diff options
Diffstat (limited to 'Master')
| -rw-r--r-- | Master/texmf-dist/doc/latex/rec-thy/README | 4 | ||||
| -rw-r--r-- | Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf | bin | 109580 -> 115691 bytes | |||
| -rw-r--r-- | Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex | 57 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty | 2064 |
4 files changed, 1115 insertions, 1010 deletions
diff --git a/Master/texmf-dist/doc/latex/rec-thy/README b/Master/texmf-dist/doc/latex/rec-thy/README index cd5256a4b5a..a7c9a3aa049 100644 --- a/Master/texmf-dist/doc/latex/rec-thy/README +++ b/Master/texmf-dist/doc/latex/rec-thy/README @@ -25,4 +25,6 @@ Github URL: https://github.com/TruePath/Recursion-Theory-Latex-Package 09/26/2017 - v2.0 - Added support for introducing requirements, the subfunction relation and probably other undocumented features 10/05/2017 - v2.1 - Fixed way packages are required so rec-thy can be loaded in a flexible order. Also fixed one or two bugs. 11/14/2017 - v2.2 - Fixed \Tdeg so it works different on symbols and vars and added \Tdegof and \Tvarof. Added \subfunneq and \supfunneq. -12/31/2017 - v2.3 - Added proof cases helper. Also fixed the issue with \ncequiv in XeLaTeX
\ No newline at end of file +12/31/2017 - v2.3 - Added proof cases helper. Also fixed the issue with \ncequiv in XeLaTeX +1/17/2018 - v2.4 - Added priority tree helpers. Should be more robust with respect to existing definitions of common commands +2/14/2018 - v2.4.1 - Moved to using xparse to define the case macros and several other macros to allow nested brackets for optional arguments. Added the recf command and cleaned up some option processing. Also worked around the mathtools/unicode-math font bug described here: https://tex.stackexchange.com/questions/335164/incompatibility-with-mathtools-and-unicode-math-in-xelatex/335177
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf Binary files differindex 0ccd3abacc1..8e895c3d9cf 100644 --- a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf +++ b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.pdf diff --git a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex index 9c5c1dd6936..f53eb41c594 100644 --- a/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex +++ b/Master/texmf-dist/doc/latex/rec-thy/rec-thy.tex @@ -15,12 +15,13 @@ % \DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it} % \DeclareMathAlphabet{\mathbrush}{T1}{pbsi}{xl}{n} \usepackage{mathspec} - +\usepackage{comment} \usepackage{unicode-math} \unimathsetup{math-style=TeX,bold-style=TeX,nabla=upright,partial=italic} \setmathfont{xits-math.otf} \setmathfont{xits-math.otf}[range={cal,bfcal},StylisticSet=1] + \usepackage{hyperxmp} \usepackage[unicode,psdextra,pdfusetitle]{hyperref} \hypersetup{% @@ -83,7 +84,7 @@ \title{The rec-thy Package} \author{Peter M. Gerdes (gerdes@invariant.org)} -\date{\today: Version 2.3} +\date{\today: Version 2.4} \begin{document} @@ -97,6 +98,8 @@ \noindent The rec-thy package is designed to help mathematicians publishing papers in the area of recursion theory (aka Computability Theory) easily use standard notation. This includes easy commands to denote Turing reductions, Turing functionals, \ce sets, stagewise computations, forcing and syntactic classes. \end{abstract} + + \section{Introduction} This package aims to provide a useful set of \LaTeX { }macros covering basic computability theory notation. Given the variation in usage in several areas this package had to pick particular notational conventions. The package author would like to encourage uniformity in these conventions but has included a multitude of package options to allow individual authors to choose alternative conventions or exclude that part of the package. Some effort has been made to align the semantic content of documents created with this package with the \LaTeX { }source. The author hopes that eventually this package may be incorporated into some larger package for typesetting papers in mathematical logic. @@ -114,14 +117,40 @@ A few general conventions are usually followed in the commands. Whenever an ope Objects that have a natural stagewise approximation generally admit an optional argument in brackets to specify a stage. For instance \( \verb=\REset[s]{e}= \) yields \( \REset[s]{e} \). An optional argument in parenthesis is used for relativization. For instance \( \verb=\REset(X){e}= \) produces \( \REset(X){e} \). A notable exception to this rule are the formula classes where square brackets are used to indicate an oracle to be placed in the superscript, e.g., \( \verb=\pizn[X]{2}= \) yields \( \pizn[X]{2} \), so as not to generate confusion with the alternative notion \( \pizn{2}(X) \). Also a lowercase first letter in a formula class indicates the lightface version while a capital first letter indicates the boldface version. -Unless indicated otherwise all macros are to be used inside math mode. Indented commands indicate an alias for the command on the line above -\( \mathfrak{u} \) +Unless indicated otherwise all macros are to be used inside math mode. Indented commands indicate an alias for the command on the line above. + + +\subsection{Priority Trees} + +Note the commands in this section double as suggestions for standardized notation. + +\begin{xtabular}{l | l | l}\toprule + \verb=\PriorityTree= & \( \PriorityTree \) & Truepath. \\ \midrule + \verb=\tpath= & \( \tpath \) & Truepath. \\ \midrule + \verb=\tpath[s]= & \( \tpath[s] \) & Approximate Truepath. \\ \midrule + \verb=\xi \leftof \eta = & \( \xi \leftof \eta \) & The left of relation for priority tree arguments \\ \midrule + \verb=\Astages{\xi}= & \( \Astages{\xi} \) & Set of stages at which \( \xi \) is active. \\ \midrule + \verb=\Vstages{\xi}= & \( \Vstages{\xi} \) & Stages where \( \xi \subfun \tpath[s] \) even if links skip \( \xi \). \\ \midrule + \verb=\reqof{\xi}= & \( \reqof{\xi} \) & Requirement implemented by a node \( \xi \). \\ \midrule + \verb=\ball[X]{y}{s}= & \( \ball[X]{y}{s} \) & Location of ball \( y\) (headed to \( X \)) at \( s \)\\ \midrule + \verb=\ball{y}{s}= & \( \ball{y}{s} \) & Location of ball \( y\) at \( s \)\\ \bottomrule + \end{xtabular} \\ + + \subsection{Computations} -To disable these commands pass the option \verb=nocomputations=. \\ +To disable these commands pass the option \verb=nocomputations=. \\ To specify an alternative symbol for either recursive functionals or recursive functions pass \verb!recfnlsym=macroname! or \verb!recfsym=macroname!. For instance, to use \( \psi \) for recursive functions and \( \Psi \) for recursive functionals pass the options \verb!recfsym=psi, recfnlsym=Psi!. \begin{xtabular}{l | l | l}\toprule \verb=\murec{x}{f(x)>1}= & \( \murec{x}{f(x)>1} \) & Least \( x \) satisfying condition. \\ \midrule - \verb=\recfnl{e}{Y}{x}= & \( \recfnl{e}{Y}{x} \) &\multirow{4}{*}{Computable functions/functionals} \\[6pt] + \verb=\recf{e}= & \( \recf{e} \) &\multirow{4}{*}{Computable functions} \\[6pt] + \verb=\recf[s]{e}= & \( \recf[s]{e} \) & \\[6pt] + \verb=\recf{e}(x)= & \( \recf{e}(x) \) & \\[6pt] + \verb=\recf[s]{e}(x)= & \( \recf[s]{e}(x) \) & \\[6pt] + \verb=\recf{e}[Y]= & \( \recf{e}[Y] \) & \\[6pt] + \verb=\recf[s]{e}[Y]= & \( \recf[s]{e}[Y] \) & \\[6pt] + \verb=\recf{e}[Y](x)= & \( \recf[s]{e}[Y](x) \) & \\[6pt] + \verb=\recf[s]{e}[Y](x)= & \( \recf[s]{e}[Y](x) \) & \\[6pt] + \verb=\recfnl{e}{Y}{x}= & \( \recfnl{e}{Y}{x} \) &\multirow{4}{*}{Computable functionals} \\[6pt] \verb=\recfnl[s]{e}{Y}{x}= & \( \recfnl[s]{e}{Y}{x} \) & \\[6pt] \verb=\recfnl{e}{Y}{}= & \( \recfnl{e}{Y}{} \) & \\[6pt] \verb=\recfnl{e}{}{x}= & \( \recfnl{e}{}{x} \) & \\[6pt] @@ -146,6 +175,7 @@ To disable these commands pass the option \verb=nocomputations=. \\ \bottomrule \end{xtabular} \\ + \subsection{Degrees} To disable these commands pass the option \verb=nodegrees=. \\ @@ -266,6 +296,8 @@ To disable these commands pass the option \verb=nomath=. \\ \subsection{Set Notation} To disable these commands pass the option \verb=nosets=.\\ +Note that \verb=\Cross= and \verb=\cross= overwrite the existing commands saving them as \verb=\CrossOrig= and \verb=\crossOrig= respectively as these commands have varying meanings between different font packages. However, the other commands avoid overwriting existing commands with that name + \begin{tabular}{l | l | l}\toprule \verb=\set{(x,y)}{x > y}= & \( \set{(x,y)}{x > y} \) & \multirow{2}{*}{Set notation} \\[6pt] \verb=\set{(x,y)}{}= & \( \set{(x,y)}{} \) & \\ \midrule @@ -280,9 +312,8 @@ To disable these commands pass the option \verb=nosets=.\\ \verb=\powset{\omega}= & \( \powset{\omega} \) & Powerset \\ \midrule \verb=\eset= & \( \eset \) & Emptyset abbreviation\\ \midrule \verb=x \nin A= & \( x \nin A \) & not an element\\ \midrule - \verb=\setcmp{X}= & \( \setcmp{X} \) & Set compliment\\[6pt] - & \( \setminuscmp{X} \) & With option \verb=minussetcmp= \\ \midrule - \verb=X \setminus Y= & \( X \setminus Y \) & Set difference \\ \midrule + \verb=\setcmp{X}= & \( \setcmp{X} \) & Set compliment\\\midrule + \verb=X \setdiff Y= & \( X \setdiff Y \) & Set difference \\ \midrule \verb=X \symdiff Y= & \( X \symdiff Y \) & Symmetric difference \\ \midrule \verb=\interior X= & \( \interior X \) & Interior \\ \midrule \verb=\closure X= & \( \closure X \) & Closure \\ \midrule @@ -350,7 +381,7 @@ To disable these commands pass the option \verb=noquants=. The commands \verb=\e \bottomrule \end{tabular} \subsection{Spaces} -To disable these commands pass the option \verb=nospaces=.