +\newcommand{\pmrts}[1]{#1_\text{ts}} %91.02 +\newcommand{\pmpot}[1]{\text{Pot}\boldsymbol{`}#1} %91.03 +\newcommand{\pmpotid}[1]{\text{Potid}\boldsymbol{`}#1} %91.04 +\newcommand{\pmpo}[1]{#1_\text{po}} %91.05 +\newcommand{\pmB}{B} %93.01 +\newcommand{\pmmin}[1]{\text{min}_{#1}} %93.02 +\newcommand{\pmMin}{\text{min}} +\newcommand{\pmmax}[1]{\text{max}_{#1}} %93.021 +\newcommand{\pmMax}{\text{max}} +\newcommand{\pmgen}[1]{\text{gen}\boldsymbol{`}#1} %93.03 +\newcommand{\pmGen}{\text{gen}} +\newcommand{\pmefr}[2]{#1\pmast#2} %95.05 +\newcommand{\pmipr}[2]{I_{#1}\textbf{`}#2} %96.01 +\newcommand{\pmjpr}[2]{J_{#1}\textbf{`}#2} %96.02 +\newcommand{\pmfr}[2]{\overset{\boldsymbol{\leftrightarrow}}{#1}\textbf{`}#2} %97.01 + +%Volume II +%Cardinal arithmetic +%Definition and Logical Properties of Cardinal Numbers +\newcommand{\pmnc}[1]{\text{Nc}\textbf{`}#1} %100.01 +\newcommand{\pmNc}{\text{Nc}} +\newcommand{\pmNC}{\text{NC}} %100.02 +\newcommand{\pmNCat}[2]{\text{NC}^{#1}({#2})} %102.01 +\newcommand{\pmnoc}[1]{\text{N}_0\text{c}\textbf{`}#1} %103.01 +\newcommand{\pmNoc}{\text{N}_0\text{c}} +\newcommand{\pmNoC}{\text{N}_0\text{C}} %103.02 +\newcommand{\pmnca}[2]{\text{N}^{#1}\text{c}\textbf{`}#2} %104.01, 104.011, etc. +\newcommand{\pmNca}[1]{\text{N}^{#1}\text{C}} %104.02, 104.021, etc. +\newcommand{\pmch}[2]{#1^{(#2)}} %104.03, 104.031, etc. +\newcommand{\pmncd}[2]{\text{N}_{#1}\text{c}\textbf{`}#2} %105.01 +\newcommand{\pmNcd}[1]{\text{N}_{#1}\text{C}} %105.02, 105.021, etc. +\newcommand{\pmcl}[2]{#1_{(#2)}} %105.03, 105.031, etc. +\newcommand{\pmncll}[3]{\text{N}_{#1#2}\text{c}\textbf{`}#3} %106.01, 106.012, etc. +\newcommand{\pmnchh}[3]{\text{N}^{#1#2}\text{c}\textbf{`}#3} %106.011 +\newcommand{\pmncaa}[3]{\text{N}_{#1}{}^{#2}\text{c}\textbf{`}#3} %106.02 +\newcommand{\pmncdd}[3]{{}^{#1}\text{N}_{#2}\text{c}\textbf{`}#3} %106.021 +\newcommand{\pmNCll}[2]{\text{N}_{#1#2}\text{C}} %106.03 +\newcommand{\pmNChh}[2]{\text{N}^{#1#2}\text{C}} +\newcommand{\pmcll}[3]{#1_{(#2#3)}} %106.04 +\newcommand{\pmchh}[3]{#1^{(#2#3)}} %106.041 +\newcommand{\pmncr}[1]{\text{N}_{00}\text{c}\textbf{`}#1} %106.01 + +%Addition, Multiplication, Exponentiation +\newcommand{\pmarsumc}{\mathrel{+}} %110.01 +\newcommand{\pmarsumnc}{\mathrel{{+}_{\text{c}}}} %110.02 +\newcommand{\pmsmsmb}{\mathrel{\overline{\text{sm}}\;\overline{\text{sm}}}} %111.01 +\newcommand{\pmcrp}[2]{\text{Crp}(#1)\textbf{`}#2} %111.02 +\newcommand{\pmsmsm}{\mathrel{\text{sm}\;\text{sm}}} %111.03 +\newcommand{\pmarsumcc}[1]{\Sigma\textbf{`}#1} %112.01 +\newcommand{\pmarsumcnc}[1]{\Sigma\pmNc\textbf{`}#1} %112.02 +\newcommand{\pmarprodc}{\times} %113.02 +\newcommand{\pmarprodnc}{\times_\text{c}} %113.03 +\newcommand{\pmarprodcnc}[1]{\Pi\pmNc\textbf{`}#1} %114.01 +\newcommand{\pmarprodcc}[1]{\text{Prod}\textbf{`}#1} %115.01 +\newcommand{\pmarcls}{\pmClsn{3}\text{arithm}} %115.02 +\newcommand{\pmarexp}[2]{#1 \mathrel{\text{exp}} #2} %116.01 +\newcommand{\pmArexp}{\text{exp}} +\newcommand{\pmarncexp}[2]{#1^{#2}} %116.02 +\newcommand{\pmarg}{\mathrel{\boldsymbol{>}}} %117.01 +\newcommand{\pmarl}{\mathrel{\boldsymbol{<}}} %117.04 +\newcommand{\pmargeq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$}}} %117.05 +\newcommand{\pmarleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %117.06 + +%Finite and infinite +\newcommand{\pmarsubt}[2]{#1 \mathrel{{-}_\text{c}} #2} %119.01 +\newcommand{\pmArsubt}{{-}_\text{c}} +\newcommand{\pmNCinduct}{\text{NC}\,\text{induct}} %120.01 +\newcommand{\pmncinduct}[1]{\text{N}_#1\text{C}\,\text{induct}} %120.011 +\newcommand{\pmClsinduct}{\text{Cls}\,\text{induct}} %120.02 +\newcommand{\pmclsinduct}[1]{\text{Cls}_{#1}\,\text{induct}} %120.021 +\newcommand{\pmInfinax}{\text{Infin}\,\text{ax}} %120.03 +\newcommand{\pminfinax}[1]{\text{Infin}\,\text{ax}(#1)} %120.04 +\newcommand{\pmspec}[1]{\text{spec}\textbf{`}#1} %120.43 +\newcommand{\pmintoo}[2]{P(#1\mathbin{\boldsymbol{-}}#2)} %121.01 +\newcommand{\pmintoc}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}}{#2})} %121.011 +\newcommand{\pmintco}[2]{P({#1}\mathbin{\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}}{#2})} %121.012 +\newcommand{\pmintcc}[2]{P({#1} \mathbin{\ooalign{$\scalebox{1.2}[.7]{$\boldsymbol{\dashv}$}$\hidewidth\cr$\scalebox{1.2}[.7]{$\boldsymbol{\vdash}$}$}} {#2})} %121.013 +\newcommand{\pmintnc}[1]{P_{#1}} %121.02 +\newcommand{\pmfinid}[1]{\text{finid}\textbf{`}#1} %121.03 +\newcommand{\pmfin}[1]{\text{fin}\textbf{`}#1} %121.031 +\newcommand{\pmintt}[2]{#1_{#2}} %121.04 +\newcommand{\pmprog}{\text{Prog}} %122.01 +\newcommand{\pmaleph}{\boldsymbol{\aleph}} %123.01 +\newcommand{\pmsucc}{\text{N}} %123.02 +\newcommand{\pmclsrefl}{\text{Cls}\;\text{refl}} %124.01 +\newcommand{\pmncrefl}{\text{NC}\;\text{refl}} %124.02 +\newcommand{\pmncmult}{\text{NC}\;\text{mult}} %124.03 +\newcommand{\pmncind}{\text{NC}\;\text{ind}} %126.01 +\newcommand{\pmnocind}[1]{\text{N}_0\text{Cinduct}\textbf{`}#1} +\newcommand{\pmNocind}{\text{N}_0\text{Cinduct}} + +%Relation-arithmetic +%Ordinal similarity and relation-numbers +\newcommand{\pmrnsm}[2]{{#1}{\raise.4ex\hbox{\textbf{\large;}}}{#2}} %150.01 +\newcommand{\pmrnsmd}[2]{#1 \mathop{\boldsymbol{\dagger}} #2} %150.02 +\newcommand{\pmrnsmdf}[1]{#1\boldsymbol{\dagger}} +\newcommand{\pmopsc}[2]{#1 \mathrel{\ooalign{${\raise-.7ex\hbox{$\pmdot$}}$\hidewidth\cr$\text{\Female}$\hidewidth\cr${\raise-.8ex\hbox{\hspace{.15cm}\textbf{,}}}$}} #2} %150.03 +\newcommand{\pmsmorb}[2]{#1 \mathrel{\overline{\text{smor}}} #2} %151.01 +\newcommand{\pmSmorb}{\overline{\text{smor}}} %151.01 +\newcommand{\pmsmor}[2]{#1 \mathrel{\text{smor}} #2} %151.02 +\newcommand{\pmSmor}{\text{smor}} +\newcommand{\pmnr}[1]{\text{Nr}\textbf{`}#1} %152.01 +\newcommand{\pmNr}{\text{Nr}} +\newcommand{\pmNR}{\text{NR}} %152.02 +\newcommand{\pmsrrn}[1]{{#1}_{s}} %153.01 +\newcommand{\pmNRat}[2]{\text{NR}^{#1}({#2})} %154.01 +\newcommand{\pmnor}[1]{\text{N}_0\text{r}\textbf{`}#1} %155.01 +\newcommand{\pmNor}{\text{N}_0\text{r}} +\newcommand{\pmNoR}{\text{N}_0\text{R}} %155.02 + +%Addition of Relations, and the Product of Two Relations +\newcommand{\pmrsum}[2]{#1\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}} #2} %160.01 +\newcommand{\pmRsum}{\mathrel{\ooalign{${\raise-.21ex\hbox{$\boldsymbol{-}$}}$\cr\hidewidth$\boldsymbol{\uparrow}$\hidewidth\cr${\raise-.19ex\hbox{$\boldsymbol{-}$}}$}}} +\newcommand{\pmrsume}[2]{#1 \mathrel{\rotatebox[origin=c]{90}{$\pmRsum$}} #2} %161.01 +\newcommand{\pmRsume}{\rotatebox[origin=c]{90}{$\pmRsum$} } +\newcommand{\pmrsumb}[2]{#1 \mathrel{\rotatebox[origin=c]{270}{$\pmRsum$}} #2} %161.02 +\newcommand{\pmRsumb}{\rotatebox[origin=c]{270}{$\pmRsum$}} +\newcommand{\pmrsumr}[1]{\Sigma\textbf{`}#1} %162.01 +\newcommand{\pmRsumr}{\Sigma} +\newcommand{\pmrsumrex}[1]{\mathrel{\text{Rel}^{#1}\text{excl}}} %163.01 +\newcommand{\pmsmorsmorb}[2]{#1 \mathrel{\overline{\text{smor}}\,\overline{\text{smor}}} #2} %164.01 +\newcommand{\pmSmorsmorb}{\overline{\text{smor}}\,\overline{\text{smor}}} +\newcommand{\pmsmorsmor}[2]{#1 \mathrel{\pmSmor\,\pmSmor} #2} %164.02 +\newcommand{\pmSmorsmor}{\pmSmor\,\pmSmor} +\newcommand{\pmrprod}[2]{#1 \times #2} %166.01 + +%First differences and the multiplication and exponentiation of relations +%On the relation of first differences among the sub-classes of a given class +\newcommand{\pmrfdcl}[3]{#2 \mathrel{#1_{\text{cl}}} #3} %170.01 +\newcommand{\pmRfdcl}[1]{#1_{\text{cl}}} +\newcommand{\pmrfdlc}[3]{#2 \mathrel{#1_{\text{lc}}} #3} %170.02 +\newcommand{\pmRfdlc}[1]{#1_{\text{lc}}} +\newcommand{\pmrfddf}[3]{#2 \mathrel{#1_{\text{df}}} #3} %171.01 +\newcommand{\pmRfddf}[1]{#1_{\text{df}}} +\newcommand{\pmrfdfd}[3]{#2 \mathrel{#1_{\text{fd}}} #3} %171.02 +\newcommand{\pmRfdfd}[1]{#1_{\text{fd}}} +\newcommand{\pmrfprod}[1]{\Pi\textbf{`}#1} %172.01 +\newcommand{\pmRfprod}[1]{\text{Prod}\textbf{`}#1} %173.01 +\newcommand{\pmrarrel}[1]{\mathrel{\text{Rel}^{#1}\text{arithm}}} %174.01 +\newcommand{\pmrexp}{\mathrel{\text{exp}}} %176.01 +\newcommand{\pmRexp}[2]{{#1}^{#2}} %176.02 +\newcommand{\pmrnsum}[2]{{#1} + {#2}} %180.01 +\newcommand{\pmRnsum}{+} +\newcommand{\pmrndsum}[2]{{#1} \mathrel{\pmcirc{+}} {#2}} %180.02 +\newcommand{\pmRndsum}{\pmcirc{+}} +\newcommand{\pmrnsumru}[2]{#1 \mathrel{\pmcirc{\pmRsumb}} #2} %181.01 +\newcommand{\pmRnsumru}{\pmcirc{\pmRsumb}} +\newcommand{\pmrnsumur}[2]{#1 \mathrel{\pmcirc{\pmRsume}} #2} %181.011 +\newcommand{\pmRnsumur}{\pmcirc{\pmRsume}} +\newcommand{\pmrn}[1]{\pmcirc{#1}} %181.02 +\newcommand{\pmrsep}[1]{\ooalign{${\raise1.5ex\hbox{\rotatebox[origin=c]{180}{\scalebox{1.4}[1.4]{$\pmbreve{\phantom{.