\\ +To disable these commands pass the option \verb=nospaces=.\\ \begin{tabular}{l | l | l}\toprule \verb=\bstrs= & \( \bstrs \) & Finite binary strings \\ \midrule @@ -364,6 +395,8 @@ To disable these commands pass the option \verb=nospaces=.\\ \subsection{Strings} To disable these commands pass the option \verb=nostrings=.\\ +To specify an alternative symbol for the empty string pass \verb!emptystr=macroname!. For instance, to use \( \lambda \) as the empty string pass \verb!emptystr=lambda!. Similarly, to specify an alternate value for the conatination symbol pass \verb!concatsym=macroname!, e.g., if you specify \verb!\def\plus{+}! and then pass \verb!concatsym=plus! the concatenation symbol would be changed to \( + \). + \begin{tabular}{l | l | l}\toprule \verb=\str{1,0,1}= & \( \str{1,0,1} \) & \multirow{2}{*}{Strings/Codes for strings} \\ \tab \verb=\code{5,8,13}= & \( \code{5,8,13} \) & \\ \midrule @@ -473,7 +506,7 @@ To disable these commands pass the option \verb=noforcing=.\\ \subsection{Syntax} To disable these commands pass the option \verb=nosyntax=.\\ All syntax classes can be relativized with an optional argument in square brackets even when not listed below. Only the \( \Delta \) formula classes are listed below since the syntax is identical for \( \Sigma \) and \( \Pi \). Capitalizing the first letter gives the boldface version in all cases (except the computable infinitary formulas as this doesn't make sense). Not all formulas/abbreviations are demonstrated below given the huge number but the enough are included to make it clear what command is required to generate the desired formula class, e.g., substituting pi for delta does what you think it does. -To change the syntax for the computable infinitary formulas you can pass the options \verb=cdeltasym=, \verb=csigmasym= and \verb=cpisym= set equal to the command to produce your desired symbol. This is UNTESTED and quite likely doesn't work yet. If you desire this feature and it doesn't work send me a bug report. +To change the syntax for the computable infinitary formulas you can pass the options \verb!cdeltasym=macroname!, \verb!csigmasym=macroname! and \verb!cpisym=macroname! where macroname is the name (without the leading \\) of the macro giving the desired symbol to use for the relevant class. \begin{xtabular}{l | l | l}\toprule \verb=\Cdeltan[X]{\alpha}= & \( \Cdeltan[X]{2} \) & The computable \( \delta^{X}_\alpha \) formulas \\ \midrule @@ -583,6 +616,8 @@ Finally to enable the mrref helper macros pass the option \verb=mrref=.\\ These \section{Release Notes} \begin{itemize} + \item[2.4.1] 2/14/2018 - Moved to using xparse to define the case macros and several other macros to allow nested brackets for optional arguments. Added the recf command and cleaned up some option processing. Also worked around the mathtools/unicode-math font bug described \href{https://tex.stackexchange.com/questions/335164/incompatibility-with-mathtools-and-unicode-math-in-xelatex/335177}{here} + \item[2.4] 1/17/2018 - Added priority tree helpers. Should be more robust with respect to existing definitions of common commands. \item[2.3] 12/31/2017 - Added proof cases helper. Also fixed the issue with \verb=\ncequiv= in \XeLaTeX \item[2.2] 11/14/2017 - Fixed \verb=\Tdeg= so it works different on symbols and vars and added \verb=\Tdegof= and \verb=\Tvarof=. Added \verb=\subfunneq= and \verb=\supfunneq=. \item[2.1] 10/05/2017 - Fixed way packages are required so rec-thy can be loaded in a flexible order. Also fixed one or two bugs. diff --git a/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty b/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty index a10b493e04f..be2e9f3c9ea 100644 --- a/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty +++ b/Master/texmf-dist/tex/latex/rec-thy/rec-thy.sty @@ -3,8 +3,13 @@ \makeatletter % \newcommand*{\@curpack}{\@currname} %rec-thy.sty \newcommand*{\@packinfo}[1]{\PackageInfo{rec-thy}{#1}} -\newcommand*{\recthy@strip}[1]{%\expandafter\newcommand{\csname #1\endcsname}{}% Makes sure arg isn't already a command -\expandafter\edef\csname #1\endcsname{\expandafter\noexpand\csname @recthy@#1\endcsname}} %leaves us a command \arg defined to do \@recthy@arg +\newcommand*{\recthy@strip}[1]{% +\ifcsname #1\endcsname% +\else% +\expandafter\edef\csname #1\endcsname{\expandafter\noexpand\csname @recthy@#1\endcsname} +\fi +} +%leaves us a command \arg defined to do \@recthy@arg % \ProvidesPackage{\@curpack} %file name is package name % Release Notes @@ -17,6 +22,11 @@ \RequirePackage{ifmtarg} \RequirePackage{xifthen} \RequirePackage{xkeyval} +\RequirePackage{etoolbox} +\robustify\( +\robustify\) +\RequirePackage{xparse} +\RequirePackage{ifxetex} \AtBeginDocument{ \ltx@ifpackageloaded{amsmath}{}{\RequirePackage{amsmath}} \ltx@ifpackageloaded{amssymb}{}{\RequirePackage{amssymb}} @@ -26,7 +36,14 @@ \ltx@ifpackageloaded{undertilde}{}{\RequirePackage{undertilde}} } - +% \ifxetex %workaround for bug...hopefully can dispense on later +% \gdef\symbf#1{\symbf{#1}} +% \fi +% \global\let\symbf=\symbf +\ifxetex +\else + \def\symbf#1{\mathbf{#1}} +\fi @@ -45,7 +62,7 @@ % % \newcommand*{\matheu}{\EuScript} % \ifpdf -% \RequirePackage{cmap} % you can search in the pdf for umlauts and ligatures +% \RequirePackage{cmap} % you can search in the pdf for umlauts and ligatures % \fi % \fi % \RequirePackage{stmaryrd} @@ -57,31 +74,32 @@ %Define boolean options true if option passed false otherwise -\newif\ifrecthy@nohyphenation \recthy@nohyphenationfalse -\newif\ifrecthy@mrref \recthy@mrreffalse -\newif\ifrecthy@nomath \recthy@nomathfalse -\newif\ifrecthy@nodelim \recthy@nodelimfalse +\newif\ifrecthy@nohyphenation \recthy@nohyphenationfalse +\newif\ifrecthy@mrref \recthy@mrreffalse +\newif\ifrecthy@nomath \recthy@nomathfalse +\newif\ifrecthy@nodelim \recthy@nodelimfalse \newif\ifrecthy@nonames \recthy@nonamesfalse \newif\ifrecthy@nosets \recthy@nosetsfalse \newif\ifrecthy@noquants\recthy@noquantsfalse -\newif\ifrecthy@nospaces \recthy@nospacesfalse -\newif\ifrecthy@nostrings \recthy@nostringsfalse -\newif\ifrecthy@notrees \recthy@notreesfalse -\newif\ifrecthy@nopair \recthy@nopairfalse -\newif\ifrecthy@nonames \recthy@nonamesfalse -\newif\ifrecthy@nosetrels \recthy@nosetrelsfalse -\newif\ifrecthy@noordinalnotations \recthy@noordinalnotationsfalse -\newif\ifrecthy@nosyntax \recthy@nosyntaxfalse -\newif\ifrecthy@nodegclasses \recthy@nodegclassesfalse -\newif\ifrecthy@noforcing \recthy@noforcingfalse -\newif\ifrecthy@nodegrees \recthy@nodegreesfalse -\newif\ifrecthy@nocomputations \recthy@nocomputationsfalse +\newif\ifrecthy@nospaces \recthy@nospacesfalse +\newif\ifrecthy@nostrings \recthy@nostringsfalse +\newif\ifrecthy@notrees \recthy@notreesfalse +\newif\ifrecthy@nopair \recthy@nopairfalse +\newif\ifrecthy@nonames \recthy@nonamesfalse +\newif\ifrecthy@nosetrels \recthy@nosetrelsfalse +\newif\ifrecthy@noordinalnotations \recthy@noordinalnotationsfalse +\newif\ifrecthy@nosyntax \recthy@nosyntaxfalse +\newif\ifrecthy@nodegclasses \recthy@nodegclassesfalse +\newif\ifrecthy@noforcing \recthy@noforcingfalse +\newif\ifrecthy@nodegrees \recthy@nodegreesfalse +\newif\ifrecthy@nocomputations \recthy@nocomputationsfalse \newif\ifrecthy@nostructresets \recthy@nostructresetsfalse \newif\ifrecthy@noreqhelper \recthy@noreqhelperfalse \newif\ifrecthy@nosubfun \recthy@nosubfunfalse \newif\ifrecthy@nopfcases \recthy@nopfcasesfalse +\newif\ifrecthy@noprioritytrees \recthy@noprioritytreesfalse \newif\ifrecthy@hyperreqs \recthy@hyperreqstrue \DeclareOptionX{nohyphenation}{\recthy@nohyphenationtrue} @@ -106,194 +124,204 @@ \DeclareOptionX{noreqhelper}{\recthy@noreqhelpertrue} \DeclareOptionX{nosubfun}{\recthy@nosubfuntrue} \DeclareOptionX{nopfcases}{\recthy@nopfcasestrue} +\DeclareOptionX{noprioritytrees}{\recthy@noprioritytreestrue} \DeclareOptionX{nohyperreqs}{\recthy@hyperreqsfalse} \DeclareOptionX{degjoin}{\def\Tjoin{\Tdegjoin}} + +\AtEndOfPackage{ + \ifrecthy@noprioritytrees + \@packinfo{Not loading Priority Tree Helper} + \else + \@packinfo{Loading Priority Tree Helper.} + \providecommand{\PriorityTree}{\mathbb{T}} + \providecommand{\tpath}[1][]{\ifthenelse{\isempty{#1}}{\symbf{f}}{\mathbb{f}_{#1}}} + \providecommand{\leftof}{\mathbin{<_L}} + \providecommand{\ball}[3][]{{\ifdefined\symbf + \symbf{\alpha} + \else + \alpha + \fi}^{#1}(#2, #3)} + \providecommand*{\Astages}[1]{\mathcal{S}_{\text{act}}^{#1}} + \providecommand*{\Vstages}[1]{\mathcal{S}^{#1}} + \providecommand{\reqof}[2][]{\mathbb{r}(#2)} + \fi +} + \let\pmg@casefont=\textsc -\DeclareOptionX{pfcasefont}[textsc]{\edef\pmg@casefont{\expandafter\noexpand\csname #1 \endcsname}} +\DeclareOptionX{pfcasefont}{\edef\pmg@casefont{\expandafter\noexpand\csname #1 \endcsname}} \AtEndOfPackage{ - \ifrecthy@nopfcases - \@packinfo{Not loading Proof Cases Helper} - \else - \@packinfo{Loading Proof Cases Helper.} - \RequirePackage{enumitem} - \ltx@ifpackageloaded{cleveref}{ - % \crefname{pfcasesnonumi}{case}{cases} - % \Crefname{pfcasesnonumi}{Case}{Cases} - \crefformat{pfcasesnonumi}{#2case~#1#3} - \Crefformat{pfcasesnonumi}{#2Case~#1#3} - % \crefname{pfcasesnonumii}{case}{cases} - % \Crefname{pfcasesnonumii}{Case}{Cases} - \crefformat{pfcasesnonumii}{#2subcase~#1#3} - \Crefformat{pfcasesnonumii}{#2Subcase~#1#3} - % \crefname{pfcasesnonumiii}{case}{cases} - % \Crefname{pfcasesnonumiii}{Case}{Cases} - \crefformat{pfcasesnonumiii}{#2subsubcase~#1#3} - \Crefformat{pfcasesnonumiii}{#2Subsubcase~#1#3} - % \crefname{pfcasesnumberedi}{case}{cases} - % \Crefname{pfcasesnumberedi}{Case}{Cases} - \crefformat{pfcasesnumberedi}{#2case~#1#3} - \Crefformat{pfcasesnumberedi}{#2Case~#1#3} - % \crefname{pfcasesnumberedii}{case}{cases} - % \Crefname{pfcasesnumberedii}{Case}{Cases} - \crefformat{pfcasesnumberedii}{#2case~#1#3} - \Crefformat{pfcasesnumberedii}{#2Case~#1#3} - % \crefname{pfcasesnumberediii}{case}{cases} - % \Crefname{pfcasesnumberediii}{Case}{Cases} - \crefformat{pfcasesnumberediii}{#2case~#1#3} - \Crefformat{pfcasesnumberediii}{#2Case~#1#3} - }{} - \newlist{pfcasesnonum}{enumerate}{3} - \setlist[pfcasesnonum]{ - label={\pmg@casefont{Case}}\protect\thiscase:~, - align=left, - labelsep=!, - itemindent=-1em, - leftmargin=2em, - labelindent=0pt, - labelwidth=0pt - } - \setlist[pfcasesnonum,1]{ - before=\def\pfcasecounter@pmg{pfcasesnonumi}, - } - \setlist[pfcasesnonum,2]{ - before=\def\pfcasecounter@pmg{pfcasesnonumii}, - } - \setlist[pfcasesnonum,3]{ - before=\def\pfcasecounter@pmg{pfcasesnonumiii}, - } - \newlist{pfcasesnumbered}{enumerate}{3} - \setlist[pfcasesnumbered]{ - align=left, - labelsep=!, - itemindent=-1em, - leftmargin=2em, - labelindent=0pt, - labelwidth=0pt - } - \setlist[pfcasesnumbered,1]{ - before=\def\pfcasecounter@pmg{pfcasesnumberedi}, - label={{\pmg@casefont{Case}}~\arabic*\protect\thiscase:~}, - ref={\arabic*}, - } - \setlist[pfcasesnumbered,2]{ - before=\def\pfcasecounter@pmg{pfcasesnumberedii}, - label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph*:\protect\thiscase.~}, - ref={\arabic{pfcasesnumberedi}\alph*}, - } - \setlist[pfcasesnumbered,3]{ - before=\def\pfcasecounter@pmg{pfcasesnumberediii}, - label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*:\protect\thiscase.~}, - ref={\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*}, - } - \newenvironment{pfcases*}{ - \providecommand{\case}[1][]{% - \if\relax\detokenize{##1}\relax - \def\thiscase{}% - \else - \def\thiscase{~##1}% - \fi - \item \ltx@ifpackageloaded{cleveref}{% - \cref@constructprefix{pfcases}{\cref@result}% - \protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result]##1}}{} \protected@edef\@currentlabel{##1}% - } - \begin{pfcasesnonum} - } - {\end{pfcasesnonum}} - - \newenvironment{pfcases}{ - \providecommand{\case}[1][]{% - \if\relax\detokenize{##1}\relax - \def\thiscase{}% - \else - \def\thiscase{~##1}% - \fi - \item \ltx@ifpackageloaded{cleveref}{% - \cref@constructprefix{\pfcasecounter@pmg}{\cref@result} - \protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result] \csname the\pfcasecounter@pmg \endcsname}}{}% - } - \begin{pfcasesnumbered}}{\end{pfcasesnumbered}} - \fi + \ifrecthy@nopfcases + \@packinfo{Not loading Proof Cases Helper} + \else + \@packinfo{Loading Proof Cases Helper.} + \RequirePackage{enumitem} + \ltx@ifpackageloaded{cleveref}{ + \crefformat{pfcasesnonumi}{#2case~#1#3} + \Crefformat{pfcasesnonumi}{#2Case~#1#3} + \crefformat{pfcasesnonumii}{#2subcase~#1#3} + \Crefformat{pfcasesnonumii}{#2Subcase~#1#3} + \crefformat{pfcasesnonumiii}{#2subsubcase~#1#3} + \Crefformat{pfcasesnonumiii}{#2Subsubcase~#1#3} + \crefformat{pfcasesnumberedi}{#2case~#1#3} + \Crefformat{pfcasesnumberedi}{#2Case~#1#3} + \crefformat{pfcasesnumberedii}{#2case~#1#3} + \Crefformat{pfcasesnumberedii}{#2Case~#1#3} + \crefformat{pfcasesnumberediii}{#2case~#1#3} + \Crefformat{pfcasesnumberediii}{#2Case~#1#3} + }{} + \newlist{pfcasesnonum}{enumerate}{3} + \setlist[pfcasesnonum]{ + label={\pmg@casefont{Case}}\protect\thiscase:~, + align=left, + labelsep=!, + itemindent=-1em, + leftmargin=2em, + labelindent=0pt, + labelwidth=0pt + } + \setlist[pfcasesnonum,1]{ + before=\def\pfcasecounter@pmg{pfcasesnonumi}, + } + \setlist[pfcasesnonum,2]{ + before=\def\pfcasecounter@pmg{pfcasesnonumii}, + } + \setlist[pfcasesnonum,3]{ + before=\def\pfcasecounter@pmg{pfcasesnonumiii}, + } + \newlist{pfcasesnumbered}{enumerate}{3} + \setlist[pfcasesnumbered]{ + align=left, + labelsep=!, + itemindent=-1em, + leftmargin=2em, + labelindent=0pt, + labelwidth=0pt + } + \setlist[pfcasesnumbered,1]{ + before=\def\pfcasecounter@pmg{pfcasesnumberedi}, + label={{\pmg@casefont{Case}}~\arabic*\protect\thiscase:~}, + ref={\arabic*}, + } + \setlist[pfcasesnumbered,2]{ + before=\def\pfcasecounter@pmg{pfcasesnumberedii}, + label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph*:\protect\thiscase.~}, + ref={\arabic{pfcasesnumberedi}\alph*}, + } + \setlist[pfcasesnumbered,3]{ + before=\def\pfcasecounter@pmg{pfcasesnumberediii}, + label={{\pmg@casefont{Case}}~\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*:\protect\thiscase.~}, + ref={\arabic{pfcasesnumberedi}\alph{pfcasesnumberedii}.\roman*}, + } + \newenvironment{pfcases*}{ + \ProvideDocumentCommand{\case}{o}{ + \IfNoValueTF{##1}{ + \def\thiscase{}% + }{ + \def\thiscase{~##1}% + } + \item \ltx@ifpackageloaded{cleveref}{% + \cref@constructprefix{pfcases}{\cref@result}% + \protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result]##1}}{} \protected@edef\@currentlabel{##1}% + } + \begin{pfcasesnonum} + } + {\end{pfcasesnonum}} + + \newenvironment{pfcases}{ + \ProvideDocumentCommand{\case}{o}{ + \IfNoValueTF{##1}{ + \def\thiscase{}% + }{ + \def\thiscase{~##1}% + } + \item \ltx@ifpackageloaded{cleveref}{% + \cref@constructprefix{\pfcasecounter@pmg}{\cref@result} + \protected@xdef\cref@currentlabel{[\pfcasecounter@pmg][][\cref@result] \csname the\pfcasecounter@pmg \endcsname}}{}% + } + \begin{pfcasesnumbered}}{\end{pfcasesnumbered}} + \fi } \AtEndOfPackage{ \ifrecthy@nosubfun - \@packinfo{Not loading subfun defs.} + \@packinfo{Not loading subfun defs.} \else - \@packinfo{Loading subfun defs.} - %DOCUMENT ME - \newcommand*{\subfun}[1][]{\prec\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\supfun}[1][]{\succ\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\nsubfun}[1][]{\nprec\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\nsupfun}[1][]{\nsucc\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\subfuneq}[1][]{\preceq\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\supfuneq}[1][]{\succeq\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\nsubfuneq}[1][]{\npreceq\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\nsupfuneq}[1][]{\nsucceq\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\subfunneq}[1][]{\precneq\ifthenelse{\isempty{#1}}{_{#1}}{}} - \newcommand*{\supfunneq}[1][]{\succneq\ifthenelse{\isempty{#1}}{_{#1}}{}} + \@packinfo{Loading subfun defs.} + %DOCUMENT ME + \NewDocumentCommand{\subfun}{o}{\prec\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\supfun}{o}{\succ\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\nsubfun}{o}{\nprec\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\nsupfun}{o}{\nsucc\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\subfuneq}{o}{\preceq\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\supfuneq}{o}{\succeq\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\nsubfuneq}{o}{\npreceq\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\nsupfuneq}{o}{\nsucceq\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\subfunneq}{o}{\precneq\IfNoValueTF{#1}{}{_{#1}}} + \NewDocumentCommand{\supfunneq}{o}{\succneq\IfNoValueTF{#1}{}{_{#1}}} \fi } -\newcommand*{\@recthy@reqscr}[1]{\mathscr{#1}} -% \DeclareOptionX{reqscr}{\newcommand{\@recthy@reqscr}[1]{#1{##1}}} +% \newcommand*{\@recthy@reqscr}[1]{\mathscr{#1}} +\let\@recthy@reqscr=\mathscr +\DeclareOptionX{reqscr}{\edef\@recthy@reqscr{\expandafter\noexpand\csname #1 \endcsname}} \AtEndOfPackage{ \ifrecthy@noreqhelper - \@packinfo{Not loading requirement assist.} + \@packinfo{Not loading requirement assist.} \else - \@packinfo{Loading requirement assist.} - \newcommand*{\req@orig}[3][]{\ensuremath{\ifthenelse{\isempty{#1}}{\@recthy@reqscr{#2}_{#3}}{\@recthy@reqscr{#2}^{#1}_{#3}}}} - \ifrecthy@hyperreqs - \newcommand*{\req}[3][]{ - \@ifundefined{hyperref}{ - \req@orig[#1]{#2}{#3} - }{ - \hyperref[\detokenize{req:#2@#1}]{\req@orig[#1]{#2}{#3}} - }} - \else - \let\req=\req@orig - \fi - \WithSuffix\def\req*{\req@orig} - % \newsavebox{\@recthy@reqbox} - % \def\defreq#1#2\par{ - % \begin{equation}\let\veqno\@@leqno% - % \tag*{#1}% - % \begin{lrbox}{\@recthy@reqbox}% + \@packinfo{Loading requirement assist.