}}$}}}}$\cr\hidewidth$#1$\hidewidth}} %182.01 +\newcommand{\pmrnsumf}[1]{\Sigma\pmNr\textbf{`}#1} %183.01 +\newcommand{\pmrnprod}[2]{#1 \mathrel{\pmcirc{\times}} #2} %184.01 +\newcommand{\pmRnprod}{\pmcirc{\times}} +\newcommand{\pmrnprodf}[1]{\Pi\pmNr\textbf{`}#1} %185.01 +\newcommand{\pmrnexp}[3]{#2 \mathrel{\pmArexp_{#1}} #3} %186.01 +\newcommand{\pmRnexp}[1]{\pmArexp_{#1}} + +%Series +%General theory of series +\newcommand{\pmtrans}{\text{trans}} %201.01 +\newcommand{\pmconnex}{\text{connex}} %202.01 +\newcommand{\pmser}{\text{Ser}} %204.01 +\newcommand{\pmseq}[3]{#1 \mathrel{\text{seq}_{#1}} #2} %206.01 +\newcommand{\pmSeq}[1]{\text{seq}_{#1}} +\newcommand{\pmprec}[3]{#1 \mathrel{\text{prec}_{#1}} #2} %206.02 +\newcommand{\pmPrec}[1]{\text{prec}_{#1}} +\newcommand{\pmlt}[1]{\text{lt}_{#1}} %207.01 +\newcommand{\pmtl}[1]{\text{tl}_{#1}} %207.01 +\newcommand{\pmlimax}[2]{\text{limax}_{#1}\textbf{`}#2} %207.03 +\newcommand{\pmLimax}[1]{\text{limax}_{#1}} +\newcommand{\pmlimin}[2]{\text{limin}_{#1}\textbf{`}#2} %207.04 +\newcommand{\pmLimin}[1]{\text{limin}_{#1}} +\newcommand{\pmcr}[1]{\text{cr}\textbf{`}{#1}} +\newcommand{\pmCr}{\text{cr}} +\newcommand{\pmcror}[1]{\text{cror}\textbf{`}{#1}} %208.01 +\newcommand{\pmCror}{\text{cror}} + +%On sections, segments, stretches, and derivatives +\newcommand{\pmsect}[1]{\text{sect}\textbf{`}{#1}} %211.01 +\newcommand{\pmSect}{\text{sect}} +\newcommand{\pmseg}[1]{\boldsymbol{\varsigma}\textbf{`}{#1}} %212.01 +\newcommand{\pmSeg}{\boldsymbol{\varsigma}} +\newcommand{\pmsym}[1]{\text{sym}\textbf{`}{#1}} %212.02 +\newcommand{\pmSym}{\text{sym}} +\newcommand{\pmsectr}[1]{{#1}_{\pmSeg}} %213.01 +\newcommand{\pmded}{\mathrel{\text{Ded}}} %214.01 +\newcommand{\pmsded}{\mathrel{\text{semi}\;\text{Ded}}} %214.02 +\newcommand{\pmstr}[1]{\text{str}\textbf{`}{#1}} %215.01 +\newcommand{\pmStr}{\text{str}} +\newcommand{\pmder}[2]{\delta_{#1}\textbf{`}#2} %216.01 +\newcommand{\pmDer}[1]{\delta_{#1}} +\newcommand{\pmdern}[3]{\delta_{#1}^{#2}\textbf{`}#3} +\newcommand{\pmden}[1]{\text{dense}\textbf{`}{#1}} %216.02 +\newcommand{\pmDen}{\text{dense}} +\newcommand{\pmclsd}[1]{\text{closed}\textbf{`}{#1}} %216.03 +\newcommand{\pmClsd}{\text{closed}} +\newcommand{\pmperf}[1]{\text{perf}\textbf{`}{#1}} %216.04 +\newcommand{\pmPerf}{\text{perf}} +\newcommand{\pmders}[1]{\rotatebox[origin=c]{180}{$\Delta$}\textbf{`}#1} %216.05 +\newcommand{\pmDers}{\rotatebox[origin=c]{180}{$\Delta$}} + +%On convergence, and the limits of functions +\newcommand{\pmconv}[3]{#1\bar{#2}_{\text{cn}}#3} %230.01 +\newcommand{\pmConv}[1]{{#1}_{\text{cn}}} %230.02 +\newcommand{\pmconvg}[3]{#1\bar{#2}_{\text{cng}}#3} +\newcommand{\pmConvg}[1]{{#1}_{\text{cng}}} +\newcommand{\pmlsc}[3]{#1\bar{#2}_{\text{sc}}#3} %231.01 +\newcommand{\pmosc}[3]{#1\bar{#2}_{\text{os}}#3} %231.02 +\newcommand{\pmlscl}[4]{(#1\bar{#2}#3)_{\text{sc}}\textbf{`}#4} %232.01 +\newcommand{\pmoscl}[4]{(#1\bar{#2}#3)_{\text{os}}\textbf{`}#4} %232.02 +\newcommand{\pmlmx}[4]{(#1\bar{#2}#3)_{\text{lmx}}\textbf{`}#4} %233.01 +\newcommand{\pmLmx}[3]{(#1\bar{#2}#3)_{\text{lmx}}} +\newcommand{\pmlimf}[4]{#1(#2#3)\textbf{`}#4} %233.02 +\newcommand{\pmLimf}[3]{#1(#2#3)} +\newcommand{\pmscf}[3]{\text{sc}(#1, #2)\boldsymbol{`}#3} %234.01 +\newcommand{\pmosf}[3]{\text{os}(#1, #2)\boldsymbol{`}#3} %234.02 +\newcommand{\pmctf}[3]{\text{ct}(#1#2)\boldsymbol{`}#3} %234.03 +\newcommand{\pmcontinf}[3]{\text{contin}(#1#2)\boldsymbol{`}#3} %234.04 +\newcommand{\pmcontin}[2]{#1 \mathrel{\text{contin}} #2} %234.05 +\newcommand{\pmContin}{\text{contin}} + +%Volume III +%Well-Ordered Series +\newcommand{\pmbord}{\text{Bord}} %250.01 +\newcommand{\pmword}{\Omega} %250.02 +\newcommand{\pmordn}{\text{NO}} %251.01 +\newcommand{\pmless}{\mathrel{\text{less}}} %254.01 +\newcommand{\pmLess}{\text{less}} +\newcommand{\pmpsc}[2]{#1 \mathrel{P_{\text{sm}}} #2} %254.02 +\newcommand{\pmPsc}{P_{\text{sm}}} +\newcommand{\pmorle}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$}}} %255.01 +\newcommand{\pmorgr}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth}}} %255.02 +\newcommand{\pmnoo}{\text{N}_0\text{O}} %255.03 +\newcommand{\pmorleq}{\mathrel{\ooalign{$\boldsymbol{<}$\cr\hidewidth$\boldsymbol{\cdot}$\cr\hidewidth${\raise-.75ex\hbox{\rotatebox[origin=c]{155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}\hspace{-.375ex}$}}} %255.04 +\newcommand{\pmorgrq}{\mathrel{\ooalign{$\boldsymbol{>}$\hidewidth\cr$\boldsymbol{\cdot}$\hidewidth\cr${\hspace{-.4ex}\raise-.75ex\hbox{\rotatebox[origin=c]{-155}{$\scalebox{1.1}{$\boldsymbol{-}$}$}}}$\hidewidth}}} %255.05 +\newcommand{\pmm}{\emph{M}} %256.01 +\newcommand{\pmn}{\emph{N}} %256.02, 263.02 +\newcommand{\pmtranc}[3]{(#1\pmast#2)\textbf{`}#3} %257.01 +\newcommand{\pmTranc}[2]{(#1\pmast#2)} %257.01 +\newcommand{\pmtrpot}[3]{#1_{#2#3}} %257.02 +\newcommand{\pma}{\emph{A}} %259.01 +\newcommand{\pmaw}{\emph{A}_{\emph{W}}} %259.02 +\newcommand{\pmwa}{\emph{W}_{\emph{A}}} %259.03 + +%Finite and Infinite Series and Ordinals +\newcommand{\pmintf}{P_{\text{fn}}} %260.01 +\newcommand{\pmserinf}{\text{Ser infin}} %261.01 +\newcommand{\pmwordinf}{\pmword\text{ infin}} %261.02 +\newcommand{\pmserfin}{\text{Ser fin}} %261.03 +\newcommand{\pmwordfin}{\pmword\text{ fin}} %261.04 +\newcommand{\pmwordind}{\pmword\text{ induct}} %261.04 +\newcommand{\pmordnfin}{\text{NO fin}} %262.01 +\newcommand{\pmordninf}{\text{NO infin}} %262.02 +\newcommand{\pmfinord}[1]{#1_r} %262.03 +\newcommand{\pmom}{\boldsymbol{\omega}} %263.01 +\newcommand{\pmpr}[1]{#1_{\text{pr}}} %264.01 +\newcommand{\pmomn}[1]{\pmom_{#1}} %265.01, 265.03, etc. +\newcommand{\pmalephn}[1]{\pmaleph_{#1}} %265.02, 265.04, etc. + +%Compact series, rational series, and continuous series +\newcommand{\pmcomp}{\mathrel{\text{comp}}} %270.01 +\newcommand{\pmComp}{\text{Comp}} +\newcommand{\pmmed}{\mathrel{\text{med}}} %271.01 +\newcommand{\pmMed}{\text{med}} +\newcommand{\pmsimp}[3]{\mathrel{#1_{#2#3}}} %272.01 +\newcommand{\pmsimps}[3]{{#1}_{#2}\textbf{`}{#3}} %273.02 +\newcommand{\pmSimp}[3]{({#1}{#2})_{#3}} %273.03 +\newcommand{\pmSimps}[2]{{#1}_{#2}} %273.04 +\newcommand{\pmrats}{\eta} %273.01 +\newcommand{\pmsfcls}[1]{#1_\pmrats} %274.01 +\newcommand{\pmsfclsm}[2]{#1_m\textbf{`}#2} %274.02 +\newcommand{\pmsfclsp}[2]{\pmbreve{#1}_P\textbf{`}{#2}} %274.03 +\newcommand{\pmsfclsmp}[1]{M_P\textbf{`}{#1}} %274.04 +\newcommand{\pmcser}{\theta} %275.01 +\newcommand{\pmcsercl}[1]{#1_\pmcser} %276.01 +\newcommand{\pmcsercls}[2]{{#1}_{#2}} %276.04 +\newcommand{\pmCsercls}[2]{{#1}_{\text{tl}}\textbf{`}{#2}} %264.05 +%Skipped some temprary definitions as repetitious + +%Quantity +%Generalization of Number +\newcommand{\pmu}{\textit{U}} %300.01 +\newcommand{\pmrnum}{\text{Rel num}} %300.02 +\newcommand{\pmrnumid}{\text{Rel num id}} %300.03 +\newcommand{\pmrpwr}[2]{#1^#2} %301.03 +\newcommand{\pmPrm}{\text{Prm}} %302.01 +\newcommand{\pmrprm}[4]{(#1,#2)\mathbin{\pmPrm_\tau}(#3,#4)} %302.02 +\newcommand{\pmprm}[4]{(#1,#2)\mathbin{\pmPrm}(#3,#4)} %302.03 +\newcommand{\pmhcf}[2]{\text{hcf}(#1,#2)} %302.04 +\newcommand{\pmHcf}{\text{hcf}} +\newcommand{\pmlcm}[2]{\text{lcm}(#1,#2)} %302.05 +\newcommand{\pmLcm}{\text{lcm}} +\newcommand{\pmrat}[2]{#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2} %303.01 +\newcommand{\pmqn}[1]{#1_q} %303.02 +\newcommand{\pmqnil}{\infty_q} %303.03 +\newcommand{\pmRat}{\text{Rat}} %303.04 +\newcommand{\pmRatdef}{\text{Rat def}} %303.05 +\newcommand{\pmqnle}[2]{#1 \mathrel{\boldsymbol{<}_r} #2} %304.01 +\newcommand{\pmQnle}{\boldsymbol{<}_r} +\newcommand{\pmqnLe}{H} %304.02 +\newcommand{\pmqnlez}{H'} %304.03 +\newcommand{\pmprodsr}[2]{#1 \times_s #2} %305.01 +\newcommand{\pmProdsr}{\times_s} +\newcommand{\pmsumsr}[2]{#1 +_s #2} %306.01 +\newcommand{\pmSumsr}{+_s} +\newcommand{\pmratn}{\text{Rat}_n} %307.01 +\newcommand{\pmratg}{\text{Rat}_g} %307.011 +\newcommand{\pmratnle}[2]{#1 \mathrel{\boldsymbol{<}_n} #2} %307.02 +\newcommand{\pmRatnle}{\boldsymbol{<}_n} +\newcommand{\pmatngr}[2]{#1 \mathrel{\boldsymbol{>}_n} #2} %307.021 +\newcommand{\pmRatngr}{\boldsymbol{>}_n} +\newcommand{\pmratgle}[2]{#1 \mathrel{\boldsymbol{<}_g} #2} %307.03 +\newcommand{\pmRatgle}{\boldsymbol{<}_g} +\newcommand{\pmratggr}[2]{#1 \mathrel{\boldsymbol{>}_g} #2} %307.031 +\newcommand{\pmRatggr}{\boldsymbol{>}_g} +\newcommand{\pmratnLe}{H_n} %307.04 +\newcommand{\pmratgLe}{H_g} %307.05 +\newcommand{\pmratssub}[2]{#1 \boldsymbol{-}_s #2} %308.01 +\newcommand{\pmsumgr}[2]{#1 +_g #2} %308.02 +\newcommand{\pmprodgr}[2]{#1 \times_g #2} %309.01 +\newcommand{\pmrenp}{\Theta} %310.01 +\newcommand{\pmrenpz}{\Theta'} %310.011 +\newcommand{\pmrenn}{\Theta_n} %310.02 +\newcommand{\pmrennz}{\Theta_n'} %310.021 +\newcommand{\pmreng}{\Theta_g} %310.03 +\newcommand{\pmconc}[1]{\text{concord}(#1)} %311.01 +\newcommand{\pmConc}{\text{concord}} +\newcommand{\pmrensumc}[2]{#1 +_p #2} %311.02 +\newcommand{\pmrensub}[2]{#1 -_p #2} %312.01 +\newcommand{\pmrensuma}[2]{#1 +_a #2} %312.02 +\newcommand{\pmrenproda}[2]{#1 \times_a #2} %313.01 +\newcommand{\pmrenrsum}[2]{#1 +_r #2} %314.01 +\newcommand{\pmrenrprod}[2]{#1 \times_r #2} %314.02 +\newcommand{\Male}{{\usefont{U}{mvs}{m}{n}\symbol{124}}} %from the Marvosym package +\newcommand{\pmrenr}{\mathop{\text{\Male}}} %314.03 +\newcommand{\pmrenrssum}[2]{#1 +_\sigma #2} %314.04 +\newcommand{\pmrenrsprod}[2]{#1 \times_\sigma #2} %313.05 + +%Vector Families +\newcommand{\pmcorr}[1]{\text{cr}\textbf{`}#1} %330.01 +\newcommand{\pmabel}{\text{Abel}} %330.02 +\newcommand{\pmvfm}[1]{\text{fm}\textbf{`}#1} %330.03 +\newcommand{\pmVfm}{\text{fm}} +\newcommand{\pmvfmcl}{\textit{FM}} %330.04 +\newcommand{\pmvffb}[1]{#1_\iota} %330.05 +\newcommand{\pmconx}[1]{\text{conx}\textbf{`}#1} %331.01 +\newcommand{\pmconxfm}{\textit{FM}\text{ conx}} %331.02 +\newcommand{\pmfrep}[2]{\text{rep}_#1\textbf{`}#2} %332.01 +\newcommand{\pmfopen}[1]{#1_\partial} %333.01 +\newcommand{\pmfopennid}[1]{#1_{\iota\partial}} %333.011 +\newcommand{\pmfmap}{\textit{FM}\text{ ap}} %333.02 +\newcommand{\pmfmapconx}{\textit{FM}\text{ ap conx}} %333.03 +\newcommand{\pmtrsp}[1]{\text{trs}\textbf{`}#1} %334.01 +\newcommand{\pmfmtrs}{\textit{FM}\text{ trs}} %334.02 +\newcommand{\pmfmconnex}{\textit{FM}\text{ connex}} %334.03 +\newcommand{\pmfmsr}{\textit{FM}\text{ sr}} %334.02 +\newcommand{\pmfmasym}{\textit{FM}\text{ asym}} %334.05 +\newcommand{\pminit}[1]{\text{init}\textbf{`}#1} %335.01 +\newcommand{\pmfminit}{\textit{FM}\text{ init}} %335.02 +\newcommand{\pmvr}[1]{\textit{V}_#1} %336.01 +\newcommand{\pmvrnid}[1]{\textit{U}_#1} %336.011 +\newcommand{\pmarvs}[1]{A_{#1}} %336.02 + +%Measurement +\newcommand{\pmfmsubm}{\textit{FM}\text{ subm}} %351.01 +\newcommand{\pmvrm}[2]{#1_#2} %352.01 +\newcommand{\pmvrmg}[2]{#1_{#2\iota}} %352.02 +\newcommand{\pmfmrt}{\textit{FM}\text{ rt}} %353.01 +\newcommand{\pmfmcx}{\textit{FM}\text{ cx}} %353.02 +\newcommand{\pmfmrtcx}{\textit{FM}\text{ rt cx}} %353.03 +\newcommand{\pmfmg}[1]{#1_g} %354.01 +\newcommand{\pmrtnet}[2]{\text{cx}_#1\textbf{`}#2} %354.02 +\newcommand{\pmfmgrp}{\textit{FM}\text{ grp}} %354.03 +\newcommand{\pmrems}[2]{#1_#2} %356.01 + +%Cyclic Families +\newcommand{\pmfmcycl}{\textit{FM}\text{ cycl}} %370.01 +\newcommand{\pmcycl}[2]{#1_#2} %370.02 +\newcommand{\pmcycli}[2]{#1_#2} %370.03 +\newcommand{\pmvser}[2]{#1_#2} %371.01 +\newcommand{\pmintsecvser}[2]{#1_#2} %372.01 +\newcommand{\pmprime}{\text{Prime}} %373.01 +\newcommand{\pmsfmid}[3]{#1_{#2#3}} %373.02 +\newcommand{\pmsmltid}[2]{(#1, #2)} %373.03 +\newcommand{\pmprrt}[3]{(#1 \rotatebox[origin=c]{10}{$\boldsymbol{/}$} #2)_{#3}} %375.01 + +\title{\texttt{principia.sty}\\ A \LaTeXe \space Package for Typesetting Whitehead and Russell's \textit{Principia Mathematica} (Version 2.0)} +\author{Landon D. C. Elkind \texttt{landon.elkind@wku.edu}} \date{\today} \begin{document} @@ -110,7 +682,7 @@ The \texttt{principia} package is designed for typesetting the Peanese notation In \textit{Principia Mathematica} some symbols occur with an argument and sometimes that same symbol occurs without an argument. For example, `$\pmsome{x}$' occurs in some formulas, but sometimes `$\pmSome$' occurs in the text when they talk about the symbol itself. \texttt{principia} is designed to accommodate these different occurrences of symbols. When a symbol is to occur without an argument, capitalize the first letter following the `\texttt{$\backslash$pm}' part of the command. E.g. \verb|\pmsome{x}| produces $\pmsome{x}$ and \verb|\pmSome| produces `$\pmSome$'. Note the former command requires an argument and the latter command does not. Not all commands in the \texttt{principia} package admit of such dual use because some symbols in \textit{Principia Mathematica} never occur without an argument or do not take an argument in the usual sense. For example, the propositional connectives do not take an `argument' in the way singular or plural descriptions do. -Version 1.3 of \texttt{principia} is adequate to typeset all notations throughout Sections A and B of \textit{Principia}'s Volume I and includes some minor fixes. See the package documentation for details. +Version 2.0 of \texttt{principia} is adequate to typeset all notations throughout Volumes I-III of \textit{Principia} and includes some minor fixes. Below are commands for Volume I. \texttt{principia}'s dependencies are \texttt{amsmath}, \texttt{amssymb}, \texttt{pifont}, and \texttt{graphicx}. Make sure to load these package by typing \texttt{$\backslash$usepackage\{graphicx\}}, etc., into the document preamble. @@ -125,7 +697,7 @@ To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in $\pmiddf$ & \verb|\pmiddf| & Identity for definitions (`$=$' differs in spacing). \\ $\pmdf$ & \verb|\pmdf| & Definition. Note the indentation. \\ $\pmdem$ & \verb|\pmdem| & This symbol begins a proof. \\ - $\pmsub{p}{q}$, $\pmsubb{p}{q}{r}{s}$, $\pmsubbb{p}{q}{r}{s}{t}{u}$, ... $\pmSub{\text{Add}}{p}{q}$, ... & \verb|\pmsub{p}{q}|, \verb|\pmsubb{p}{q}{r}{s}|, \verb|\pmsubbb{p}{q}| \par \hfill \verb|{r}{s}{t}{u}|, ... \verb|\pmSub{\text{Add}{p}{q}| & Substitution into theorems. Add `b's to the end of \verb|\pmsub| to increase the number of substitutions (up to four `b's). Each extra `b' adds two arguments. To substitute and specify the theorem as well, capitalize the `s' in \verb|\pmsub|. \\ + $\pmsub{p}{q}$, $\pmsubb{p}{q}{r}{s}$, $\pmsubbb{p}{q}{r}{s}{t}{u}$, ... $\pmSub{\text{Add}}{p}{q}$, ... & \verb|\pmsub{p}{q}|, \verb|\pmsubb{p}{q}{r}{s}|, \verb|\pmsubbb{p}{q}| \par \hfill \verb|{r}{s}{t}{u}|, ... \verb|\pmSub{\text{Add}}{p}{q}| & Substitution into theorems. Add `b's to the end of \verb|\pmsub| to increase the number of substitutions (up to four `b's). Each extra `b' adds two arguments. To substitute and specify the theorem as well, capitalize the `s' in \verb|\pmsub|. \\ $\pmdot$, $\pmdott$, $\pmdottt$, $\pmdotttt$, $\pmdottttt$, $\pmdotttttt$ & \verb|\pmdot|, \verb|\pmdott|, \verb|\pmdottt|, ... & Add `t's to the end of \verb|\pmdot| to increase the number of dots (up to six `t's). \\ $\pmand$, $\pmandd$, $\pmanddd$, $\pmandddd$, $\pmanddddd$, $\pmandddddd$ & \verb|\pmand|, \verb|\pmandd|, \verb|\pmanddd|, ...& Add `d's to the end of \verb|\pmand| command to increase the number of dots (up to six `d's). \\ $\pmor$ & \verb|\pmor| & Disjunction. \\ @@ -149,7 +721,105 @@ To load \texttt{principia}, type \texttt{$\backslash$usepackage\{principia\}} in \noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}} $=$, $\pmnid$ & \verb|=|, \verb|\pmnid| & Identity and its negation. \\ $\pmdsc{x}$ & \verb|\pmdsc{x}| & Definite description. \\ - $\pmexists$ & \verb|\pmexists| & Existence. + $\pmexists$ & \verb|\pmexists| & Existence. \\ + $\pmcls{z}{\psi z}$ & \verb|\pmcls{z}{\psi z}| & The class of $z$s satisfying $\psi$. \\ + $\pmcin$ & \verb|\pmcin| & The class membership symbol. \\ + $\pmClsn{n}$, $\pmCls$ & \verb|\pmClsn{n}|, \verb|\pmCls| & The class of classes of individuals. \\ + $\pmscl{\alpha}$, $\pmsCl$ & \verb|\pmscl{\alpha}|, \verb|\pmsCl| & The subclasses of a class $\alpha$. \\ + $\pmsrl{R}$, $\pmsRl$ & \verb|\pmsrl{R}|, \verb|\pmsRl| & The sub-relations of a relation $R$. \\ + $\pmcuni$ & \verb|\pmcuni| & The universal class. \\ + $\pmcnull$ & \verb|\pmcnull| & The null class. \\ + $\pmcexists$ & \verb|\pmcexists| & The existence of a class. \\ + $\pmccmp{\alpha}$ & \verb|\pmccmp{\alpha}| & This command requires one argument. \\ + $\pmcmin{\alpha}{\beta}$ & \verb|\pmcmin{\alpha}{\beta}| & This command requires two arguments. \\ + $\pmccup$ & \verb|\pmccup| & Class union. \\ + $\pmccap$ & \verb|\pmccap| & Class intersection. \\ + $\pmcinc$ & \verb|\pmcinc| & Class inclusion. \\ + $\pmrel{x}{y}{\phi(x,y)}$ & \verb|\pmrel{x}{y}{\phi(x,y)}| & The relation in extension given by $\phi$. \\ + $\pmrele{a}{x}{y}{R}{b}$ & \verb|\pmrele{a}{x}{y}{R}{b}| & This command requires five arguments. \\ + $\pmrelep{a}{R}{b}$ & \verb|\pmrelep{a}{R}{b}| & This command requires three arguments. \\ + $\pmrin$ & \verb|\pmrin| & The relation membership symbol. \\ + $\pmReln{n}$, $\pmRel$ & \verb|\pmReln{n}|, \verb|\pmRel| & The class of relations ($n$-many `of relations'). \\ + $\pmruni$ & \verb|\pmruni| & The universal relation. \\ + $\pmrnull$ & \verb|\pmrnull| & The null relation. \\ + $\pmrexists$ & \verb|\pmrexists| & This symbol prefixes relations. \\ + $\pmrcmp{R}$ & \verb|\pmrcmp{\alpha}| & This command requires one argument. \\ + $\pmrmin{R}{S}$ & \verb|\pmcmin{R}{S}| & This command requires two arguments. \\ + $\pmrcup$ & \verb|\pmrcup| & Relation union. \\ + $\pmrcap$ & \verb|\pmrcap| & Relation intersection. \\ + $\pmrinc$ & \verb|\pmrinc| & Relation inclusion. \\ + $\pmcrel{R}$ & \verb|\pmcrel{R}| & The converse of a relation. \\ + $\pmCnv$ & \verb|\pmCnv| & The command for `Cnv'. \\ + $\pmdscf{R}{x}$ & \verb|\pmdscf{R}{x}| & A singular descriptive function. \\ + $\pmdscff{R}{\beta}$ & \verb|\pmdscff{R}{\beta}| & A plural descriptive function. \\ + $\pmdscfff{R}{\kappa}$ & \verb|\pmdscfff{R}{\kappa}| & A plural descriptive function. \\ + $\pmdscfe{R}{\beta}$ & \verb|\pmdscfe{R}{\beta}| & The existence of a plural descriptive function. +\end{tabular} + +\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}} + $\pmdscfr{R}{x}$, `$\pmdscfR{R}$'& \verb|\pmdscfr{R}{x}|, \verb|\pmdscfR{R}| & The relation of $\pmdscfr{R}{\beta}$ to $\beta$. \\ + $\pmdm{R}$, $\pmDm$ & \verb|\pmdm{R}|, \verb|\pmDm| & The domain of a relation $R$. \\ + $\pmcdm{R}$, $\pmCdm$ & \verb|\pmcdm{R}|, \verb|\pmCdm| & The converse domain of a relation $R$. \\ + $\pmcmp{R}$, $\pmCmp$ & \verb|\pmcmp{R}|, \verb|\pmCmp| & The campus of a relation $R$. \\ + $\pmfld{R}$, $\pmFld$ & \verb|\pmfld{R}|, \verb|\pmFld| & The field of a relation $R$. \\ + $\pmrrf{R}{x}$, $\pmRrf{R}$ & \verb|\pmrrf{R}{x}|, \verb|\pmRrf{R}| & The referents of a given relation. \\ + $\pmrrl{R}{x}$, $\pmRrl{R}$ & \verb|\pmrrl{R}{x}|, \verb|\pmRrl{R}| & The relata of a given relation. \\ + $\pmsg{R}$, $\pmSg$ & \verb|\pmsg{R}|, \verb|\pmSg| & \\ + $\pmgs{R}$, $\pmGs$ & \verb|\pmgs{R}|, \verb|\pmGs| & \\ + $\pmrprd{R}{S}$, $\pmRprd$ & \verb|\pmrprd{R}{S}|, \verb|\pmrprd| & The relative product of $R$ and $S$. \\ + $\pmrprdn{R}{n}$ & \verb|\pmrprdn{R}{n}| & The $n$th relative product of $R$. \\ + $\pmrprdd{R}{S}$, $\pmRprdd$ & \verb|\pmrprdd{R}{S}|, \verb|\pmrprdd| & The double relative product of $R$ and $S$. \\ + $\pmrlcd{\alpha}{R}$ & \verb|\pmrld{\alpha}{R}| & The limitation of $R$'s domain to $\alpha$. \\ + $\pmrlcd{R}{\beta}$ & \verb|\pmrld{R}{\beta}| & The limitation of $R$'s converse domain to $\beta$. \\ + $\pmrlf{\alpha}{R}{\beta}$ & \verb|\pmrlf{\alpha}{R}{\beta}| & The limitation of $R$'s field to $\alpha$ and $\beta$, resp. \\ + $\pmrlF{P}{\alpha}$ & \verb|\pmrlF{\alpha}{R}{\beta}| & The limitation of $P$'s field to $\alpha$. \\ + $\pmrl{\alpha}{\beta}$ & \verb|\pmrl{\alpha}{\beta}| & The relation made of all $x$s in $\alpha$ and $y$s in $\beta$. \\ + $\pmop$ & \verb|\pmop| & The operation symbol. \\ + $\pmopc{\alpha}{y}$ & \verb|\pmopc{\alpha}{y}| & The relation of $x$s in $\alpha$ taken to $y$ by $\pmop$. \\ + $\pmccsum{\alpha}$ & \verb|\pmccsum{\alpha}| & The sum of a class of classes. \\ + $\pmccprd{\alpha}$ & \verb|\pmccprd{\alpha}| & The product of a class of classes. \\ + $\pmcrsum{\alpha}$ & \verb|\pmcrsum{\alpha}| & The sum of a class of relations. \\ + $\pmcrprd{\alpha}$ & \verb|\pmcrprd{\alpha}| & The product of a class of relations. \\ + $\pmrid$, $\pmrdiv$ & \verb|\pmrid|, \verb|\pmrdiv| & The relations of identity and diversity. \\ + $\pmcunit{x}$, $\pmcUnit$ & \verb|\pmcunit{x}|, \verb|\pmcUnit| & The unit class. \\ + $\pmcunits{\alpha}$ & \verb|\pmcunits{\alpha}| & The sum of unit classes of $\alpha$'s elements. \\ + $\pmrn{n}$ & \verb|\pmrn{n}| & The ordinal number $n$. \\ + $\pmdn{n}$ & \verb|\pmdn{n}| & The class of relations equal to an $n$-tuple. \\ + $\pmoc{x}{y}$ & \verb|\pmoc{x}{y}| & The ordinal number restricted to $R=(x,y)$. \\ + $\pmrt{x}$, $\pmrti{n}{x}$ & \verb|\pmrt{x}|, \verb|\pmrti{n}{x}| & The relative type of $x$ ($n$-many `type of's). \\ + $\pmrtc{n}{\alpha}$ & \verb|\pmrtc{n}{\alpha}| & The relative type of $\alpha$ ($n$-many `type of's). \\ + $\pmrtri{n}{R}$, $\pmrtrc{n}{R}$ & \verb|\pmrtri{n}{R}|, \verb|\pmrtrc{n}{R}| & The relative type of (with $n$-many `type of's) $R$ from individuals to individuals, or from classes to classes. `$nm$' can replace `$n$'. +\end{tabular} + +\noindent \begin{tabular}{@{}p{3cm} | p{5cm} | p{8.25cm}} + $\pmrtric{n}{m}{R}$, $\pmrtrci{n}{m}{R}$ & \verb|\pmrtric{n}{R}|, \verb|\pmrtrci{n}{R}| & The relative type of $R$ from individuals to classes, or from classes to individuals. \\ + $\pmrtdi{\alpha}{x}$, $\pmrtdri{R}{(x,y)}$ & \verb|\pmrtdi{\alpha}{x}|, \verb|\pmrtdri{R}{(x,y)}| & The result of determining that the members of $\alpha$ ($R$) belong to the relative type of $x$ (in the domain, and of $y$ in the converse domain). \\ + $\pmrtdc{\alpha}{x}$, $\pmrtdrc{R}{x,y}$ & \verb|\pmrtdc{\alpha}{x}|, \verb|\pmrtdrc{R}{x,y}| & The result of determining that the members of $\alpha$ ($R$) belong to the relative type of $\pmrt{x}$ (in the domain, and of $\pmrt{y}$ in the converse domain). \\ + $\pmrdc{\alpha}{\beta}$ & \verb|\pmrdc{\alpha}{\beta}| & The class of relations $R$ with domain contained in $\alpha$ and converse domain in $\beta$. \\ + $\pmoneone$, $\pmonemany$, $\pmmanyone$ & \verb|\pmoneone|, \verb|\pmonemany|, \verb|\pmmanyone| & The class of one-one, or one-many, or many-one, relations. Note \verb|\pmrdc| can be used here. \\ + $\pmsm$, $\pmsmbar$ & \verb|\pmsm|, \verb|\pmsmbar| & The similarity relation. \\ + $\pmselp{\kappa}$, $\pmSelp$ & \verb|\pmselp{\kappa}|, \verb|\pmSelp| & The $P$-selections from $\kappa$ \\ + $\pmsele{\kappa}$, $\pmSele$ & \verb|\pmsele{\kappa}|, \verb|\pmSele| & The $\pmcin$-selections from $\kappa$ \\ + $\pmself{\kappa}$, $\pmSelf$ & \verb|\pmself{\kappa}|, \verb|\pmSelf| & The $F$-selections from $\kappa$ \\ + $\pmexc$ & \verb|\pmexc| & The class of pairwise-disjoint classes. \\ + $\pmexcn$ & \verb|\pmexcn| & The class of pairwise-disjoint non-null classes. \\ + $\pmexcc{\gamma}$ & \verb|\pmexcc{\gamma}| & A class of mutually exclusive classes in $\gamma$. \\ + $\pmselc{P}{y}$ & \verb|\pmselc{P}{y}| & The class of couples $(y, \pmdscf{P}{y})$. \\ + $\pmmultc$ & \verb|\pmmultc| & The class of multipliable classes. \\ + $\pmmultr$ & \verb|\pmmultr| & The class of multipliable relations. \\ + $\pmmultax$ & \verb|\pmmultax| & The multiplicative axiom. \\ + $\pmanc{R}$, $\pmancc{R}$ & \verb|\pmanc{R}|, \verb|\pmancc{R}| & The ancestral and its converse. \\ + $\pmrst{R}$, $\pmrts{R}$ & \verb|\pmrst{R}|, \verb|\pmrts{R}| & The powers of the ancestral and its converse. \\ + $\pmmin{P}$, $\pmmax{P}$ & \verb|\pmmin{P}|, \verb|\pmmax{P}| & The minimum and maximum under $P$. \\ + $\pmpot{R}$, $\pmpotid{R}$ & \verb|\pmpot{R}|, \verb|\pmpotid{R}| & The products (strict and not) of an ancestral. \\ + $\pmpo{R}$ & \verb|\pmpo{R}| & The product of a class of ancestrals $R$. \\ + $\pmB$ & \verb|\pmB| & The relation of beginning under $P$. \\ + $\pmgen{P}$ & \verb|\pmgen{P}| & The generation of $P$. \\ + $\pmefr{P}{Q}$ & \verb|\pmefr{P}{Q}| & The equi-factor relation. \\ + $\pmipr{R}{x}$ & \verb|\pmipr{R}{x}| & The non-distinct posterity of $x$ under $R$. \\ + $\pmjpr{R}{x}$ & \verb|\pmjpr{R}{x}| & The distinct posterity of $x$ under $R$. \\ + $\pmfr{R}{x}$ & \verb|\pmfr{R}{x}| & The ancestry and posterity of $x$ under $R$. \\ + $\pmnc{\kappa}$, $\pmNc$ & \verb|\pmnc{\kappa}|, \verb|\pmNc| & The cardinal number of $\kappa$. \end{tabular} \end{document} \ No newline at end of file diff --git a/macros/latex/contrib/schulmathematik/README b/macros/latex/contrib/schulmathematik/README index 12614cf2c1..d585dab53a 100644 --- a/macros/latex/contrib/schulmathematik/README +++ b/macros/latex/contrib/schulmathematik/README @@ -2,8 +2,8 @@ The schulmathematik bundle provides LaTeX commands and document classes for German-speaking teachers of mathematics and physics. Package author: K. Wehr -Version: 1.3 -Date: 12 August 2022 +Version: 1.4 +Date: 13 March 2023 The schulmathematik bundle is subject to the LaTeX Project Public License, version 1.3 or later. diff --git a/macros/latex/contrib/schulmathematik/schulma-ab.cls b/macros/latex/contrib/schulmathematik/schulma-ab.cls index 61a6cb7597..67e62262e8 100644 --- a/macros/latex/contrib/schulmathematik/schulma-ab.cls +++ b/macros/latex/contrib/schulmathematik/schulma-ab.cls @@ -1,8 +1,8 @@ % schulmathematik bundle: document class schulma-ab -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \NeedsTeXFormat{LaTeX2e} -\ProvidesExplClass{schulma-ab}{2022-08-12}{1.3}{Dokumentenklasse fuer Arbeitsblaetter} +\ProvidesExplClass{schulma-ab}{2023-03-13}{1.4}{Dokumentenklasse fuer Arbeitsblaetter} \tl_new:N \g_schulma_ab_kurs_tl \tl_new:N \g_schulma_ab_thema_tl diff --git a/macros/latex/contrib/schulmathematik/schulma-gutachten.cls b/macros/latex/contrib/schulmathematik/schulma-gutachten.cls index 996f85bb4b..cc0ae472a0 100644 --- a/macros/latex/contrib/schulmathematik/schulma-gutachten.cls +++ b/macros/latex/contrib/schulmathematik/schulma-gutachten.cls @@ -1,8 +1,8 @@ % schulmathematik bundle: document class schulma-gutachten -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \NeedsTeXFormat{LaTeX2e} -\ProvidesExplClass{schulma-gutachten}{2022-08-12}{1.3}{Dokumentenklasse fuer Gutachten ueber schriftliche Abiturklausuren} +\ProvidesExplClass{schulma-gutachten}{2023-03-13}{1.4}{Dokumentenklasse fuer Gutachten ueber schriftliche Abiturklausuren} \bool_new:N \g_schulma_gutachten_bell_bool \bool_new:N \g_schulma_gutachten_oesterreich_bool diff --git a/macros/latex/contrib/schulmathematik/schulma-klausur.cls b/macros/latex/contrib/schulmathematik/schulma-klausur.cls index 96e6e023e4..87c1411af6 100644 --- a/macros/latex/contrib/schulmathematik/schulma-klausur.cls +++ b/macros/latex/contrib/schulmathematik/schulma-klausur.cls @@ -1,8 +1,8 @@ % schulmathematik bundle: document class schulma-klausur -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \NeedsTeXFormat{LaTeX2e} -\ProvidesExplClass{schulma-klausur}{2022-08-12}{1.3}{Dokumentenklasse fuer Klausuren} +\ProvidesExplClass{schulma-klausur}{2023-03-13}{1.4}{Dokumentenklasse fuer Klausuren} \RequirePackage {etoolbox} @@ -10,6 +10,7 @@ \str_new:N \g_schulma_klausur_titel_str \str_new:N \g_schulma_klausur_teiltitel_str \str_new:N \g_schulma_klausur_bearbeitungszeit_str +\str_new:N \g_schulma_klausur_formeldokumentseiten_str \tl_new:N \g_schulma_klausur_kurs_tl \tl_new:N \g_schulma_klausur_nummer_tl @@ -20,8 +21,8 @@ \bool_new:N \g_schulma_klausur_oesterreich_bool \bool_new:N \g_schulma_klausur_afuenfquer_bool \bool_new:N \g_schulma_klausur_schriftliche_lernkontrolle_bool -\bool_new:N \g_schulma_klausur_zwei_gruppen_bool \bool_new:N \g_schulma_klausur_gruppe_a_bool +\bool_new:N \g_schulma_klausur_gruppe_b_bool \bool_new:N \g_schulma_klausur_pqformel_bool \bool_new:N \g_schulma_klausur_differenzenquotient_bool \bool_new:N \g_schulma_klausur_differentialquotient_bool @@ -53,6 +54,14 @@ \frac {f(x)-f(x\sb{0})} {x-x\sb{0}} \] } +\msg_new:nnn {schulma-klausur} {Gruppe fehlt} + { + In~Zeile~ \msg_line_number: \c_space_tl + wird~der~Befehl~ \Gruppen \c_space_tl + verwendet.~Es~wurde~aber~keine~der~Klassenoptionen~GruppeA~und~GruppeB~ + gesetzt.~Ausgegeben~wird~der~Text~für~Gruppe~A. + } + \msg_new:nnn {schulma-klausur} {Aufgabennachricht} { Aufgabe~ \arabic {Aufgabe} :~ @@ -80,8 +89,6 @@ \tl_set:Nn \l_schulma_klausur_aufgabentitel_tl {Aufgabe} -\bool_gset_true:N \g_schulma_klausur_gruppe_a_bool - \DeclareOption {SLK} { \bool_gset_true:N \g_schulma_klausur_schriftliche_lernkontrolle_bool @@ -118,12 +125,13 @@ \DeclareOption {GruppeA} { - \bool_gset_true:N \g_schulma_klausur_zwei_gruppen_bool + \bool_gset_true:N \g_schulma_klausur_gruppe_a_bool + \bool_gset_false:N \g_schulma_klausur_gruppe_b_bool } \DeclareOption {GruppeB} { - \bool_gset_true:N \g_schulma_klausur_zwei_gruppen_bool + \bool_gset_true:N \g_schulma_klausur_gruppe_b_bool \bool_gset_false:N \g_schulma_klausur_gruppe_a_bool } @@ -155,6 +163,11 @@ \tl_gset:Nn \g_schulma_klausur_nummer_tl {#1} } +\NewDocumentCommand \Formeldokument {m} + { + \str_gset:Nn \g_schulma_klausur_formeldokumentseiten_str {#1} + } + \newcounter {Aufgabe} \newcounter {Teilaufgabe} [Aufgabe] @@ -214,6 +227,30 @@ \FarbeAufgabe } + \NewDocumentCommand \Gruppen {smm} + { + \bool_if:nTF \g_schulma_klausur_gruppe_a_bool {#2} + { + \bool_if:nTF \g_schulma_klausur_gruppe_b_bool {#3} + { + \IfBooleanTF {#1} + { + \fbox { \textbf{A} } \nobreakspace #2 + \c_space_tl + \fbox { \textbf{B} } \nobreakspace #3 + } + { + \par + \medskip + \fbox { \textbf {A} } \c_space_tl #2 + \par + \medskip + \fbox { \textbf {B} } \c_space_tl #3 + } + } + } + } + \resetcounteronoverlays {Teilaufgabe} \NewDocumentEnvironment {Teilaufgaben} { } @@ -302,6 +339,8 @@ \AtBeginDocument {\schulma_klausur_kopf:} + \RequirePackage {pdfpages} + \pretocmd {\enddocument} { \end {list} @@ -350,6 +389,13 @@ \c_schulma_klausur_differentialquotient_tl } } + \str_if_empty:NF \g_schulma_klausur_formeldokumentseiten_str + { + \includepdf [ pages = \g_schulma_klausur_formeldokumentseiten_str ] + { + M_Dokument_mit_mathematischen_Formeln + } + } }{}{} % pretocmd hat vier Argumente \AtEndDocument { \msg_note:nn {schulma-klausur} {Aufgabensumme} } @@ -382,6 +428,18 @@ \peek_catcode:NF \c_space_token {\c_space_tl} } + \NewDocumentCommand \Gruppen {smm} + { + \bool_if:NTF \g_schulma_klausur_gruppe_a_bool {#2} + { + \bool_if:NTF \g_schulma_klausur_gruppe_b_bool {#3} + { + \msg_warning:nn {schulma-klausur} {Gruppe fehlt} + #2 + } + } + } + \bool_if:NTF \g_schulma_klausur_afuenfquer_bool { \KOMAoption {paper} {landscape} @@ -515,11 +573,6 @@ \date { \printdate {#1} } % isodate-Befehl } -\NewDocumentCommand \Gruppen {mm} - { - \bool_if:NTF \g_schulma_klausur_gruppe_a_bool {#1} {#2} - } - \DeclareDocumentCommand \Aufgabentitel {m} { \tl_set:Nn \l_schulma_klausur_aufgabentitel_tl {#1} @@ -575,11 +628,8 @@ \g_schulma_klausur_nummer_tl } - \bool_if:NT \g_schulma_klausur_zwei_gruppen_bool - { - \c_space_tl - \bool_if:NTF \g_schulma_klausur_gruppe_a_bool {(A)} {(B)} - } + \bool_if:NT \g_schulma_klausur_gruppe_a_bool { \c_space_tl (A) } + \bool_if:NT \g_schulma_klausur_gruppe_b_bool { \c_space_tl (B) } \tl_if_empty:NF \g_schulma_klausur_untertitel_tl { diff --git a/macros/latex/contrib/schulmathematik/schulma-komp.cls b/macros/latex/contrib/schulmathematik/schulma-komp.cls index 2a811c79a9..994235e93a 100644 --- a/macros/latex/contrib/schulmathematik/schulma-komp.cls +++ b/macros/latex/contrib/schulmathematik/schulma-komp.cls @@ -1,8 +1,8 @@ % schulmathematik bundle: document class schulma-komp -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \NeedsTeXFormat{LaTeX2e} -\ProvidesExplClass{schulma-komp}{2022-08-12}{1.3}{Dokumentenklasse fuer Kompetenzlisten} +\ProvidesExplClass{schulma-komp}{2023-03-13}{1.4}{Dokumentenklasse fuer Kompetenzlisten} \ProcessOptions \relax diff --git a/macros/latex/contrib/schulmathematik/schulma-mdlprf.cls b/macros/latex/contrib/schulmathematik/schulma-mdlprf.cls index 3633352413..75e3a27fbc 100644 --- a/macros/latex/contrib/schulmathematik/schulma-mdlprf.cls +++ b/macros/latex/contrib/schulmathematik/schulma-mdlprf.cls @@ -1,8 +1,8 @@ % schulmathematik bundle: document class schulma-mdlprf -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \NeedsTeXFormat{LaTeX2e} -\ProvidesExplClass{schulma-mdlprf}{2022-08-12}{1.3}{Dokumentenklasse fuer muendliche Abiturpruefungen} +\ProvidesExplClass{schulma-mdlprf}{2023-03-13}{1.4}{Dokumentenklasse fuer muendliche Abiturpruefungen} \bool_new:N \g_schulma_mdlprf_oesterreich_bool \bool_new:N \g_schulma_mdlprf_pruefer_weiblich_bool diff --git a/macros/latex/contrib/schulmathematik/schulma-physik.sty b/macros/latex/contrib/schulmathematik/schulma-physik.sty index b3996d6cc2..975093e906 100644 --- a/macros/latex/contrib/schulmathematik/schulma-physik.sty +++ b/macros/latex/contrib/schulmathematik/schulma-physik.sty @@ -1,7 +1,16 @@ % schulmathematik bundle: package schulma-physik -% Version 1.3 -% 12. August 2022 -\ProvidesExplPackage{schulma-physik}{2022-08-12}{1.3}{Befehle für die Schulphysik} +% Version 1.4 +% 13. März 2023 +\ProvidesExplPackage{schulma-physik}{2023-03-13}{1.4}{Befehle für die Schulphysik} + +\newif \ifschulma@physik@circuitikz % keine expl3-Syntax möglich, da von circuits.ee.IEC nicht unterstützt + +\DeclareOption {circuitikz} + { + \schulma@physik@circuitikztrue + } + +\ProcessOptions \relax \RequirePackage {siunitx} \RequirePackage {tikz} @@ -21,7 +30,7 @@ \NewDocumentCommand \tqty {m m} { \ensuremath - { + { \group_begin: \textstyle \qty [ per-mode = fraction ] {#1} {#2} @@ -34,7 +43,7 @@ \NewDocumentCommand \tunit {m} { \ensuremath - { + { \group_begin: \textstyle \unit [ per-mode = fraction ] {#1} @@ -108,57 +117,154 @@ \dim_const:Nn \c_schulma_physik_messschieber_b_schieber_dim {17mm} \dim_const:Nn \c_schulma_physik_messschieber_l_fenster_dim {25mm} \dim_const:Nn \c_schulma_physik_messschieber_b_fenster_dim {1cm} +\dim_const:Nn \c_schulma_physik_messschieber_randabstand_dim {1mm} -\NewDocumentCommand \Messschieber {m} +\bool_new:N \l_schulma_physik_messschieber_cm_bool +\bool_new:N \l_schulma_physik_messschieber_inch_bool + +\msg_new:nnn {schulma-physik} {falsche Option} + { + #1~ist~keine~gültige~Option~für~einen~Messschieber. + } + +\NewDocumentCommand \Messschieber {om} { + \IfValueTF {#1} + { + \str_case:nnF {#1} + { + {cm} { + \bool_set_true:N \l_schulma_physik_messschieber_cm_bool + \bool_set_false:N \l_schulma_physik_messschieber_inch_bool + } + {inch} { + \bool_set_false:N \l_schulma_physik_messschieber_cm_bool + \bool_set_true:N \l_schulma_physik_messschieber_inch_bool + } + {cm+inch} { + \bool_set_true:N \l_schulma_physik_messschieber_cm_bool + \bool_set_true:N \l_schulma_physik_messschieber_inch_bool + } + } + { + \msg_warning:nnn {schulma-physik} {falsche Option} {#1} + } + } + { + \bool_set_true:N \l_schulma_physik_messschieber_cm_bool + \bool_set_false:N \l_schulma_physik_messschieber_inch_bool + } + \begin {tikzpicture} [ font = \sffamily ] % Hauptskala - \draw ( -1.6cm , -0.5 * \c_schulma_physik_messschieber_b_skala_dim + 0.5 * \c_schulma_physik_messschieber_b_fenster_dim ) - -- ++ ( \c_schulma_physik_messschieber_l_skala_dim , 0 ) node [ above~left ] { \small cm } + \draw ( -1.6cm , 0 ) + -- ++ ( \c_schulma_physik_messschieber_l_skala_dim , 0 ) + \bool_if:NT \l_schulma_physik_messschieber_cm_bool { node [ above~left ] { \small cm } } -- ++ ( 0 , \c_schulma_physik_messschieber_b_skala_dim ) + \bool_if:NT \l_schulma_physik_messschieber_inch_bool { node [ below~left ] { \small inch } } -- ++ ( - \c_schulma_physik_messschieber_l_skala_dim , 0) -- cycle ; - \int_step_inline:nnn {0} {120} + \bool_if:NT \l_schulma_physik_messschieber_cm_bool { - \int_set:Nn \l_tmpa_int { \int_mod:nn {##1} {10} } - \int_compare:nNnTF {\l_tmpa_int} = {0} + \int_step_inline:nnn {0} {120} { - \draw (##1*1mm,-1mm)--(##1*1mm,6mm) node [ left , xshift=2pt , yshift = -2pt ] - { \footnotesize \int_eval:n {##1/10} } ; + \int_set:Nn \l_tmpa_int { \int_mod:nn {##1} {10} } + \int_compare:nNnTF {\l_tmpa_int} = {0} + { + \draw ( ##1*1mm , \c_schulma_physik_messschieber_randabstand_dim ) -- ++ ( 0, 6.5mm ) + node [ left = -2pt , yshift = -2.5pt ] { \footnotesize \int_eval:n {##1/10} } ; + } + { + \int_compare:nNnTF {\l_tmpa_int} = {5} + { + \draw ( ##1*1mm , \c_schulma_physik_messschieber_randabstand_dim ) -- ++ ( 0 , 5.25mm ); + } + { + \draw ( ##1*1mm , \c_schulma_physik_messschieber_randabstand_dim ) -- ++ ( 0 , 4mm ); + } + } } + } + \bool_if:NT \l_schulma_physik_messschieber_inch_bool + { + \int_step_inline:nnn {0} {80} { - \int_compare:nNnTF {\l_tmpa_int} = {5} + \int_set:Nn \l_tmpa_int { \int_mod:nn {##1} {16} } + \int_compare:nNnTF {\l_tmpa_int} = {0} { - \draw (##1*1mm,-1mm)--(##1*1mm,4.5mm); + \draw ( ##1*0.0625in , \c_schulma_physik_messschieber_b_skala_dim - \c_schulma_physik_messschieber_randabstand_dim ) -- ++ (0,-6mm) + node [ left = -2pt , yshift = 3pt ] { \footnotesize \int_eval:n {##1/16} } ; } { - \draw (##1*1mm,-1mm)--(##1*1mm,3mm); + \int_compare:nNnTF {\l_tmpa_int} = {8} + { + \draw (##1*0.0625in , \c_schulma_physik_messschieber_b_skala_dim - \c_schulma_physik_messschieber_randabstand_dim ) -- ++ (0,-5mm) ; + } + { + \int_if_even:nTF {##1} + { + \draw ( ##1*0.0625in , \c_schulma_physik_messschieber_b_skala_dim - \c_schulma_physik_messschieber_randabstand_dim ) -- ++ (0,-4mm) ; + } + { + \draw ( ##1*0.0625in , \c_schulma_physik_messschieber_b_skala_dim - \c_schulma_physik_messschieber_randabstand_dim ) -- ++ (0,-3mm) ; + } + } } } } % Schieber \draw [ fill = white , even~odd~rule ] - ( #1cm - 0.5 * \c_schulma_physik_messschieber_l_schieber_dim + 4.5mm , - -0.5 * \c_schulma_physik_messschieber_b_schieber_dim + 0.5 * \c_schulma_physik_messschieber_b_fenster_dim ) + ( #2cm - 0.5 * \c_schulma_physik_messschieber_l_schieber_dim + 4.5mm , + -0.5 * \c_schulma_physik_messschieber_b_schieber_dim + 0.5 * \c_schulma_physik_messschieber_b_skala_dim ) rectangle ++ ( \c_schulma_physik_messschieber_l_schieber_dim , \c_schulma_physik_messschieber_b_schieber_dim ) { [rounded~corners = 0.5 * \c_schulma_physik_messschieber_b_fenster_dim ] - ( #1cm - 0.5 * \c_schulma_physik_messschieber_l_fenster_dim + 4.5mm , 0 ) + ( #2cm - 0.5 * \c_schulma_physik_messschieber_l_fenster_dim + 4.5mm , + 0.5 \c_schulma_physik_messschieber_b_skala_dim - 0.5 \c_schulma_physik_messschieber_b_fenster_dim ) rectangle ++ ( \c_schulma_physik_messschieber_l_fenster_dim , \c_schulma_physik_messschieber_b_fenster_dim ) } ; % Noniusskala - \int_step_inline:nnn {0} {10} + \bool_if:NT \l_schulma_physik_messschieber_cm_bool { - \int_set:Nn \l_tmpa_int { \int_mod:nn {##1} {10} } - \int_compare:nNnTF {\l_tmpa_int} = {0} + \int_step_inline:nnn {0} {10} { - \draw ( #1cm + ##1 * 0.9mm , 0 ) -- ( #1cm + ##1 * 0.9mm , -1.6mm ) ; + \int_set:Nn \l_tmpa_int { \int_mod:nn {##1} {10} } + \int_compare:nNnTF {\l_tmpa_int} = {0} + { + \draw ( #2cm + ##1 * 0.9mm , 0.5 \c_schulma_physik_messschieber_b_skala_dim - 0.5 \c_schulma_physik_messschieber_b_fenster_dim ) + -- ++ ( 0 , -1.6mm ) ; + } + { + \int_compare:nNnTF {\l_tmpa_int} = {5} + { + \draw ( #2cm + ##1 * 0.9mm , 0.5 \c_schulma_physik_messschieber_b_skala_dim - 0.5 \c_schulma_physik_messschieber_b_fenster_dim ) + -- ++ ( 0 , -1.3mm ) ; + } + { + \draw ( #2cm + ##1 * 0.9mm , 0.5 \c_schulma_physik_messschieber_b_skala_dim - 0.5 \c_schulma_physik_messschieber_b_fenster_dim ) + -- ++ ( 0 , -1mm ) ; + } + } } + } + \bool_if:NT \l_schulma_physik_messschieber_inch_bool + { + \int_step_inline:nnn {0} {8} { - \int_compare:nNnTF {\l_tmpa_int} = {5} + \int_set:Nn \l_tmpa_int { \int_mod:nn {##1} {4} } + \int_compare:nNnTF {\l_tmpa_int} = {0} { - \draw ( #1cm + ##1 * 0.9mm , 0 ) -- ( #1cm + ##1 * 0.9mm , -1.3mm ) ; + \draw ( #2cm + ##1 * 0.0546875in , 0.5 * \c_schulma_physik_messschieber_b_skala_dim + 0.5 * \c_schulma_physik_messschieber_b_fenster_dim ) + -- ++ ( 0 , 1.6mm ) ; } { - \draw ( #1cm + ##1 * 