} + \newcommand*{\req@orig}[3][]{\ensuremath{\ifthenelse{\isempty{#1}}{\@recthy@reqscr{#2}_{#3}}{\@recthy@reqscr{#2}^{#1}_{#3}}}} + \ifrecthy@hyperreqs + \newcommand*{\req}[3][]{ + \@ifundefined{hyperref}{ + \req@orig[#1]{#2}{#3} + }{ + \hyperref[\detokenize{req:#2@#1}]{\req@orig[#1]{#2}{#3}} + }} + \else + \let\req=\req@orig + \fi + \WithSuffix\def\req*{\req@orig} + % \newsavebox{\@recthy@reqbox} + % \def\defreq#1#2\par{ + % \begin{equation}\let\veqno\@@leqno% + % \tag*{#1}% + % \begin{lrbox}{\@recthy@reqbox}% % \begin{minipage}{\textwidth}#2\end{minipage}% % \end{lrbox}% % \makebox[0pt]{\usebox{\@recthy@reqbox}}% - % \end{equation}} - \newtagform{colon}{}{:} - \newenvironment{requirement}[1]{ - \let\@origif@fleqn@pmg=\if@fleqn - \let\@origiftagsleft@pmg=\iftagsleft@ - \@fleqntrue - \setlength\@mathmargin{1.5cm} - \tagsleft@true - \usetagform{colon} - % \let\maketag@@@orig@pmg=\maketag@@@ - % \def\maketag@@@#1{\hbox{\m@th\normalfont#1:}} - \begin{equation}\tag{#1} - }{ - \end{equation} - \let\if@fleqn=\@origif@fleqn@pmg - \let\iftagsleft@=\@origiftagsleft@pmg - \usetagform{default} - % \let\maketag@@@=\maketag@@@orig@pmg - } - - \newenvironment{require}[3][]{ - \begin{requirement}{\req*[#1]{#2}{#3}} \label{\detokenize{req:#2@#1}} - }{ - \end{requirement} - } - \newcommand*{\refreq}[2][]{\ref{\detokenize{req:#2@#1}}} + % \end{equation}} + \newtagform{colon}{}{:} + \newenvironment{requirement}[1]{ + \let\@origif@fleqn@pmg=\if@fleqn + \let\@origiftagsleft@pmg=\iftagsleft@ + \@fleqntrue + \setlength\@mathmargin{1.5cm} + \tagsleft@true + \usetagform{colon} + % \let\maketag@@@orig@pmg=\maketag@@@ + % \def\maketag@@@#1{\hbox{\m@th\normalfont#1:}} + \begin{equation}\tag{#1} + }{ + \end{equation} + \let\if@fleqn=\@origif@fleqn@pmg + \let\iftagsleft@=\@origiftagsleft@pmg + \usetagform{default} + % \let\maketag@@@=\maketag@@@orig@pmg + } + + \newenvironment{require}[3][]{ + \begin{requirement}{\req*[#1]{#2}{#3}} \label{\detokenize{req:#2@#1}} + }{ + \end{requirement} + } + \newcommand*{\refreq}[2][]{\ref{\detokenize{req:#2@#1}}} \fi } @@ -302,10 +330,11 @@ \AtEndOfPackage{ \ifrecthy@nostructresets - \@packinfo{Not loading r.e. set structs w/ containment.} + \@packinfo{Not loading r.e. set structs w/ containment.} \else - \@packinfo{Loading r.e. set structs w/ containment.} -\newcommand*{\promptdif}{\setminus_{\downarrow}} + \@packinfo{Loading r.e. set structs w/ containment.} +\let\@orig@setminus=\setminus +\newcommand*{\promptdif}{\@orig@setminus_{\downarrow}} \let\setbefore=\promptdif \let\promptminus=\promptdif \let\promptsetminus=\promptdif @@ -327,7 +356,7 @@ \AtEndOfPackage{ \ifrecthy@nohyphenation - \@packinfo{No hyphenation loading.} + \@packinfo{No hyphenation loading.} \else \hyphenation{ra-tion-als ra-tion-al Harrington Slaman Cholak Knight Gerdes Lange} \fi @@ -336,20 +365,20 @@ \AtEndOfPackage{ \ifrecthy@mrref - \@packinfo{MRref helper loading} - \RequirePackage{hyperref} - \def\recthy@checkMR MR#1#2#3 #4\relax% - {\ifx#1M% - \ifx#2R\recthy@MR{#3}\else\recthy@MR{#1#2#3}\fi - \else - \recthy@MR{#1#2#3}% - \fi} - \def\MR#1{\recthy@checkMR MR#1 \relax} - \newcommand{\recthy@MR}[1]{\recthy@MRhref{#1}{MR #1}} - % % \MRhref is called by the amsart/book/proc definition of \MR. - \newcommand{\recthy@MRhref}[2]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}} + \@packinfo{MRref helper loading} + \RequirePackage{hyperref} + \def\recthy@checkMR MR#1#2#3 #4\relax% + {\ifx#1M% + \ifx#2R\recthy@MR{#3}\else\recthy@MR{#1#2#3}\fi + \else + \recthy@MR{#1#2#3}% + \fi} + \def\MR#1{\recthy@checkMR MR#1 \relax} + \newcommand{\recthy@MR}[1]{\recthy@MRhref{#1}{MR #1}} + % % \MRhref is called by the amsart/book/proc definition of \MR. + \newcommand{\recthy@MRhref}[2]{\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}} \else - \@packinfo{MRref helper not loading} + \@packinfo{MRref helper not loading} \fi } @@ -357,31 +386,49 @@ \newcommand*{\@recthy@ensuretext}[1]{\ensuremath{\text{#1}}} \AtEndOfPackage{ \ifrecthy@nomath - \@packinfo{No math loading.} + \@packinfo{No math loading.} \else - \@packinfo{math loading.} - \newcommand*{\eqdef}{\stackrel{\text{\tiny def}}{=}} %\newcommand*{\eqdef}{\ensuremath{=\limits_{\text{\tiny def}}}} - \newcommand*{\iffdef}{\stackrel{\text{\tiny def}}{\iff}} - \DeclareMathOperator{\aut}{Aut} - \DeclareMathOperator{\Ord}{Ord} - - \newcommand*{\meet}{\mathbin{\wedge}} - \newcommand*{\join}{\mathbin{\vee}} - \newcommand*{\Meet}{\mathop{\bigwedge}} - \let\MnJoin=\Join - \renewcommand*{\Join}{\mathop{\bigvee}} - \recthy@strip{abs} - \DeclareMathOperator{\dom}{dom} - \DeclareMathOperator{\rng}{rng} - \newcommand*{\restr}[1]{\mathpunct{\restriction_{#1}}} - \newcommand*{\ordpair}[2]{\left( #1, #2 \right) } - %%%%%%%%Function commands - \newcommand*{\map}[2]{:#1\mapsto #2} - \newcommand*{\functo}[3]{#1\map{#2}{#3}} - \newcommand*{\compfunc}{\mathbin{\circ}} - \let\compose=\compfunc - \let\funcomp=\compfunc - \recthy@strip{ensuretext} + \@packinfo{math loading.} + \providecommand*{\eqdef}{\stackrel{\text{\tiny def}}{=}} %\newcommand*{\eqdef}{\ensuremath{=\limits_{\text{\tiny def}}}} + \providecommand*{\iffdef}{\stackrel{\text{\tiny def}}{\iff}} + \ifdefined\aut + \else + \DeclareMathOperator{\aut}{Aut} + \fi + \ifdefined\Ord + \else + \DeclareMathOperator{\Ord}{Ord} + \fi + + \providecommand*{\meet}{\mathbin{\wedge}} + \providecommand*{\join}{\mathbin{\vee}} + \providecommand*{\Meet}{\mathop{\bigwedge}} + \let\MnJoin=\Join + \renewcommand*{\Join}{\mathop{\bigvee}} + \recthy@strip{abs} + \ifdefined\dom + \else + \DeclareMathOperator{\dom}{dom} + \fi + \ifdefined\rng + \else + \DeclareMathOperator{\rng}{rng} + \fi + \providecommand*{\restr}[1]{\mathpunct{\restriction_{#1}}} + \providecommand*{\ordpair}[2]{\left( #1, #2 \right) } + %%%%%%%%Function commands + \providecommand*{\map}[2]{:#1\mapsto #2} + \providecommand*{\functo}[3]{#1\map{#2}{#3}} + \providecommand*{\compfunc}{\mathbin{\circ}} + \ifdefined\compose + \else + \let\compose=\compfunc + \fi + \ifdefined\funcomp + \else + \let\funcomp=\compfunc + \fi + \recthy@strip{ensuretext} \fi } @@ -395,15 +442,15 @@ \newdimen\@recthy@gnArgHgt \newcommand{\@recthy@godelnum}[1]{% - \setbox\@recthy@gnBoxA=\hbox{$#1$}% - \@recthy@gnArgHgt=\ht\@recthy@gnBoxA% - \ifnum \@recthy@gnArgHgt<\@recthy@gnCornerHgt - \@recthy@gnArgHgt=0pt% - \else - \advance \@recthy@gnArgHgt by -\@recthy@gnCornerHgt% - \fi - \raise\@recthy@gnArgHgt\hbox{$\ulcorner$} \box\@recthy@gnBoxA % - \raise\@recthy@gnArgHgt\hbox{$\urcorner$}} + \setbox\@recthy@gnBoxA=\hbox{$#1$}% + \@recthy@gnArgHgt=\ht\@recthy@gnBoxA% + \ifnum \@recthy@gnArgHgt<\@recthy@gnCornerHgt + \@recthy@gnArgHgt=0pt% + \else + \advance \@recthy@gnArgHgt by -\@recthy@gnCornerHgt% + \fi + \raise\@recthy@gnArgHgt\hbox{$\ulcorner$} \box\@recthy@gnBoxA % + \raise\@recthy@gnArgHgt\hbox{$\urcorner$}} @@ -414,13 +461,13 @@ \AtEndOfPackage{ \ifrecthy@nodelim - \@packinfo{No delimiters loading.} + \@packinfo{No delimiters loading.} \else - \newcommand*{\godelnum}[1]{\@recthy@godelnum{#1}} - \let\cornerquote=\godelnum - \let\gcode=\godelnum - \recthy@strip{llangle} - \recthy@strip{rrangle} + \newcommand*{\godelnum}[1]{\@recthy@godelnum{#1}} + \let\cornerquote=\godelnum + \let\gcode=\godelnum + \recthy@strip{llangle} + \recthy@strip{rrangle} \fi } @@ -441,52 +488,57 @@ \AtEndOfPackage{ \ifrecthy@nonames - \@packinfo{No names loading.} + \@packinfo{No names loading.} \else - \@packinfo{Names loading.} - \recthy@strip{re} - \recthy@strip{ce} - \recthy@strip{REA} - \recthy@strip{CEA} - \recthy@strip{recursive} - \recthy@strip{computable} - \recthy@strip{recursivelyEnumerable} - \recthy@strip{computablyEnumerable} - \recthy@strip{Recursive} - \recthy@strip{Computable} - \recthy@strip{RecursivelyEnumerable} - \recthy@strip{ComputablyEnumerable} + \@packinfo{Names loading.} + \recthy@strip{re} + \recthy@strip{ce} + \recthy@strip{REA} + \recthy@strip{CEA} + \recthy@strip{recursive} + \recthy@strip{computable} + \recthy@strip{recursivelyEnumerable} + \recthy@strip{computablyEnumerable} + \recthy@strip{Recursive} + \recthy@strip{Computable} + \recthy@strip{RecursivelyEnumerable} + \recthy@strip{ComputablyEnumerable} \fi } \DeclareOptionX{reterms}{% - \let\@recthy@ce=\@recthy@re - \let\@recthy@computable=\@recthy@recursive - \let\@recthy@computablyEnumerable=\@recthy@recursivelyEnumerable - \let\@recthy@ComputablyEnumerable=\@recthy@RecursivelyEnumerable - } %Make all references to ce change to re + \let\@recthy@ce=\@recthy@re + \let\@recthy@computable=\@recthy@recursive + \let\@recthy@computablyEnumerable=\@recthy@recursivelyEnumerable + \let\@recthy@ComputablyEnumerable=\@recthy@RecursivelyEnumerable + } %Make all references to ce change to re - \DeclareOptionX{reaterms}{% - \let\@recthy@CEA=\@recthy@REA - } + \DeclareOptionX{reaterms}{% + \let\@recthy@CEA=\@recthy@REA + } \DeclareOptionX{ceterms}{% - \let\@recthy@re=\@recthy@ce - \let\@recthy@recursive=\@recthy@computable - \let\@recthy@recursivelyEnumerable=\@recthy@computablyEnumerable - \let\@recthy@RecursivelyEnumerable=\@recthy@ComputablyEnumerable - } %Make all references to re change to ce + \let\@recthy@re=\@recthy@ce + \let\@recthy@recursive=\@recthy@computable + \let\@recthy@recursivelyEnumerable=\@recthy@computablyEnumerable + \let\@recthy@RecursivelyEnumerable=\@recthy@ComputablyEnumerable + } %Make all references to re change to ce \DeclareOptionX{ceaterms}{% - \let\@recthy@REA=\@recthy@CEA - } + \let\@recthy@REA=\@recthy@CEA + } % Set stuff -\def\@recthy@set#1{\def\@set@argi@pmg{#1}\@ifnextchar\bgroup\@setst@pmg\@setplain@pmg} -\newcommand*{\@setst@pmg}[1]{\ifthenelse{\isempty{#1}}{\@setplain@pmg}{\left \{ \@set@argi@pmg \middle | #1\right \}}} -\newcommand*{\@setplain@pmg}{\left \{ \@set@argi@pmg \right \}} + +\NewDocumentCommand{\@recthy@set}{oG{}}{\left \{ #1 \ifthenelse{\isempty{#2}}{}{\middle | #2} \right \}} + +% \def\@recthy@set#1{\def\@set@argi@pmg{#1}\@ifnextchar\bgroup\@setst@pmg\@setplain@pmg} +% \newcommand*{\@setst@pmg}[1]{\ifthenelse{\isempty{#1}}{\@setplain@pmg}{\left \{ \@set@argi@pmg \middle | #1\right \}}} +% \newcommand*{\@setplain@pmg}{\left \{ \@set@argi@pmg \right \}} % \newcommand*{\@recthy@set}[2]{\ifthenelse{\isempty{#2}}{\left \{ #1 \right \}}{\left \{ #1 \middle | #2\right \}} } +% \DeclareOptionX{setminussym}[@recthy@defaultsetminusSYM]{\edef\@recthy@setminusSYM{\expandafter\noexpand\csname #1 \endcsname}} + \newcommand*{\@recthy@card}[1]{\lvert#1\rvert} \newcommand*{\@recthy@union}{\mathbin{\cup}} @@ -496,170 +548,172 @@ \newcommand*{\@recthy@nin}{\notin} \newcommand*{\@recthy@powset}[1]{\mathcal{P}\left(#1\right)} \newcommand*{\@recthy@eset}{\emptyset} -\newcommand*{\@recthy@setcmpminusSYM}{\backsim} -\newcommand*{\@recthy@setminuscmp}[1]{\mathop{\@recthy@setcmpminusSYM} #1} +% \newcommand*{\@recthy@setcmpminusSYM}{\backsim} +% \newcommand*{\@recthy@setminuscmp}[1]{\mathop{\@recthy@setcmpminusSYM} #1} \newcommand*{\@recthy@setovercmp}[1]{\overline{#1}} \let\@recthy@setcmp=\@recthy@setovercmp -\def\@recthy@setminusSYM{-} +\def\@recthy@setdiffSYM{-} +\newcommand*{\@recthy@setdiff}{\mathbin{\@recthy@setdiffSYM}} + +\DeclareOptionX{setdiffsym}{\edef\@recthy@setdiffSYM{\expandafter\noexpand\csname #1 \endcsname}} -\DeclareOptionX{setminussym}{\def\@recthy@setminusSYM{#1}} -\DeclareOptionX{setcmpminussym}{\def\@recthy@setminusSYM{#1}} -\DeclareOptionX{minussetcmp}{\let\@recthy@setcmp=\@recthy@setminuscmp} -\newcommand*{\@recthy@setminus}{\mathbin{\@recthy@setminusSYM}} \AtEndOfPackage{ \WithSuffix\def\@recthy@setcmp[#1]#2{#1\@recthy@setminus#2} \ifrecthy@nosets - \@packinfo{No set cmds loading.} + \@packinfo{No set cmds loading.} \else - \@packinfo{Set cmds loading.} - \recthy@strip{set} - \recthy@strip{card} - \recthy@strip{union} - \recthy@strip{Union} - \recthy@strip{isect} - \recthy@strip{Isect} - \recthy@strip{powset} - \recthy@strip{eset} - \recthy@strip{nin} - \recthy@strip{setcmp} - \recthy@strip{setovercmp} - \recthy@strip{setminuscmp} - \recthy@strip{setminus} - \newcommand*{\cross}{\mathbin{\times}} - \let\CrossOrig=\Cross - \def\Cross{} - \renewcommand*{\Cross}{\mathop{\Pi}} - \newcommand*{\symdiff}{\mathbin{\Delta}} - \DeclareMathOperator{\interior}{int} - \DeclareMathOperator{\closure}{cl} + \@packinfo{Set cmds loading.} + \recthy@strip{set} + \recthy@strip{card} + \recthy@strip{union} + \recthy@strip{Union} + \recthy@strip{isect} + \recthy@strip{Isect} + \recthy@strip{powset} + \recthy@strip{eset} + \recthy@strip{nin} + \recthy@strip{setcmp} + % \recthy@strip{setovercmp} + % \recthy@strip{setminuscmp} + \recthy@strip{setdiff} + \let\crossOrig=\cross + \def\cross{} + \renewcommand*{\cross}{\mathbin{\times}} + \let\CrossOrig=\Cross + \def\Cross{} + \renewcommand*{\Cross}{\mathop{\Pi}} + \providecommand*{\symdiff}{\mathbin{\Delta}} + \ifdefined\interior + \else + \DeclareMathOperator{\interior}{int} + \fi + \ifdefined\closure + \else + \DeclareMathOperator{\closure}{cl} + \fi \fi } \AtEndOfPackage{ \ifrecthy@noquants - \@packinfo{No quants loading.} + \@packinfo{No quants loading.} \else - \@packinfo{Quants loading.} - \newcommand*{\existsuniq}{\exists !} - \newcommand*{\nexistsuniq}{\nexists !} - \WithSuffix\def\existsuniq(#1){\left(\existsuniq\, #1 \right)\!} - \WithSuffix\def\nexistsuniq(#1){\left(\nexistsuniq\, #1 \right)\!} - \WithSuffix\def\existsuniq[#1]{\left[\existsuniq\, #1 \right]\!} - \WithSuffix\def\nexistsuniq[#1]{\left[\nexistsuniq\, #1 \right]\!} - - \newcommand*{\forallae}{\forall^{*}} - \WithSuffix\def\forallae(#1){\left(\forallae\, #1\right)\!} - \WithSuffix\def\forallae[#1]{\left[\forallae\, #1\right]\!} - - \newcommand*{\existsinf}{\exists^{\infty}} - \WithSuffix\def\existsinf(#1){\left(\existsinf\, #1\right)\!} - \WithSuffix\def\existsinf[#1]{\left[\existsinf\, #1\right]\!} - - \newcommand*{\nexistsinf}{\nexists^{\infty}} - \WithSuffix\def\nexistsinf(#1){\left(\nexistsinf\, #1\right)\!} - \WithSuffix\def\nexistsinf[#1]{\left[\nexistsinf\, #1\right]\!} - - \WithSuffix\def\exists(#1){\left(\exists\, #1 \right)\!} - \WithSuffix\def\forall(#1){\left(\forall\, #1 \right)\!} - \WithSuffix\def\nexists(#1){\left(\nexists\, #1 \right)\!} - \WithSuffix\def\exists[#1]{\left[\exists\, #1 \right]\!} - \WithSuffix\def\forall[#1]{\left[\forall\, #1 \right]\!} - \WithSuffix\def\nexists[#1]{\left[\nexists\, #1 \right]\!} - \WithSuffix\def\forall*{\forallae} - \WithSuffix\def\exists*{\existsinf} - \WithSuffix\def\nexists*{\nexistsinf} - \WithSuffix\def\exists!{\existsuniq} - - - - - \newcommand*{\True}{\top} - \newcommand*{\False}{\bot} - - \newcommand*{\Land}{\mathop{\bigwedge}} - \newcommand*{\Lor}{\mathop{\bigvee}} - \newcommand*{\LLand}{\mathop{\bigwedge\mkern-15mu\bigwedge}} - \newcommand*{\LLor}{\mathop{\bigvee\mkern-15mu\bigvee}} - - \newcommand*{\liff}{\ensuremath{\leftrightarrow}} - \newcommand*{\limplies}{\ensuremath{\rightarrow}} + \@packinfo{Quants loading.} + \newcommand*{\existsuniq}{\exists !} + \newcommand*{\nexistsuniq}{\nexists !} + \WithSuffix\def\existsuniq(#1){\left(\existsuniq\, #1 \right)\!} + \WithSuffix\def\nexistsuniq(#1){\left(\nexistsuniq\, #1 \right)\!} + \WithSuffix\def\existsuniq[#1]{\left[\existsuniq\, #1 \right]\!} + \WithSuffix\def\nexistsuniq[#1]{\left[\nexistsuniq\, #1 \right]\!} + + \newcommand*{\forallae}{\forall^{*}} + \WithSuffix\def\forallae(#1){\left(\forallae\, #1\right)\!} + \WithSuffix\def\forallae[#1]{\left[\forallae\, #1\right]\!} + + \providecommand*{\existsinf}{\exists^{\infty}} + \WithSuffix\def\existsinf(#1){\left(\existsinf\, #1\right)\!} + \WithSuffix\def\existsinf[#1]{\left[\existsinf\, #1\right]\!} + + \providecommand*{\nexistsinf}{\nexists^{\infty}} + \WithSuffix\def\nexistsinf(#1){\left(\nexistsinf\, #1\right)\!} + \WithSuffix\def\nexistsinf[#1]{\left[\nexistsinf\, #1\right]\!} + + \WithSuffix\def\exists(#1){\left(\exists\, #1 \right)\!} + \WithSuffix\def\forall(#1){\left(\forall\, #1 \right)\!} + \WithSuffix\def\nexists(#1){\left(\nexists\, #1 \right)\!} + \WithSuffix\def\exists[#1]{\left[\exists\, #1 \right]\!} + \WithSuffix\def\forall[#1]{\left[\forall\, #1 \right]\!} + \WithSuffix\def\nexists[#1]{\left[\nexists\, #1 \right]\!} + \WithSuffix\def\forall*{\forallae} + \WithSuffix\def\exists*{\existsinf} + \WithSuffix\def\nexists*{\nexistsinf} + \WithSuffix\def\exists!{\existsuniq} + + + + + \providecommand*{\True}{\top} + \providecommand*{\False}{\bot} + + \providecommand*{\Land}{\mathop{\bigwedge}} + \providecommand*{\Lor}{\mathop{\bigvee}} + \providecommand*{\LLand}{\mathop{\bigwedge\mkern-15mu\bigwedge}} + \providecommand*{\LLor}{\mathop{\bigvee\mkern-15mu\bigvee}} + + \providecommand*{\liff}{\ensuremath{\leftrightarrow}} + \providecommand*{\limplies}{\ensuremath{\rightarrow}} \fi } \AtEndOfPackage{ \ifrecthy@nospaces - \@packinfo{No spaces loading.} + \@packinfo{No spaces loading.} \else - \@packinfo{Spaces loading.} + \@packinfo{Spaces loading.} - \newcommand*{\bstrs}{2^{<\omega}} - \newcommand*{\wstrs}{\omega^{<\omega}} + \providecommand*{\bstrs}{2^{<\omega}} + \providecommand*{\wstrs}{\omega^{<\omega}} - \newcommand*{\cantor}{2^{\omega}} - % \WithSuffix\def\cantor*{\left(2\union \diverge \right)^{\omega}} - \newcommand*{\baire}{\omega^{\omega}} - % \WithSuffix\def\baire*{\left(\omega \union \diverge \right)^{\omega}} - \newcommand*{\Baire}{\mathcal{N}} + \providecommand*{\cantor}{2^{\omega}} + % \WithSuffix\def\cantor*{\left(2\union \diverge \right)^{\omega}} + \providecommand*{\baire}{\omega^{\omega}} + % \WithSuffix\def\baire*{\left(\omega \union \diverge \right)^{\omega}} + \providecommand*{\Baire}{\mathcal{N}} \fi } -% \newcommand*{\recfnlSYM}{\Phi} -% -% \DeclareOptionX{recfn}{\def\recfnlSYM{#1}} +%Strings +\def\@recthy@concatSYM{\widehat{\;}} +\def\@recthy@EmptyStr{\mathopen{\@recthy@llangle}\mathclose{\@recthy@rrangle}} -%Strings +\DeclareOptionX{emptystr}{\edef\@recthy@EmptyStr{\expandafter\noexpand\csname #1 \endcsname}} +\DeclareOptionX{concatsym}{\edef\@recthy@concatSYM{\expandafter\noexpand\csname #1 \endcsname}} -\newcommand*{\@recthy@EmptyStr}{\lambda} -\newcommand*{\@recthy@concatSYM}{\hat{\;}} -% \DeclareOptionX<\@recthy@family>{emptystr}[]{\def\@recthy@EmptyStr{#1}} -% \DeclareOptionX<\@recthy@family>{concat}[]{\def\@recthy@concatSYM{#1}} -\DeclareOptionX{emptystr}{\def\@recthy@EmptyStr{#1}} -\DeclareOptionX{concat}{\def\@recthy@concatSYM{#1}} \AtEndOfPackage{ \ifrecthy@nostrings - \@packinfo{No strings loading.