0.9mm , 0 ) -- ( #1cm + ##1 * 0.9mm , -1mm ) ; + \int_compare:nNnTF {\l_tmpa_int} = {2} + { + \draw ( #2cm + ##1 * 0.0546875in , 0.5 * \c_schulma_physik_messschieber_b_skala_dim + 0.5 * \c_schulma_physik_messschieber_b_fenster_dim ) + -- ++ ( 0 , 1.3mm ) ; + } + { + \draw ( #2cm + ##1 * 0.0546875in , 0.5 * \c_schulma_physik_messschieber_b_skala_dim + 0.5 * \c_schulma_physik_messschieber_b_fenster_dim ) + -- ++ ( 0 , 1mm ) ; + } } } } @@ -241,99 +347,185 @@ \end{tikzpicture} } -\ExplSyntaxOff +\dim_new:N \l_schulma_physik_kraftmesser_breite_skala_dim +\dim_set:Nn \l_schulma_physik_kraftmesser_breite_skala_dim {1cm} +\dim_new:N \l_schulma_physik_kraftmesser_laenge_skala_dim +\dim_set:Nn \l_schulma_physik_kraftmesser_laenge_skala_dim {9cm} +\dim_new:N \l_schulma_physik_kraftmesser_breite_huelse_dim +\dim_set:Nn \l_schulma_physik_kraftmesser_breite_huelse_dim {1.1cm} +\dim_new:N \l_schulma_physik_kraftmesser_laenge_huelse_dim +\dim_set:Nn \l_schulma_physik_kraftmesser_laenge_huelse_dim {3cm} +\dim_new:N \l_schulma_physik_kraftmesser_offset_huelse_dim +\dim_set:Nn \l_schulma_physik_kraftmesser_offset_huelse_dim {0.5pt} -\usetikzlibrary{circuits.ee.IEC} - -\pgfdeclareshape{doppelbuchse} - {% - \inheritsavedanchors[from=rectangle ee]% - \inheritanchor[from=rectangle ee]{center}% - \inheritanchor[from=rectangle ee]{north}% - \inheritanchor[from=rectangle ee]{south}% - \inheritanchor[from=rectangle ee]{east}% - \inheritanchor[from=rectangle ee]{west}% - \inheritanchor[from=rectangle ee]{north east}% - \inheritanchor[from=rectangle ee]{north west}% - \inheritanchor[from=rectangle ee]{south east}% - \inheritanchor[from=rectangle ee]{south west}% - \inheritanchor[from=rectangle ee]{input}% - \inheritanchor[from=rectangle ee]{output}% - \inheritanchorborder[from=rectangle ee]% - \backgroundpath{ - \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}% - \pgf@xa=\pgf@x \pgf@ya=\pgf@y - \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}}% - \pgf@xb=\pgf@x \pgf@yb=\pgf@y - \pgfutil@tempdima=\pgf@yb% - \advance\pgfutil@tempdima by -\pgf@ya% - \pgfutil@tempdima=0.5\pgfutil@tempdima% - \advance\pgf@xa by \pgfutil@tempdima% - \advance\pgf@xb by -\pgfutil@tempdima% - {\pgfpathcircle{\pgfqpoint{\pgf@xa}{0pt}}{\pgfutil@tempdima}} - {\pgfpathcircle{\pgfqpoint{\pgf@xb}{0pt}}{\pgfutil@tempdima}} - }% - } -\tikzset +\NewDocumentCommand \Kraftmesser {mm} { - bulb IEC graphic/.style= + \begin{tikzpicture} [ font = { \sffamily \bfseries \footnotesize } ] + % Haken + \draw [ very~thick ] ( 0 , -#1/#2 * \l_schulma_physik_kraftmesser_laenge_skala_dim ) -- ++ (0,-6mm) arc [ start~angle = 90 , end~angle = 380 , radius = 2mm ] ; + % ausziehbare Skala + \int_step_inline:nn { \fp_eval:n { round ( 10*#1/#2 + 1 ) } } { - circuit symbol lines, - circuit symbol size=width 1.9 height 1.9, - shape=generic circle IEC, - /pgf/generic circle IEC/before background= + \int_if_even:nTF {##1} { - \pgfpathmoveto{\pgfpointpolar{-135}{1pt}} - \pgfpathlineto{\pgfpointpolar{45}{1pt}} - \pgfpathmoveto{\pgfpointpolar{-45}{1pt}} - \pgfpathlineto{\pgfpointpolar{135}{1pt}} - \pgfusepathqstroke - }, - transform shape, - }, - capacitor IEC graphic/.style= - { - circuit symbol lines, - circuit symbol size=width 0.8 height 2.4, - transform shape, - shape=capacitor IEC, - }, - amperemeter graphic/.style= - { - circuit symbol open, - circuit symbol size=width 2 height 2, - transform shape, - shape=generic circle IEC, - info=center:{\sffamily A} - }, - voltmeter graphic/.style= - { - circuit symbol open, - circuit symbol size=width 2 height 2, - transform shape, - shape=generic circle IEC, - info=center:{\sffamily V} - }, - circuit declare symbol=messgeraet, - set messgeraet graphic= + \str_set:Nn \l_tmpa_str {red} + } + { + \str_set:Nn \l_tmpa_str {white} + } + + \draw [ fill = \l_tmpa_str ] + ( -0.5 * \l_schulma_physik_kraftmesser_breite_skala_dim , \fp_to_decimal:n { -#1/#2 + (##1-1)/10 } * \l_schulma_physik_kraftmesser_laenge_skala_dim ) + to [ out = -20 , in = 200 ] node [above] { \int_compare:nNnT {##1} = {1} {N} } + ++ ( \l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) + -- ++ ( 0, 0.1 * \l_schulma_physik_kraftmesser_laenge_skala_dim ) + to [ out = 200 , in = -20 ] + node [ below , inner~sep = 2pt ] { \num [ mode = text , reset-text-family = false , reset-text-series = false ] { \fp_to_decimal:n {##1/10*#2} } } + ++ ( -\l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) -- cycle ; + } + % Überstand der Skala + \draw [ fill = white ] ( -0.5 * \l_schulma_physik_kraftmesser_breite_skala_dim , -#1/#2 * \l_schulma_physik_kraftmesser_laenge_skala_dim - 1.5mm ) + to [ out = -20 , in = 200 ] ++ ( \l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) -- ++ (0,1.5mm) + to [ out = 200 , in = -20 ] ++ ( -\l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) -- cycle ; + % mittlere Striche + \begin {scope} + \clip ( 0.25 \l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) + rectangle ( 0.5 \l_schulma_physik_kraftmesser_breite_skala_dim , -#1/#2 * \l_schulma_physik_kraftmesser_laenge_skala_dim ) ; + \int_step_inline:nn { \fp_eval:n { ceil ( 100*#1/#2 ) } } { - circuit symbol open, - circuit symbol size=width 2 height 2, - transform shape, - shape=generic circle IEC, - /pgf/generic circle IEC/before background= + \int_compare:nNnT { \int_mod:nn {##1} {10} } = {5} { - \draw[annotation arrow,->] (0.58pt,-0.58pt)--(-0.58pt,0.58pt); + \draw ( -0.5 \l_schulma_physik_kraftmesser_breite_skala_dim , \fp_to_decimal:n { -#1/#2 + ##1/100 } * \l_schulma_physik_kraftmesser_laenge_skala_dim ) + to [ out = -20 , in = 200 ] ++ ( \l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) ; } - }, - circuit declare symbol=spannungsquelle, - set spannungsquelle graphic= + } + \end {scope} + % kleine Striche + \begin {scope} + \clip ( 0.35 \l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) + rectangle ( 0.5 \l_schulma_physik_kraftmesser_breite_skala_dim , -#1/#2 * \l_schulma_physik_kraftmesser_laenge_skala_dim ) ; + \int_step_inline:nn { \fp_eval:n { ceil ( 100*#1/#2 ) } } { - circuit symbol open, - circuit symbol size=width 2.4 height 0.5, - transform shape, - shape=doppelbuchse, - outer sep=0pt - }, + \int_compare:nNnT { \int_mod:nn {##1} {5} } > {0} + { + \draw ( -0.5 \l_schulma_physik_kraftmesser_breite_skala_dim , \fp_to_decimal:n { -#1/#2 + ##1/100 } * \l_schulma_physik_kraftmesser_laenge_skala_dim ) + to [ out = -20 , in = 200 ] ++ ( \l_schulma_physik_kraftmesser_breite_skala_dim , 0 ) ; + } + } + \end {scope} + % Hülse + \draw [ fill = cyan ] ( -0.5 * \l_schulma_physik_kraftmesser_breite_huelse_dim , \l_schulma_physik_kraftmesser_offset_huelse_dim ) + -- ++ ( 0 , \l_schulma_physik_kraftmesser_laenge_huelse_dim ) + to [ out = -20 , in = 200 ] ++ ( 0.5 * \l_schulma_physik_kraftmesser_breite_huelse_dim , 0 ) + to [ out = 20 , in = 160 ] ++ ( 0.5 * \l_schulma_physik_kraftmesser_breite_huelse_dim , 0 ) -- ++ ( 0 , -\l_schulma_physik_kraftmesser_laenge_huelse_dim ) + to [ out = 200 , in = -20 ] cycle ; + \draw [ fill = cyan!60 ] + ( -0.5 * \l_schulma_physik_kraftmesser_breite_huelse_dim , \l_schulma_physik_kraftmesser_laenge_huelse_dim + \l_schulma_physik_kraftmesser_offset_huelse_dim ) + to [ out = 20 , in = 160 ] ++ ( 0.5 \l_schulma_physik_kraftmesser_breite_huelse_dim , 0 ) + to [ out = 200 , in = -20 ] cycle ; + \end{tikzpicture} } + + +\ExplSyntaxOff + +\ifschulma@physik@circuitikz + \RequirePackage{circuitikz} + \ctikzset{resistor=european,inductor=american} +\else + \usetikzlibrary{circuits.ee.IEC} + + \pgfdeclareshape{doppelbuchse} + {% + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}% + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}}% + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfutil@tempdima=\pgf@yb% + \advance\pgfutil@tempdima by -\pgf@ya% + \pgfutil@tempdima=0.5\pgfutil@tempdima% + \advance\pgf@xa by \pgfutil@tempdima% + \advance\pgf@xb by -\pgfutil@tempdima% + {\pgfpathcircle{\pgfqpoint{\pgf@xa}{0pt}}{\pgfutil@tempdima}} + {\pgfpathcircle{\pgfqpoint{\pgf@xb}{0pt}}{\pgfutil@tempdima}} + }% + } + + \tikzset + { + bulb IEC graphic/.style= + { + circuit symbol lines, + circuit symbol size=width 1.9 height 1.9, + shape=generic circle IEC, + /pgf/generic circle IEC/before background= + { + \pgfpathmoveto{\pgfpointpolar{-135}{1pt}} + \pgfpathlineto{\pgfpointpolar{45}{1pt}} + \pgfpathmoveto{\pgfpointpolar{-45}{1pt}} + \pgfpathlineto{\pgfpointpolar{135}{1pt}} + \pgfusepathqstroke + }, + transform shape, + }, + capacitor IEC graphic/.style= + { + circuit symbol lines, + circuit symbol size=width 0.8 height 2.4, + transform shape, + shape=capacitor IEC, + }, + amperemeter graphic/.style= + { + circuit symbol open, + circuit symbol size=width 2 height 2, + transform shape, + shape=generic circle IEC, + info=center:{\sffamily A} + }, + voltmeter graphic/.style= + { + circuit symbol open, + circuit symbol size=width 2 height 2, + transform shape, + shape=generic circle IEC, + info=center:{\sffamily V} + }, + circuit declare symbol=messgeraet, + set messgeraet graphic= + { + circuit symbol open, + circuit symbol size=width 2 height 2, + transform shape, + shape=generic circle IEC, + /pgf/generic circle IEC/before background= + { + \draw[annotation arrow,->] (0.58pt,-0.58pt)--(-0.58pt,0.58pt); + } + }, + circuit declare symbol=spannungsquelle, + set spannungsquelle graphic= + { + circuit symbol open, + circuit symbol size=width 2.4 height 0.5, + transform shape, + shape=doppelbuchse, + outer sep=0pt + }, + } +\fi diff --git a/macros/latex/contrib/schulmathematik/schulma-praes.cls b/macros/latex/contrib/schulmathematik/schulma-praes.cls index eeac2ce3c9..718cfad904 100644 --- a/macros/latex/contrib/schulmathematik/schulma-praes.cls +++ b/macros/latex/contrib/schulmathematik/schulma-praes.cls @@ -1,8 +1,8 @@ % schulmathematik bundle: document class schulma-praes -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \NeedsTeXFormat{LaTeX2e} -\ProvidesExplClass{schulma-praes}{2022-08-12}{1.3}{Dokumentenklasse fuer Bildschirmpraesentationen} +\ProvidesExplClass{schulma-praes}{2023-03-13}{1.4}{Dokumentenklasse fuer Bildschirmpraesentationen} \bool_new:N \g_schulma_praes_seitenzahlen_bool \bool_new:N \g_schulma_praes_druck_bool diff --git a/macros/latex/contrib/schulmathematik/schulma.sty b/macros/latex/contrib/schulmathematik/schulma.sty index 6d25a7e445..b11db88d5e 100644 --- a/macros/latex/contrib/schulmathematik/schulma.sty +++ b/macros/latex/contrib/schulmathematik/schulma.sty @@ -1,13 +1,27 @@ % schulmathematik bundle: package schulma -% Version 1.3 -% 12. August 2022 -\ProvidesExplPackage{schulma}{2022-08-12}{1.3}{Befehle für die Schulmathematik} +% Version 1.4 +% 13. März 2023 +\ProvidesExplPackage{schulma}{2023-03-13}{1.4}{Befehle für die Schulmathematik} + +\bool_new:N \g_schulma_icomma_bool +\bool_gset_true:N \g_schulma_icomma_bool + +\DeclareOption {ohne-icomma} + { + \bool_gset_false:N \g_schulma_icomma_bool + } + +\ProcessOptions \relax \RequirePackage [intlimits] {mathtools} \RequirePackage {autoaligne} -\RequirePackage {icomma}% verträgt sich nicht mit libertinus-otf \RequirePackage {pgfplots} +\bool_if:NT \g_schulma_icomma_bool + { + \RequirePackage {icomma} + } + \ExplSyntaxOff \usetikzlibrary{shapes.misc} \ExplSyntaxOn diff --git a/macros/latex/contrib/schulmathematik/schulmathematik.pdf b/macros/latex/contrib/schulmathematik/schulmathematik.pdf index 949258def0..0ec8ca5e2c 100644 Binary files a/macros/latex/contrib/schulmathematik/schulmathematik.pdf and b/macros/latex/contrib/schulmathematik/schulmathematik.pdf differ diff --git a/macros/latex/contrib/schulmathematik/schulmathematik.tex b/macros/latex/contrib/schulmathematik/schulmathematik.tex index 73211a02db..b23f955927 100644 --- a/macros/latex/contrib/schulmathematik/schulmathematik.tex +++ b/macros/latex/contrib/schulmathematik/schulmathematik.tex @@ -1,15 +1,16 @@ % Manual of the schulmathematik bundle -% Version 1.3 -% 12. August 2022 +% Version 1.4 +% 13. März 2023 \documentclass{scrartcl} \usepackage[babelshorthands]{polyglossia} \usepackage{longtable} -\usepackage{schulma} +\usepackage[ohne-icomma]{schulma} \usepackage{schulma-physik} \usepackage{chemmacros} \usepackage{tasks} \usepackage{beamerarticle} \usepackage{unicode-math} +\usepackage{icomma} \makeatletter \let\example\@undefined @@ -28,6 +29,7 @@ pdfauthor={K. Wehr}]{hyperref} \setmainlanguage{german} +\pghyphenation{german}{Pa-ket-op-tion} \makeatletter % tasks: j überspringen @@ -332,6 +334,12 @@ \ExplSyntaxOff +\newcommand\PaketbeschreibungSchulma{\Paketbeschreibung{schulma} +Stellt Mathematikbefehle zur Verfügung wie in Abschnitt \ref{schulma} beschrieben.} + +\newcommand\PaketbeschreibungSchulmaPhysik{\Paketbeschreibung{schulma-physik} +Stellt Physikbefehle zur Verfügung wie in Abschnitt \ref{schulma-physik} beschrieben.} + \newcommand\LsgBeschreibungA{Innerhalb dieser Umgebung kann die Lösung einer Aufgabe oder Teilaufgabe eingegeben werden. Sie erscheint nur in der Musterlösung (d.\,h. bei Verwendung der Klassenoption \Option{Musterloesung}). @@ -359,7 +367,7 @@ Schulmathematik \medskip \large -Version 1.3 +Version 1.4 \medskip \normalsize @@ -400,6 +408,12 @@ Das Bündelpaket \emph{Schulmathematik} stellt zwei \LaTeX-Pakete und sechs Doku \label{schulma} Das Paket \Paket{schulma} wird von den Dokumentenklassen \Klasse{schulma-ab}, \Klasse{schulma-klausur}, \Klasse{schulma-praes} und \Klasse{schulma-mdlprf} geladen. Bei Verwendung einer anderen Dokumentenklasse kann es manuell mit \verb:\usepackage{schulma}: geladen werden. +\subsubsection*{Paketoptionen} +\begin{Liste} +\Optionsbeschreibung{ohne-icomma} +Wenn diese Option gewählt wird, wird das Paket \Paket{icomma} nicht von \Paket{schulma} geladen. Dies ist nötig, falls das Paket \Paket{unicode-math} verwendet wird. Bei Bedarf kann \Paket{icomma} dann manuell \emph{nach} \Paket{unicode-math} geladen werden; in diesem Fall tritt keine Inkompatibilität auf. +\end{Liste} + \subsubsection*{Geladene Pakete und Bibliotheken} \begin{Liste} \Paketbeschreibung{mathtools}[mit der Option \Option{intlimits}] @@ -506,6 +520,12 @@ Hierbei handelt es sich um einen TikZ-Knotentyp, der der Markierung von Punkten \label{schulma-physik} Das Paket \Paket{schulma-physik} wird von den Dokumentenklassen \Klasse{schulma-ab}, \Klasse{schulma-klausur}, \Klasse{schulma-praes} und \Klasse{schulma-mdlprf} geladen. Bei Verwendung einer anderen Dokumentenklasse kann es manuell mit \verb:\usepackage{schulma-physik}: geladen werden. +\subsubsection*{Paketoptionen} +\begin{Liste} +\Optionsbeschreibung{circuitikz} +Wenn diese Option gewählt wird, wird das Paket \Paket{circuitikz} anstelle der hierzu inkompatiblen TikZ-Bibliothek \Paket{circuits.ee.IEC} geladen. +\end{Liste} + \subsubsection*{Geladene Pakete und Bibliotheken} \begin{Liste} \Paketbeschreibung{siunitx}[mit den Optionen \Option{locale=DE} und \Option{uncertainty-mode=separate}]\label{siunitx}% @@ -520,22 +540,31 @@ Details zur Syntax und weitere Einstellungsmöglichkeiten sind der \Paket{siunit \Paketbeschreibung{tikz} Mit Hilfe dieses Pakets kann eine Vielfalt graphischer Darstellungen angefertigt werden. \Paketbeschreibung{circuits.ee.IEC} -Diese TikZ-Bibliothek ermöglicht die Darstellung von Schaltbildern. +Diese TikZ-Bibliothek ermöglicht die Darstellung von Schaltbildern. Wenn die Paketoption \Option{circuitikz} gewählt wird, wird sie nicht geladen. +\Paketbeschreibung{circuitikz}[mit den Optionen \Option{resistor=european} und \Option{inductor=american}] +Das Paket stellt eine Alternative zur vorgenannten TikZ-Bibliothek dar und wird nur geladen, wenn die Paketoption \Option{circuitikz} gewählt wird. \end{Liste} -\newpage \subsubsection*{Befehle} \begin{Liste} -\Befehlsbeschreibung{Messschieber}[\marg{Messwert}] -Gibt die Skala eines Messschiebers (auch Schieblehre genannt) mit dem angegebenen \meta{Messwert} aus. Der Messwert ist mit Dezimalpunkt in Zentimetern ohne die Einheit anzugeben. -\begin{example} +\Befehlsbeschreibung{Messschieber}[\Oarg{\choices{cm|inch|cm+inch}}\marg{Messwert}] +Gibt die Skala eines Messschiebers (auch Schieblehre genannt) mit dem angegebenen \meta{Messwert} aus. Der Messwert ist mit Dezimalpunkt in Zentimetern ohne die Einheit anzugeben. Das optionale Argument legt die verwendete Skala fest; wenn keines angegeben ist, wird eine Zentimeterskala ausgegeben. +\begin{example}[pre-output={\setlength\parindent{0pt}}] \Messschieber{4.73} + \Messschieber[inch]{4.73} + \Messschieber[cm+inch]{4.73} \end{example} \Befehlsbeschreibung{Messschraube}[\marg{Messwert}] Gibt die Skala einer Messschraube (auch Mikrometerschraube genannt) mit dem angegebenen \meta{Messwert} aus. Der Messwert ist mit Dezimalpunkt in Millimetern ohne die Einheit anzugeben. \begin{sidebyside} \Messschraube{6.18} \end{sidebyside} +\Befehlsbeschreibung{Kraftmesser}[\marg{Messwert}\marg{Maximalausschlag}] +Gibt einen Federkraftmesser mit dem angegebenen \meta{Messwert} (einzugeben mit Dezimalpunkt) und \meta{Maximalausschlag} (jeweils in Newton) aus. Der Maximalausschlag wird in 10 große und 100 kleine Skalenteile unterteilt. Er kann durch den Messwert auch moderat überschritten werden. +\begin{sidebyside} + \Kraftmesser{3.4}{10} + \Kraftmesser{2.4}{5} +\end{sidebyside} \Befehlsbeschreibung{Massstab}[\marg{Zahl 1}\marg{Einheit 1}\marg{Zahl 2}\marg{Einheit 2}] Dient zur Definition eines Maßstabs. Für Zahlenwerte und Einheiten gilt die Syntax des \Paket{siunitx}-Pakets. \begin{sidebyside} @@ -603,8 +632,9 @@ Gibt das auf drei gültige Stellen gerundete plancksche Wirkungsquantum aus. \subsubsection*{Schaltbilder} Schaltzeichen werden durch die TikZ-Bibliothek \Paket{circuits.ee.IEC} in Form von TikZ"=Knotentypen zur Verfügung gestellt. Für die Zwecke der Schulphysik ändert das Paket \Paket{schulma-physik} das Aussehen einiger Symbole leicht ab und fügt weitere hinzu. -Für die Schulphysik wichtige Schaltsymbole zeigt die folgende Übersicht. Weitere sind der \Paket{tikz}-Anleitung zu entnehmen.\footnote{Unabhängig von der TikZ-Bibliothek \Paket{circuits.ee.IEC} existiert zur Anfertigung von Schaltbildern das Paket \Paket{circuitikz}, dessen Eignung für die Schulphysik ich bisher nicht überprüft habe.} +Für die Schulphysik wichtige Schaltsymbole zeigt die folgende Übersicht. Weitere sind der \Paket{tikz}-Anleitung zu entnehmen. Mit \dag{} markierte Knotentypen wurden gegenüber der TikZ-Bibliothek \Paket{circuits.ee.IEC} modifiziert, mit \ddag{} markierte neu hinzugefügt. +\newpage \begin{longtable}{l>{\begin{minipage}[c][8mm][c]{3cm}}l<{\end{minipage}}l} \emph{Bauteil} & \emph{Symbol} & \emph{Knotentyp} \\ Glühlampe & \Schaltbeispiel{bulb} & \texttt{bulb}\textsuperscript{\dag} \\ @@ -640,6 +670,8 @@ Messgerät & \Schaltbeispiel{messgeraet} & \texttt{messgeraet}\textsuperscript{\ \end{tikzpicture} \end{example} +Falls auf den umfangreicheren Schaltzeichenbestand des Pakets \Paket{circuitikz} zurückgegriffen werden soll, ist die Paketoption \Option{circuitikz} zu wählen. Die oben genannten Ergänzungen stehen dann nicht zur Verfügung. + \subsubsection*{Nuklide} Zur Darstellung von Nukliden empfiehlt es sich, das Paket \Paket{chemmacros} zu laden. Da die Nuklidschreibweise eher selten benötigt wird, wird dieses Paket nicht automatisch geladen. @@ -669,10 +701,8 @@ Gibt die Musterlösung der Aufgabe aus, die innerhalb der Umgebung \Umgebung{Lsg \subsubsection*{Geladene Pakete} \begin{Liste} -\Paketbeschreibung{schulma} -Stellt Mathematikbefehle zur Verfügung wie in Abschnitt \ref{schulma} beschrieben. -\Paketbeschreibung{schulma-physik} -Stellt Physikbefehle zur Verfügung wie in Abschnitt \ref{schulma-physik} beschrieben. +\PaketbeschreibungSchulma +\PaketbeschreibungSchulmaPhysik \Paketbeschreibung{adjustbox}\label{adjustbox}% Dieses Paket erlaubt es, die vertikale Ausrichtung von Abbildungen zu beeinflussen. Indirekt wird hierdurch das Paket \Paket{graphicx} geladen, dass die Einbindung externer Bilddateien ermöglicht. \begin{example} @@ -686,7 +716,7 @@ Dieses Paket erlaubt es, die vertikale Ausrichtung von Abbildungen zu beeinfluss \end{adjustbox} \end{enumerate} \end{example} -\Paketbeschreibung{tasks} +\Paketbeschreibung{tasks}\label{tasks} Ermöglicht die Anzeige von Päckchenaufgaben. Die folgenden Voreinstellungen werden vorgenommen: \begin{itemize} @@ -917,16 +947,26 @@ Erzeugt eine Bildschirmpräsentation mit der Musterlösung der Klausur, die inne \end{Liste} \subsubsection*{Geladene Pakete} \begin{Liste} +\PaketbeschreibungSchulma +\PaketbeschreibungSchulmaPhysik +\Paketbeschreibung{adjustbox} +\emph{Siehe S. \pageref{adjustbox}.