} + \@packinfo{No strings loading.} \else - \@packinfo{Strings loading.} + \@packinfo{Strings loading.} \newcommand*{\closedn}[1]{{#1}^\blacktriangledown} - \newcommand*{\str}[1]{\mathopen{\@recthy@llangle}#1\mathclose{\@recthy@rrangle}} - \newcommand*{\code}{\str} - \newcommand*{\EmptyStr}{\@recthy@EmptyStr} - \newcommand*{\estr}{\EmptyStr} - \newcommand*{\decode}[2]{(#1)_{#2}} - \newcommand*{\godelpair}[2]{\mathopen{\langle} #1, #2 \mathclose{\rangle}} - \newcommand*{\gpair}{\godelpair} - \newcommand*{\concat}{\mathbin{\@recthy@concatSYM}} - \WithSuffix\def\concat[#1]{\concat\str{#1}} - \newcommand*{\strpred}[1]{{#1}^{-}} - \newcommand*{\lh}[2][]{\@recthy@abs{#2}_{#1}} %% Gives length of a string - \newcommand*{\incompat}{\mathrel{\mid}} %incompatible stringes FIX SPACING - \newcommand*{\incomp}{\incompat} - \newcommand*{\compat}{\mathrel{\nmid}} - \newcommand*{\setcol}[2]{{#1}^{[#2]}} - \ifrecthy@nopair - \@packinfo{No redefining pair.} - \else - \@packinfo{pair=godelpair.} - \newcommand*{\pair}{\godelpair} - \fi + \newcommand*{\str}[1]{\mathopen{\@recthy@llangle}#1\mathclose{\@recthy@rrangle}} + \newcommand*{\code}{\str} + \newcommand*{\EmptyStr}{\@recthy@EmptyStr} + \newcommand*{\estr}{\EmptyStr} + \newcommand*{\decode}[2]{(#1)_{#2}} + \providecommand*{\godelpair}[2]{\mathopen{\langle} #1, #2 \mathclose{\rangle}} + \newcommand*{\gpair}{\godelpair} + \newcommand*{\concat}{\mathbin{\@recthy@concatSYM}} + \WithSuffix\def\concat[#1]{\concat\str{#1}} + \newcommand*{\strpred}[1]{{#1}^{-}} + \providecommand*{\lh}[2][]{\@recthy@abs{#2}_{#1}} %% Gives length of a string + \providecommand*{\incompat}{\mathrel{\mid}} %incompatible stringes FIX SPACING + \providecommand*{\incomp}{\incompat} + \providecommand*{\compat}{\mathrel{\nmid}} + \newcommand*{\setcol}[2]{{#1}^{[#2]}} + \ifrecthy@nopair + \@packinfo{No redefining pair.} + \else + \@packinfo{pair=godelpair.} + \newcommand*{\pair}{\godelpair} + \fi \fi } \AtEndOfPackage{ \ifrecthy@notrees - \@packinfo{No trees loading.} + \@packinfo{No trees loading.} \else - \@packinfo{Trees loading.} - \newcommand*{\CBderiv}[2][1]{#2^{\langle#1\rangle}} - \newcommand*{\pruneTree}[1]{\CBderiv[\infty]{#1}} - \newcommand*{\hgt}[1]{\lVert #1 \rVert} + \@packinfo{Trees loading.} + \newcommand*{\CBderiv}[2][1]{#2^{\langle#1\rangle}} + \newcommand*{\pruneTree}[1]{\CBderiv[\infty]{#1}} + \newcommand*{\hgt}[1]{\lVert #1 \rVert} \fi } @@ -678,37 +732,37 @@ %re set relations \AtEndOfPackage{ \ifrecthy@nosetrels - \@packinfo{No setrels loading.} + \@packinfo{No setrels loading.} \else - \@packinfo{setrels loading.} - - \WithSuffix\def\subset*{\subset^{*}} - \WithSuffix\def\supset*{\supset^{*}} - \WithSuffix\def\subseteq*{\subseteq^{*}} - \WithSuffix\def\supseteq*{\supseteq^{*}} - \providecommand*{\nsupset}{\not\supset} - \providecommand*{\nsubset}{\not\subset} - \WithSuffix\def\nsubset*{\nsubset^{*}} - \WithSuffix\def\nsupset*{\nsupset^{*}} - \WithSuffix\def\nsubseteq*{\nsubseteq^{*}} - \WithSuffix\def\nsupseteq*{\nsupseteq^{*}} - % \WithSuffix\def\subsetneq*{\subsetneq^{*}} - % \WithSuffix\def\supsetneq*{\supsetneq^{*}} - - \newcommand*{\eq}{=} - \WithSuffix\def\eq*{=^{*}} - \newcommand*{\eqae}{=^{*}} + \@packinfo{setrels loading.} + + \WithSuffix\def\subset*{\subset^{*}} + \WithSuffix\def\supset*{\supset^{*}} + \WithSuffix\def\subseteq*{\subseteq^{*}} + \WithSuffix\def\supseteq*{\supseteq^{*}} + \providecommand*{\nsupset}{\not\supset} + \providecommand*{\nsubset}{\not\subset} + \WithSuffix\def\nsubset*{\nsubset^{*}} + \WithSuffix\def\nsupset*{\nsupset^{*}} + \WithSuffix\def\nsubseteq*{\nsubseteq^{*}} + \WithSuffix\def\nsupseteq*{\nsupseteq^{*}} + % \WithSuffix\def\subsetneq*{\subsetneq^{*}} + % \WithSuffix\def\supsetneq*{\supsetneq^{*}} + + \newcommand*{\eq}{=} + \WithSuffix\def\eq*{=^{*}} + \newcommand*{\eqae}{=^{*}} \newcommand*{\neqae}{\neq^{*}} - \WithSuffix\def\neq*{\neq^{*}} - - \newcommand*{\infsubset}{\subset_{\infty}} - \WithSuffix\def\infsubset*{\infsubset^{*}} - \let\subsetnaeq=\infsubset - \newcommand*{\infsupset}{\supset_{\infty}} - \WithSuffix\def\infsupset*{\infsupset^{*}} - \let\supsetnaeq=\infsupset - \newcommand*{\majsubset}{\subset_{m}} - \newcommand*{\majsupset}{\supset_{m}} + \WithSuffix\def\neq*{\neq^{*}} + + \newcommand*{\infsubset}{\subset_{\infty}} + \WithSuffix\def\infsubset*{\infsubset^{*}} + \let\subsetnaeq=\infsubset + \newcommand*{\infsupset}{\supset_{\infty}} + \WithSuffix\def\infsupset*{\infsupset^{*}} + \let\supsetnaeq=\infsupset + \newcommand*{\majsubset}{\subset_{m}} + \newcommand*{\majsupset}{\supset_{m}} \fi } @@ -727,49 +781,49 @@ \AtEndOfPackage{ \ifrecthy@noordinalnotations - \@packinfo{No ordinal notations loading.} + \@packinfo{No ordinal notations loading.} \else - \@packinfo{ordinal notations loading.} + \@packinfo{ordinal notations loading.} -\newcommand*{\wck}{\ensuremath{\omega^{ck}_1}} +\providecommand*{\wck}{\ensuremath{\omega^{ck}_1}} % \newcommand*{\ordtype}[1]{\ensuremath{\@recthy@abs{#1}_{\kleeneO}}} - \newcommand*{\ordzero}{\ensuremath{0}} + \newcommand*{\ordzero}{\ensuremath{0}} \def\kleeneOSYM{\mathcal{O}} - \newcommand*{\kleeneO}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\@kleeneObody} - \newcommand*{\@kleeneObody}{\kleeneOSYM\ifdefined\@PMG@parenarg - ^{\@PMG@parenarg}% - \fi% - \ifdefined\@PMG@braketarg - _{\abs{\@PMG@braketarg}}% - \fi} - \WithSuffix\def\@kleeneObody(#1){\def\@PMG@parenarg{#1}\@kleeneObody} - \WithSuffix\def\@kleeneObody[#1]{\def\@PMG@braketarg{#1}\@kleeneObody} - \WithSuffix\def\@kleeneObody*{\def\kleeneOSYM{\overline{\mathcal{O}}}\@kleeneObody} + \newcommand*{\kleeneO}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\@kleeneObody} + \newcommand*{\@kleeneObody}{\kleeneOSYM\ifdefined\@PMG@parenarg + ^{\@PMG@parenarg}% + \fi% + \ifdefined\@PMG@braketarg + _{\abs{\@PMG@braketarg}}% + \fi} + \WithSuffix\def\@kleeneObody(#1){\def\@PMG@parenarg{#1}\@kleeneObody} + \WithSuffix\def\@kleeneObody[#1]{\def\@PMG@braketarg{#1}\@kleeneObody} + \WithSuffix\def\@kleeneObody*{\def\kleeneOSYM{\overline{\mathcal{O}}}\@kleeneObody} \newcommand*{\kleeneObelow}[2][]{\kleeneOSYM_{<#2\ifthenelse{\isempty{#1}}{}{, #1}}} \let\kleeneOless\kleeneObelow - \newcommand*{\kleeneOuniq}{\kleeneO*} - \let\ordNotations=\kleeneO - \let\uniqOrdNotations=\kleeneOuniq - \newcommand*{\kleeneless}[1][]{<_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \let\kleenel=\kleeneless - \newcommand*{\kleeneleq}[1][]{\leq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \newcommand*{\kleenenless}[1][]{\nless_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \let\kleenenl=\kleenenless - \newcommand*{\kleenenleq}[1][]{\nleq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \newcommand*{\kleenegtr}[1][]{>_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \let\kleeneg=\kleenegtr - \newcommand*{\kleenegeq}[1][]{\geq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \newcommand*{\kleenengtr}[1][]{\ngtr_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \let\kleeneng=\kleenengtr - \newcommand*{\kleenengeq}[1][]{\ngeq_{\kleeneO\ifthenelse{\isempty{#1}}{}{,#1}}} - \newcommand*{\kleenePlus}{\mathbin{+_{\kleeneO}}} - \newcommand*{\kleeneMul}{\cdot_{\kleeneO}} - \newcommand*{\kleenehgt}[1]{\lVert #1\rVert_{\kleeneO}} - \let\hgtO=\kleenehgt - \newcommand*{\kleenelim}[2]{{#1}_{[#2]}} - \newcommand*{\kleenepred}[1]{{#1}^{-}} + \newcommand*{\kleeneOuniq}{\kleeneO*} + \let\ordNotations=\kleeneO + \let\uniqOrdNotations=\kleeneOuniq + \NewDocumentCommand{\kleeneless}{o}{<_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \let\kleenel=\kleeneless + \NewDocumentCommand{\kleeneleq}{o}{\leq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \NewDocumentCommand{\kleenenless}{o}{\nless_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \let\kleenenl=\kleenenless + \NewDocumentCommand{\kleenenleq}{o}{\nleq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \NewDocumentCommand{\kleenegtr}{o}{>_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \let\kleeneg=\kleenegtr + \NewDocumentCommand{\kleenegeq}{o}{\geq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \NewDocumentCommand{\kleenengtr}{o}{\ngtr_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \let\kleeneng=\kleenengtr + \NewDocumentCommand{\kleenengeq}{o}{\ngeq_{\kleeneO\IfNoValueTF{#1}{}{,#1}}} + \newcommand*{\kleenePlus}{\mathbin{+_{\kleeneO}}} + \newcommand*{\kleeneMul}{\cdot_{\kleeneO}} + \newcommand*{\kleenehgt}[1]{\lVert #1\rVert_{\kleeneO}} + \let\hgtO=\kleenehgt + \newcommand*{\kleenelim}[2]{{#1}_{[#2]}} + \newcommand*{\kleenepred}[1]{{#1}^{-}} \fi } @@ -787,19 +841,19 @@ % Forcing \AtEndOfPackage{ \ifrecthy@noforcing - \@packinfo{No forcing loading.} + \@packinfo{No forcing loading.} \else - \@packinfo{forcing loading.} - \newcommand*{\forces}{\def\@PMG@frcparenarg{}\def\@PMG@frcbraketarg{}\def\@PMG@curfrcsym{\Vdash}\@forcesBody} - \newcommand*{\@forcesBody}{\mathrel{{\@PMG@curfrcsym}^{\@PMG@frcparenarg}_{\@PMG@frcbraketarg}}} - \WithSuffix\def\@forcesBody(#1){\def\@PMG@frcparenarg{#1}\@forcesBody} - \WithSuffix\def\@forcesBody[#1]{\def\@PMG@frcbraketarg{#1}\@forcesBody} - \WithSuffix\def\@forcesBody*{\let\@PMG@curfrcsym=\@PMG@VdashStar\@forcesBody} - - % \long\def\forces@[#1][#2]{\Vdash^{#2}_{#1}} - % \newcommand{\forces}{\optparams{\forces@}{[][]}% - % } - \newcommand*{\frc}{\forces} + \@packinfo{forcing loading.