} +\Paketbeschreibung{tasks} +\emph{Siehe S. \pageref{tasks}.} \Paketbeschreibung{geometry}[mit den Optionen \Option{hmargin=2.5cm} und \Option{top=2.7cm}] Paket zur Einstellung der Seitenränder. Der linke und rechte Rand werden auf \qty{2,5}{cm} festgelegt. Der obere Rand wird auf \qty{2,7}{cm} vergrößert, damit er Platz für das Namensfeld bietet. Bei Verwendung der Klassenoption \Option{A5quer} wird zusätzlich die Option \Option{bottom=3cm} gesetzt, um genügend Platz für die Seitenzahl zu schaffen. \Paketbeschreibung{scrlayer-scrpage} Dieses Paket wird für die Voreinstellung des Seitenkopfes und -fußes benötigt. Es kann auch zur freien Gestaltung von Kopf- und Fußzeilen genutzt werden. Details sind der KOMA-Script-Anleitung \texttt{scrguide} zu entnehmen. +\Paketbeschreibung{pdfpages} +Das Paket ermöglicht die Einbindung externer PDF-Dateien. Es wird für den Befehl \Befehl{Formeldokument} (siehe S. \pageref{formeldokument}) benötigt. \Paketbeschreibung{comment} Mit Hilfe dieses Pakets werden die Lösungen der Aufgaben, die innerhalb der Umgebung \Umgebung{Lsg} (s.\,u.) eingegeben wurden, in der Klausur ausgeblendet. \Paketbeschreibung{beamerarticle} Dieses Paket sorgt dafür, das spezifische Befehle für Bildschirmpräsentationen wie Folienspezifikationen oder die \Umgebung{frame}-Umgebung, die in den Klausuraufgaben zwecks Aufbereitung für die Musterlösung verwendet werden können, bei der Erstellung der Klausur ignoriert werden. +\Paketbeschreibung{babel}[mit der Option \Option{ngerman}] +\emph{Siehe S. \pageref{babel}.} \Paketbeschreibung{datetime2}[mit der Option \Option{useregional=text}] Gibt das Datum der Klausur in der Langform »1. März 2021« aus. Österreichische Benutzer verwenden die Klassenoption \Option{AT}, um »Jänner« statt »Januar« zu erhalten. \end{Liste} @@ -950,6 +990,8 @@ Legt die Bearbeitungszeit der Klausur oder des Klausurteils in Minuten fest. Legt die in der Klausur oder im Klausurteil erlaubten Hilfsmittel (z.\,B. Taschenrechner, Formelsammlung) fest. \Befehlsbeschreibung{Loesungsdatum}[\marg{Datum}] Legt das Datum der Besprechung der Musterlösung fest, das bei Verwendung der Klassenoption \Option{Musterloesung} auf der Titelseite der Bildschirmpräsentation erscheint. Das Eingabeformat ist \texttt{JJJJ-MM-TT}. +\Befehlsbeschreibung{Formeldokument}[\marg{Seitenzahlen}]\label{formeldokument}% +Bindet die gewählten Seiten aus dem »Dokument mit mathematischen Formeln« des IQB mit Hilfe des Pakets \Paket{pdfpages} am Ende der Klausur ein. Das Dokument muss sich unter dem Namen \texttt{M\_Dokument\_mit\_mathematischen\_Formeln.pdf} im Suchbaum befinden.\footnote{Die PDF-Datei mit dem Formeldokument ist erhältlich unter \url{https://www.iqb.hu-berlin.de/abitur/abitur/dokumente/mathematik/}.} \end{Liste} \subsubsection*{Befehle und Umgebungen im Dokumentenkörper} \begin{Liste} @@ -977,8 +1019,8 @@ Dient zur manuellen Umschaltung auf die Textfarbe der Lösung. Der \meta{Teil der Aufgabe}, der Argument dieses Befehls ist, erscheint nur in der Klausur, aber nicht in der Musterlösung. Dies ist nützlich für ergänzende Bearbeitungshinweise, die in der Musterlösung nicht benötigt werden, sowie für Abbildungen, die in der Musterlösung anders dargestellt werden sollen. \Befehlsbeschreibung{NurLoesung}[\marg{Teil der Aufgabe}] Der \meta{Teil der Aufgabe}, der Argument dieses Befehls ist, erscheint nur in der Musterlösung, aber nicht in der Klausur. Dies ist beispielsweise nützlich, wenn für die Musterlösung Abbildungen anders skaliert werden müssen. Im Gegensatz zur Umgebung \Umgebung{Lsg} beginnt dieser Befehl keinen neuen Absatz und schaltet auch nicht die Farbe um. -\Befehlsbeschreibung{Gruppen}[\marg{Text für Gruppe A}\marg{Text für Gruppe B}] -Mit diesem Befehl können unterschiedliche Aufgabentexte für zwei Klausurgruppen A und B eingegeben werden. Welcher davon in der Klausur erscheint, hängt davon ab, ob die Klassenoption \Option{GruppeA} oder die Klassenoption \Option{GruppeB} verwendet wird. Wird keine dieser Optionen gesetzt, wird der Text für Gruppe A ausgegeben. +\Befehlsbeschreibung{Gruppen}[\sarg\marg{Text für Gruppe A}\marg{Text für Gruppe B}] +Mit diesem Befehl können unterschiedliche Aufgabentexte für zwei Klausurgruppen A und B eingegeben werden. Welcher davon in der Klausur erscheint, hängt davon ab, ob die Klassenoption \Option{GruppeA} oder die Klassenoption \Option{GruppeB} verwendet wird. Wird keine dieser Optionen gesetzt, wird in der Klausur der Text für Gruppe A ausgegeben, in der Musterlösung der Text für beide Gruppen, getrennt durch einen Absatz. Mit der Sternversion des Befehls wird in der Musterlösung zwischen den Texten beider Gruppen kein neuer Absatz begonnen. \Befehlsbeschreibung{Notenspiegel}[\marg{kommaseparierte Notenliste}] Erstellt in der Musterlösung eine eigene Folie mit dem Notenspiegel mit Schulnoten von 1 bis 6. Die \meta{kommaseparierte Notenliste} kann gänzlich unsortiert sein, z.\,B. \texttt{3,2,5,2,2,1,4,6,4,3}. \Befehlsbeschreibung{Notenpunktspiegel}[\marg{kommaseparierte Notenliste}] @@ -1091,10 +1133,8 @@ Diese Option ist anzugeben, falls der Prüfer weiblich ist. Dies wirkt sich auf \emph{Siehe S. \pageref{babel}.} \Paketbeschreibung{datetime2}[mit den Optionen \Option{useregional=text} und \Option{showseconds=false}] Dieses Paket dient zur Formatierung des Datums und der Uhrzeit. Das Datum wird in der Langform »1. März 2021« ausgegeben, die Uhrzeit in der Form »15:30 Uhr«. -\Paketbeschreibung{schulma} -Stellt Mathematikbefehle zur Verfügung wie in Abschnitt \ref{schulma} beschrieben. -\Paketbeschreibung{schulma-physik} -Stellt Physikbefehle zur Verfügung wie in Abschnitt \ref{schulma-physik} beschrieben. +\PaketbeschreibungSchulma +\PaketbeschreibungSchulmaPhysik \end{Liste} \subsubsection*{Befehle in der Präambel} \begin{Liste} @@ -1160,12 +1200,20 @@ Bei Verwendung der Klassenoption \Option{A5quer} wird jetzt auch tatsächlich da Für die Musterlösung wird bei Verwendung der Umgebung \Umgebung{Teilaufgaben} innerhalb der Umgebung \Umgebung{Lsg} nur noch die Aufgabenmarke in Aufgabenfarbe angezeigt, der folgende Text dagegen in Lösungsfarbe. \item \textbf{\Klasse{schulma-gutachten}:} Anpassung an die Version 3 des \Paket{siunitx}-Pakets \end{itemize} -\item[1.3] \today +\item[1.3] 12. August 2022 \begin{itemize} \item \textbf{\Paket{schulma-physik}:} globale Einstellung der \Paket{siunitx}-Option \Option{uncertainty-mode=""separate}; Verwendung eines aufrechten $\symup{\pi}$ in der Ausgabe des Befehls \Befehl{MFK}, wenn das Paket \Paket{unicode-math} geladen ist; Aktualisierung des Hinweises zur Nuklidschreibweise mit dem Paket \Paket{chemmacros} \item \textbf{\Klasse{schulma-ab}:} Anpassung der vertikalen Abstände innerhalb der \verb:tasks:"=Umgebung an die Umgebung \Umgebung{Teilaufgaben} \item \textbf{\Klasse{schulma-klausur}:} Anpassung der vertikalen Abstände innerhalb der \verb:tasks:-Umgebung an die Umgebung \Umgebung{Teilaufgaben}; neues optionales Argument des Befehls \Befehl{Aufgabe} für die Bearbeitungszeit; Ausgabe von Informationen zu den Aufgaben auf dem Terminal \end{itemize} +\item[1.4] \today +\begin{itemize} +\item \textbf{\Paket{schulma}:} neue Paketoption \Option{ohne-icomma} +\item \textbf{\Paket{schulma-physik}:} neue Paketoption \Option{circuitikz}; neue Optionen \Option{cm}, \Option{inch} und \Option{cm+inch} für den Befehl \Befehl{Messschieber}, um eine Zollskala alternativ oder zusätzlich zur Zentimeterskala auszugeben; neuer Befehl \Befehl{Kraftmesser} +\item \textbf{\Klasse{schulma-klausur}:} neuer Befehl \Befehl{Formeldokument} + +Das Verhalten des Befehls \Befehl{Gruppen} wurde für den Fall geändert, dass keine der Klassenoptionen \Option{GruppeA} und \Option{GruppeB} gewählt wurde: In der Musterlösung werden die Texte für beide Gruppen ausgegeben; in der Klausur wird weiterhin der Text für Gruppe A abgedruckt, aber eine Warnung ausgegeben. Damit verbunden ist die Einführung einer Sternversion des Befehls \Befehl{Gruppen}. +\end{itemize} \end{description} \end{document} diff --git a/support/autoconf/.DS_Store b/support/autoconf/.DS_Store deleted file mode 100644 index 5008ddfcf5..0000000000 Binary files a/support/autoconf/.DS_Store and /dev/null differ diff --git a/systems/mac/textures/.DS_Store b/systems/mac/textures/.DS_Store deleted file mode 100644 index 5008ddfcf5..0000000000 Binary files a/systems/mac/textures/.DS_Store and /dev/null differ diff --git a/timestamp b/timestamp index 95391d7c41..5fd31df50d 100644 --- a/timestamp +++ b/timestamp @@ -2,4 +2,4 @@ # The source CTAN of this site's material: dante.ctan.org # The year-month-day-hour-minute of this site's material: -2023-03-13-02-02 +2023-03-14-02-02 -- cgit v1.2.3