} + \providecommand*{\forces}{\def\@PMG@frcparenarg{}\def\@PMG@frcbraketarg{}\def\@PMG@curfrcsym{\Vdash}\@forcesBody} + \newcommand*{\@forcesBody}{\mathrel{{\@PMG@curfrcsym}^{\@PMG@frcparenarg}_{\@PMG@frcbraketarg}}} + \WithSuffix\def\@forcesBody(#1){\def\@PMG@frcparenarg{#1}\@forcesBody} + \WithSuffix\def\@forcesBody[#1]{\def\@PMG@frcbraketarg{#1}\@forcesBody} + \WithSuffix\def\@forcesBody*{\let\@PMG@curfrcsym=\@PMG@VdashStar\@forcesBody} + + % \long\def\forces@[#1][#2]{\Vdash^{#2}_{#1}} + % \newcommand{\forces}{\optparams{\forces@}{[][]}% + % } + \providecommand*{\frc}{\forces} \fi } @@ -810,390 +864,394 @@ \newcommand*{\@recthy@CSigma}{\prescript{\mathcal{C}}{}{\Sigma}} \newcommand*{\@recthy@CPi}{\prescript{\mathcal{C}}{}{\Pi}} -\DeclareOptionX<\@recthy@family>{cdeltasym}[]{\def\@recthy@CDelta{#1}} -\DeclareOptionX<\@recthy@family>{csigmasym}[]{\def\@recthy@CSigma{#1}} -\DeclareOptionX<\@recthy@family>{cpisym}[]{\def\@recthy@CPi{#1}} +\DeclareOptionX{cdeltasym}{\edef\@recthy@CDelta{\expandafter\noexpand\csname #1 \endcsname}} +\DeclareOptionX{csigmasym}{\edef\@recthy@CSigma{\expandafter\noexpand\csname #1 \endcsname}} +\DeclareOptionX{cpisym}{\edef\@recthy@CPi{\expandafter\noexpand\csname #1 \endcsname}} + +% \DeclareOptionX<\@recthy@family>{cdeltasym}[]{\def\@recthy@CDelta{#1}} +% \DeclareOptionX<\@recthy@family>{csigmasym}[]{\def\@recthy@CSigma{#1}} +% \DeclareOptionX<\@recthy@family>{cpisym}[]{\def\@recthy@CPi{#1}} \AtEndOfPackage{ \ifrecthy@nosyntax - \@packinfo{No syntax loading.} + \@packinfo{No syntax loading.} \else - \@packinfo{syntax loading.} - \recthy@strip{CDelta} - \recthy@strip{CSigma} - \recthy@strip{CPi} - \newcommand*{\deltan}[1]{\Delta_{#1}} - \WithSuffix\def\deltan[#1]#2{\Delta^{#1}_{#2}} - % \WithSuffix\def\deltan(#1)#2{\deltan{#2}\!\left(#1\right)} - \newcommand*{\deltaZeroN}[1]{\Delta^{0}_{#1}} - \WithSuffix\def\deltaZeroN[#1]#2{\Delta^{0,#1}_{#2}} - % \WithSuffix\def\deltaZeroN(#1)#2{\deltaZeroN{#2}\!\left(#1\right)} - \newcommand*{\deltaZeroTwo}{\deltaZeroN{2}} - \WithSuffix\def\deltaZeroTwo[#1]{\deltaZeroN[#1]{2}} - % \WithSuffix\def\deltaZeroTwo(#1){\deltaZeroN[#1]{2}} - \newcommand*{\deltaZeroThree}{\deltaZeroN{3}} - \WithSuffix\def\deltaZeroThree[#1]{\deltaZeroN[#1]{3}} - % \WithSuffix\def\deltaZeroThree(#1){\deltaZeroN[#1]{3}} - \newcommand*{\deltaZeroOne}{\deltaZeroN{1}} - \WithSuffix\def\deltaZeroOne[#1]{\deltaZeroN[#1]{1}} - % \WithSuffix\def\deltaZeroOne(#1){\deltaZeroN[#1]{1}} - \newcommand*{\deltaZeroZero}{\deltaZeroN{0}} - \WithSuffix\def\deltaZeroZero[#1]{\deltaZeroN[#1]{0}} - % \WithSuffix\def\deltaZeroZero(#1){\deltaZeroN[#1]{0}} - - - \newcommand*{\deltaOneN}[1]{\deltan{#1}^1} - \WithSuffix\def\deltaOneN[#1]#2{\Delta^{1,#1}_{#2}} - % \WithSuffix\def\deltaOneN(#1)#2{\deltaOneN{#2}\!\left(#1\right)} - \newcommand*{\deltaOneOne}{\deltaOneN{1}} - \WithSuffix\def\deltaOneOne[#1]{\deltaOneN[#1]{1}} - % \WithSuffix\def\deltaOneOne(#1){\deltaOneN[#1]{1}} - \newcommand*{\deltaOneTwo}{\deltaOneN{2}} - \WithSuffix\def\deltaOneTwo[#1]{\deltaOneN[#1]{2}} - % \WithSuffix\def\deltaOneTwo(#1){\deltaOneN[#1]{2}} - \newcommand*{\deltaOneThree}{\deltaOneN{3}} - \WithSuffix\def\deltaOneThree[#1]{\deltaOneN[#1]{3}} - % \WithSuffix\def\deltaOneThree(#1){\deltaOneN[#1]{3}} - - - - \newcommand*{\sigman}[1]{\Sigma_{#1}} - \WithSuffix\def\sigman[#1]#2{\Sigma^{#1}_{#2}} - % \WithSuffix\def\sigman(#1)#2{\sigman{#2}\!\left(#1\right)} - \newcommand*{\sigmaZeroN}[1]{\Sigma^{0}_{#1}} - \WithSuffix\def\sigmaZeroN[#1]#2{\Sigma^{0,#1}_{#2}} - % \WithSuffix\def\sigmaZeroN(#1)#2{\sigmaZeroN{#2}\!\left(#1\right)} - \newcommand*{\sigmaZeroOne}{\sigmaZeroN{1}} - \WithSuffix\def\sigmaZeroOne[#1]{\sigmaZeroN[#1]{1}} - % \WithSuffix\def\sigmaZeroOne(#1){\sigmaZeroN[#1]{1}} - \newcommand*{\sigmaZeroTwo}{\sigmaZeroN{2}} - \WithSuffix\def\sigmaZeroTwo[#1]{\sigmaZeroN[#1]{2}} - % \WithSuffix\def\sigmaZeroTwo(#1){\sigmaZeroN[#1]{2}} - \newcommand*{\sigmaZeroThree}{\sigmaZeroN{3}} - \WithSuffix\def\sigmaZeroThree[#1]{\sigmaZeroN[#1]{3}} - % \WithSuffix\def\sigmaZeroThree(#1){\sigmaZeroN[#1]{3}} - - - - \newcommand*{\sigmaOneN}[1]{\Sigma^1_{#1}} - \WithSuffix\def\sigmaOneN[#1]#2{\Sigma^{1,#1}_{#2}} - % \WithSuffix\def\sigmaOneN(#1)#2{\sigmaOneN{#2}\!\left(#1\right)} - \newcommand*{\sigmaOneOne}{\sigmaOneN{1}} - \WithSuffix\def\sigmaOneOne[#1]{\sigmaOneN[#1]{1}} - % \WithSuffix\def\sigmaOneOne(#1){\sigmaOneN[#1]{1}} - \newcommand*{\sigmaOneTwo}{\sigmaOneN{2}} - \WithSuffix\def\sigmaOneTwo[#1]{\sigmaOneN[#1]{2}} - % \WithSuffix\def\sigmaOneTwo(#1){\sigmaOneN[#1]{2}} - \newcommand*{\sigmaOneThree}{\sigmaOneN{3}} - \WithSuffix\def\sigmaOneThree[#1]{\sigmaOneN[#1]{3}} - % \WithSuffix\def\sigmaOneThree(#1){\sigmaOneN[#1]{3}} - - - - \newcommand*{\pin}[1]{\Pi_{#1}} - \WithSuffix\def\pin[#1]#2{\Pi^{#1}_{#2}} - % \WithSuffix\def\pin(#1)#2{\pin{#2}\!\left(#1\right)} - \newcommand*{\piZeroN}[1]{\Pi^0_{#1}} - \WithSuffix\def\piZeroN[#1]#2{\Pi^{0,#1}_{#2}} - % \WithSuffix\def\piZeroN(#1)#2{\piZeroN{#2}\left(#1\right)} - \newcommand*{\piZeroOne}{\piZeroN{1}} - \WithSuffix\def\piZeroOne[#1]{\piZeroN[#1]{1}} - % \WithSuffix\def\piZeroOne(#1){\piZeroN[#1]{1}} - \newcommand*{\piZeroTwo}{\piZeroN{2}} - \WithSuffix\def\piZeroTwo[#1]{\piZeroN[#1]{2}} - % \WithSuffix\def\piZeroTwo(#1){\piZeroN[#1]{2}} - \newcommand*{\piZeroThree}{\piZeroN{3}} - \WithSuffix\def\piZeroThree[#1]{\piZeroN[#1]{3}} - % \WithSuffix\def\piZeroThree(#1){\piZeroN[#1]{3}} - - \newcommand*{\piOneN}[1]{\Pi^1_{#1}} - \WithSuffix\def\piOneN[#1]#2{\Pi^{1,#1}_{#2}} - % \WithSuffix\def\piOneN(#1)#2{\piOneN{#2}\!\left(#1\right)} - \newcommand*{\piOneOne}{\piOneN{1}} - \WithSuffix\def\piOneOne[#1]{\piOneN[#1]{1}} - % \WithSuffix\def\piOneOne(#1){\piOneN[#1]{1}} - \newcommand*{\piOneTwo}{\piOneN{2}} - \WithSuffix\def\piOneTwo[#1]{\piOneN[#1]{2}} - % \WithSuffix\def\piOneTwo(#1){\piOneN[#1]{2}} - \newcommand*{\piOneThree}{\piOneN{3}} - \WithSuffix\def\piOneThree[#1]{\piOneN[#1]{3}} - % \WithSuffix\def\piOneThree(#1){\piOneN[#1]{3}} - - - - %%%ABREVIATIONS - \newcommand*{\deltaz}{\deltaN{0}} - \newcommand*{\deltazn}{\deltaZeroN} - \newcommand*{\deltazii}{\deltaZeroTwo} - \newcommand*{\deltazi}{\deltaZeroOne} - \newcommand*{\deltazz}{\deltaZeroZero} - \newcommand*{\deltaziii}{\deltaZeroThree} - \newcommand*{\deltaIn}{\deltaOneN} - \newcommand*{\deltaIi}{\deltaOneOne} - \newcommand*{\deltaoneone}{\deltaOneOne} - \newcommand*{\deltaIii}{\deltaOneTwo} - \newcommand*{\deltaIiii}{\deltaOneThree} - \newcommand*{\sigmazn}{\sigmaZeroN} - \newcommand*{\sigmazi}{\sigmaZeroOne} - \newcommand*{\sigmazii}{\sigmaZeroTwo} - \newcommand*{\sigmaziii}{\sigmaZeroThree} - \newcommand*{\sigmaIn}{\sigmaOneN} - \newcommand*{\sigmaIi}{\sigmaOneOne} - \newcommand*{\sigmaIii}{\sigmaOneTwo} - \newcommand*{\sigmaIiii}{\sigmaOneThree} - \newcommand*{\pizn}{\piZeroN} - \newcommand*{\pizi}{\piZeroOne} - \newcommand*{\pizii}{\piZeroTwo} - \newcommand*{\piziii}{\piZeroThree} - \newcommand*{\piIn}{\piOneN} - \newcommand*{\piIi}{\piOneOne} - \newcommand*{\piIii}{\piOneTwo} - \newcommand*{\piIiii}{\piOneThree} - - %%%%%%%%%%%%% - % \newcommand*{\sigmapizn}[1]{\sigmazn{#1} \union \pizn{#1}} - % \WithSuffix\def\sigmapizn[#1]#2{\sigmazn[#1]{#2} \union \pizn[#1]{#2}} - % \WithSuffix\def\sigmapizn(#1)#2{\sigmazn[#1]{#2} \union \pizn[#1]{#2}} - % \let\pisigmazn=\sigmapizn - %%%%%%%%%%%%%% - - %%%%%%%% - % Logics - %\newcommand*{\equiv} - \newcommand*{\logic}[2]{\mathcal{L}_{#1,#2}} - % \newcommand*{\logicwiw}{\logic{\omega_{1}}{\omega}} - % \newcommand*{\Clogic}[2]{\mathcal{CL}_{#1,#2}} - % \newcommand*{\FOlogic}{\logic{\omega}{\omega}} - % \newcommand*{\hyplogic}[1][]{\Clogic{\omega_{1}}{\omega}\ifthenelse{\isempty{#1}}{}{\left(#1\right)} } - - - - %May never use...specific notation for computable formulas...supplanted by \( \sigmazn{\alpha} \) notation. - %%%%%%%%%%% - - - - - - \newcommand*{\Cdeltan}[1]{\CDelta_{#1}} - \WithSuffix\def\Cdeltan[#1]#2{\Cdeltan{#2}^{#1}} - \newcommand*{\Cpin}[1]{\CPi_{#1}} - \WithSuffix\def\Cpin[#1]#2{\Cpin{#2}^{#1}} - \newcommand*{\Csigman}[1]{\CSigma_{#1}} - \WithSuffix\def\Csigman[#1]#2{\CSigma_{#2}^{#1}} + \@packinfo{syntax loading.} + \recthy@strip{CDelta} + \recthy@strip{CSigma} + \recthy@strip{CPi} + \newcommand*{\deltan}[1]{\Delta_{#1}} + \WithSuffix\def\deltan[#1]#2{\Delta^{#1}_{#2}} + % \WithSuffix\def\deltan(#1)#2{\deltan{#2}\!\left(#1\right)} + \newcommand*{\deltaZeroN}[1]{\Delta^{0}_{#1}} + \WithSuffix\def\deltaZeroN[#1]#2{\Delta^{0,#1}_{#2}} + % \WithSuffix\def\deltaZeroN(#1)#2{\deltaZeroN{#2}\!\left(#1\right)} + \newcommand*{\deltaZeroTwo}{\deltaZeroN{2}} + \WithSuffix\def\deltaZeroTwo[#1]{\deltaZeroN[#1]{2}} + % \WithSuffix\def\deltaZeroTwo(#1){\deltaZeroN[#1]{2}} + \newcommand*{\deltaZeroThree}{\deltaZeroN{3}} + \WithSuffix\def\deltaZeroThree[#1]{\deltaZeroN[#1]{3}} + % \WithSuffix\def\deltaZeroThree(#1){\deltaZeroN[#1]{3}} + \newcommand*{\deltaZeroOne}{\deltaZeroN{1}} + \WithSuffix\def\deltaZeroOne[#1]{\deltaZeroN[#1]{1}} + % \WithSuffix\def\deltaZeroOne(#1){\deltaZeroN[#1]{1}} + \newcommand*{\deltaZeroZero}{\deltaZeroN{0}} + \WithSuffix\def\deltaZeroZero[#1]{\deltaZeroN[#1]{0}} + % \WithSuffix\def\deltaZeroZero(#1){\deltaZeroN[#1]{0}} + + + \newcommand*{\deltaOneN}[1]{\deltan{#1}^1} + \WithSuffix\def\deltaOneN[#1]#2{\Delta^{1,#1}_{#2}} + % \WithSuffix\def\deltaOneN(#1)#2{\deltaOneN{#2}\!\left(#1\right)} + \newcommand*{\deltaOneOne}{\deltaOneN{1}} + \WithSuffix\def\deltaOneOne[#1]{\deltaOneN[#1]{1}} + % \WithSuffix\def\deltaOneOne(#1){\deltaOneN[#1]{1}} + \newcommand*{\deltaOneTwo}{\deltaOneN{2}} + \WithSuffix\def\deltaOneTwo[#1]{\deltaOneN[#1]{2}} + % \WithSuffix\def\deltaOneTwo(#1){\deltaOneN[#1]{2}} + \newcommand*{\deltaOneThree}{\deltaOneN{3}} + \WithSuffix\def\deltaOneThree[#1]{\deltaOneN[#1]{3}} + % \WithSuffix\def\deltaOneThree(#1){\deltaOneN[#1]{3}} + + + + \newcommand*{\sigman}[1]{\Sigma_{#1}} + \WithSuffix\def\sigman[#1]#2{\Sigma^{#1}_{#2}} + % \WithSuffix\def\sigman(#1)#2{\sigman{#2}\!\left(#1\right)} + \newcommand*{\sigmaZeroN}[1]{\Sigma^{0}_{#1}} + \WithSuffix\def\sigmaZeroN[#1]#2{\Sigma^{0,#1}_{#2}} + % \WithSuffix\def\sigmaZeroN(#1)#2{\sigmaZeroN{#2}\!\left(#1\right)} + \newcommand*{\sigmaZeroOne}{\sigmaZeroN{1}} + \WithSuffix\def\sigmaZeroOne[#1]{\sigmaZeroN[#1]{1}} + % \WithSuffix\def\sigmaZeroOne(#1){\sigmaZeroN[#1]{1}} + \newcommand*{\sigmaZeroTwo}{\sigmaZeroN{2}} + \WithSuffix\def\sigmaZeroTwo[#1]{\sigmaZeroN[#1]{2}} + % \WithSuffix\def\sigmaZeroTwo(#1){\sigmaZeroN[#1]{2}} + \newcommand*{\sigmaZeroThree}{\sigmaZeroN{3}} + \WithSuffix\def\sigmaZeroThree[#1]{\sigmaZeroN[#1]{3}} + % \WithSuffix\def\sigmaZeroThree(#1){\sigmaZeroN[#1]{3}} + + + + \newcommand*{\sigmaOneN}[1]{\Sigma^1_{#1}} + \WithSuffix\def\sigmaOneN[#1]#2{\Sigma^{1,#1}_{#2}} + % \WithSuffix\def\sigmaOneN(#1)#2{\sigmaOneN{#2}\!\left(#1\right)} + \newcommand*{\sigmaOneOne}{\sigmaOneN{1}} + \WithSuffix\def\sigmaOneOne[#1]{\sigmaOneN[#1]{1}} + % \WithSuffix\def\sigmaOneOne(#1){\sigmaOneN[#1]{1}} + \newcommand*{\sigmaOneTwo}{\sigmaOneN{2}} + \WithSuffix\def\sigmaOneTwo[#1]{\sigmaOneN[#1]{2}} + % \WithSuffix\def\sigmaOneTwo(#1){\sigmaOneN[#1]{2}} + \newcommand*{\sigmaOneThree}{\sigmaOneN{3}} + \WithSuffix\def\sigmaOneThree[#1]{\sigmaOneN[#1]{3}} + % \WithSuffix\def\sigmaOneThree(#1){\sigmaOneN[#1]{3}} + + + + \newcommand*{\pin}[1]{\Pi_{#1}} + \WithSuffix\def\pin[#1]#2{\Pi^{#1}_{#2}} + % \WithSuffix\def\pin(#1)#2{\pin{#2}\!\left(#1\right)} + \newcommand*{\piZeroN}[1]{\Pi^0_{#1}} + \WithSuffix\def\piZeroN[#1]#2{\Pi^{0,#1}_{#2}} + % \WithSuffix\def\piZeroN(#1)#2{\piZeroN{#2}\left(#1\right)} + \newcommand*{\piZeroOne}{\piZeroN{1}} + \WithSuffix\def\piZeroOne[#1]{\piZeroN[#1]{1}} + % \WithSuffix\def\piZeroOne(#1){\piZeroN[#1]{1}} + \newcommand*{\piZeroTwo}{\piZeroN{2}} + \WithSuffix\def\piZeroTwo[#1]{\piZeroN[#1]{2}} + % \WithSuffix\def\piZeroTwo(#1){\piZeroN[#1]{2}} + \newcommand*{\piZeroThree}{\piZeroN{3}} + \WithSuffix\def\piZeroThree[#1]{\piZeroN[#1]{3}} + % \WithSuffix\def\piZeroThree(#1){\piZeroN[#1]{3}} + + \newcommand*{\piOneN}[1]{\Pi^1_{#1}} + \WithSuffix\def\piOneN[#1]#2{\Pi^{1,#1}_{#2}} + % \WithSuffix\def\piOneN(#1)#2{\piOneN{#2}\!\left(#1\right)} + \newcommand*{\piOneOne}{\piOneN{1}} + \WithSuffix\def\piOneOne[#1]{\piOneN[#1]{1}} + % \WithSuffix\def\piOneOne(#1){\piOneN[#1]{1}} + \newcommand*{\piOneTwo}{\piOneN{2}} + \WithSuffix\def\piOneTwo[#1]{\piOneN[#1]{2}} + % \WithSuffix\def\piOneTwo(#1){\piOneN[#1]{2}} + \newcommand*{\piOneThree}{\piOneN{3}} + \WithSuffix\def\piOneThree[#1]{\piOneN[#1]{3}} + % \WithSuffix\def\piOneThree(#1){\piOneN[#1]{3}} + + + + %%%ABREVIATIONS + \newcommand*{\deltaz}{\deltaN{0}} + \newcommand*{\deltazn}{\deltaZeroN} + \newcommand*{\deltazii}{\deltaZeroTwo} + \newcommand*{\deltazi}{\deltaZeroOne} + \newcommand*{\deltazz}{\deltaZeroZero} + \newcommand*{\deltaziii}{\deltaZeroThree} + \newcommand*{\deltaIn}{\deltaOneN} + \newcommand*{\deltaIi}{\deltaOneOne} + \newcommand*{\deltaoneone}{\deltaOneOne} + \newcommand*{\deltaIii}{\deltaOneTwo} + \newcommand*{\deltaIiii}{\deltaOneThree} + \newcommand*{\sigmazn}{\sigmaZeroN} + \newcommand*{\sigmazi}{\sigmaZeroOne} + \newcommand*{\sigmazii}{\sigmaZeroTwo} + \newcommand*{\sigmaziii}{\sigmaZeroThree} + \newcommand*{\sigmaIn}{\sigmaOneN} + \newcommand*{\sigmaIi}{\sigmaOneOne} + \newcommand*{\sigmaIii}{\sigmaOneTwo} + \newcommand*{\sigmaIiii}{\sigmaOneThree} + \newcommand*{\pizn}{\piZeroN} + \newcommand*{\pizi}{\piZeroOne} + \newcommand*{\pizii}{\piZeroTwo} + \newcommand*{\piziii}{\piZeroThree} + \newcommand*{\piIn}{\piOneN} + \newcommand*{\piIi}{\piOneOne} + \newcommand*{\piIii}{\piOneTwo} + \newcommand*{\piIiii}{\piOneThree} + + %%%%%%%%%%%%% + % \newcommand*{\sigmapizn}[1]{\sigmazn{#1} \union \pizn{#1}} + % \WithSuffix\def\sigmapizn[#1]#2{\sigmazn[#1]{#2} \union \pizn[#1]{#2}} + % \WithSuffix\def\sigmapizn(#1)#2{\sigmazn[#1]{#2} \union \pizn[#1]{#2}} + % \let\pisigmazn=\sigmapizn + %%%%%%%%%%%%%% + + %%%%%%%% + % Logics + %\newcommand*{\equiv} + \newcommand*{\logic}[2]{\mathcal{L}_{#1,#2}} + % \newcommand*{\logicwiw}{\logic{\omega_{1}}{\omega}} + % \newcommand*{\Clogic}[2]{\mathcal{CL}_{#1,#2}} + % \newcommand*{\FOlogic}{\logic{\omega}{\omega}} + % \NewDocumentCommand{\hyplogic}{o}{\Clogic{\omega_{1}}{\omega}\ifthenelse{\isempty{#1}}{}{\left(#1\right)} } + + + + %May never use...specific notation for computable formulas...supplanted by \( \sigmazn{\alpha} \) notation. + %%%%%%%%%%% + + + + + + \newcommand*{\Cdeltan}[1]{\CDelta_{#1}} + \WithSuffix\def\Cdeltan[#1]#2{\Cdeltan{#2}^{#1}} + \newcommand*{\Cpin}[1]{\CPi_{#1}} + \WithSuffix\def\Cpin[#1]#2{\Cpin{#2}^{#1}} + \newcommand*{\Csigman}[1]{\CSigma_{#1}} + \WithSuffix\def\Csigman[#1]#2{\CSigma_{#2}^{#1}} \newcommand*{\CdeltaZeroN}[1]{\Cdeltan[0]{#1}} - \newcommand*{\CdeltaZeroTwo}{\CdeltaZeroN{2}} - \newcommand*{\CdeltaZeroThree}{\CdeltaZeroN{3}} - \newcommand*{\CdeltaZeroOne}{\CdeltaZeroN{1}} - \newcommand*{\CdeltaZeroZero}{\CdeltaZeroN{0}} - \newcommand*{\CdeltaOneN}[1]{\Cdeltan[1]{#1}} - \newcommand*{\CdeltaOneOne}{\CdeltaOneN{1}} - \newcommand*{\CdeltaOneTwo}{\CdeltaOneN{2}} - \newcommand*{\CdeltaOneThree}{\CdeltaOneN{3}} + \newcommand*{\CdeltaZeroTwo}{\CdeltaZeroN{2}} + \newcommand*{\CdeltaZeroThree}{\CdeltaZeroN{3}} + \newcommand*{\CdeltaZeroOne}{\CdeltaZeroN{1}} + \newcommand*{\CdeltaZeroZero}{\CdeltaZeroN{0}} + \newcommand*{\CdeltaOneN}[1]{\Cdeltan[1]{#1}} + \newcommand*{\CdeltaOneOne}{\CdeltaOneN{1}} + \newcommand*{\CdeltaOneTwo}{\CdeltaOneN{2}} + \newcommand*{\CdeltaOneThree}{\CdeltaOneN{3}} \newcommand*{\CpiZeroN}[1]{\Cpin[0]{#1}} - \newcommand*{\CpiOneN}[1]{\Cpin[1]{#1}} - \newcommand*{\CpiOneOne}{\CpiOneN{1}} - \newcommand*{\CpiOneThree}{\CpiOneN{3}} - \newcommand*{\CpiOneTwo}{\CpiOneN{2}} - \newcommand*{\CpiZeroOne}{\CpiZeroN{1}} - \newcommand*{\CpiZeroThree}{\CpiZeroN{3}} - \newcommand*{\CpiZeroTwo}{\CpiZeroN{2}} - \newcommand*{\CsigmaOneN}[1]{\Csigman[1]{#1}} - \newcommand*{\CsigmaOneOne}{\CsigmaOneN{1}} - \newcommand*{\CsigmaOneThree}{\CsigmaOneN{3}} - \newcommand*{\CsigmaOneTwo}{\CsigmaOneN{2}} - \newcommand*{\CsigmaZeroN}[1]{\Csigman[0]{#1}} - \newcommand*{\CsigmaZeroOne}{\CsigmaZeroN{1}} - \newcommand*{\CsigmaZeroThree}{\CsigmaZeroN{3}} - \newcommand*{\CsigmaZeroTwo}{\CsigmaZeroN{2}} - - - \WithSuffix\def\CsigmaOneN[#1]#2{\Csigma[1,#1]{#2}} - \WithSuffix\def\CsigmaOneOne[#1]{\CsigmaOneN[#1]{1}} - \WithSuffix\def\CsigmaOneThree[#1]{\CsigmaOneN[#1]{3}} - \WithSuffix\def\CsigmaOneTwo[#1]{\CsigmaOneN[#1]{2}} - \WithSuffix\def\CsigmaZeroN[#1]#2{\Csigma[0,#1]{#2}} - \WithSuffix\def\CsigmaZeroOne[#1]{\CsigmaZeroN[#1]{1}} - \WithSuffix\def\CsigmaZeroThree[#1]{\CsigmaZeroN[#1]{3}} - \WithSuffix\def\CsigmaZeroTwo[#1]{\CsigmaZeroN[#1]{2}} + \newcommand*{\CpiOneN}[1]{\Cpin[1]{#1}} + \newcommand*{\CpiOneOne}{\CpiOneN{1}} + \newcommand*{\CpiOneThree}{\CpiOneN{3}} + \newcommand*{\CpiOneTwo}{\CpiOneN{2}} + \newcommand*{\CpiZeroOne}{\CpiZeroN{1}} + \newcommand*{\CpiZeroThree}{\CpiZeroN{3}} + \newcommand*{\CpiZeroTwo}{\CpiZeroN{2}} + \newcommand*{\CsigmaOneN}[1]{\Csigman[1]{#1}} + \newcommand*{\CsigmaOneOne}{\CsigmaOneN{1}} + \newcommand*{\CsigmaOneThree}{\CsigmaOneN{3}} + \newcommand*{\CsigmaOneTwo}{\CsigmaOneN{2}} + \newcommand*{\CsigmaZeroN}[1]{\Csigman[0]{#1}} + \newcommand*{\CsigmaZeroOne}{\CsigmaZeroN{1}} + \newcommand*{\CsigmaZeroThree}{\CsigmaZeroN{3}} + \newcommand*{\CsigmaZeroTwo}{\CsigmaZeroN{2}} + + + \WithSuffix\def\CsigmaOneN[#1]#2{\Csigma[1,#1]{#2}} + \WithSuffix\def\CsigmaOneOne[#1]{\CsigmaOneN[#1]{1}} + \WithSuffix\def\CsigmaOneThree[#1]{\CsigmaOneN[#1]{3}} + \WithSuffix\def\CsigmaOneTwo[#1]{\CsigmaOneN[#1]{2}} + \WithSuffix\def\CsigmaZeroN[#1]#2{\Csigma[0,#1]{#2}} + \WithSuffix\def\CsigmaZeroOne[#1]{\CsigmaZeroN[#1]{1}} + \WithSuffix\def\CsigmaZeroThree[#1]{\CsigmaZeroN[#1]{3}} + \WithSuffix\def\CsigmaZeroTwo[#1]{\CsigmaZeroN[#1]{2}} \WithSuffix\def\CpiOneN[#1]#2{\Cpi[1,#1]{#2}} - \WithSuffix\def\CpiOneOne[#1]{\CpiOneN[#1]{1}} - \WithSuffix\def\CpiOneThree[#1]{\CpiOneN[#1]{3}} - \WithSuffix\def\CpiOneTwo[#1]{\CpiOneN[#1]{2}} - \WithSuffix\def\CpiZeroN[#1]#2{\Cpi[0,#1]{#2}} - \WithSuffix\def\CpiZeroOne[#1]{\CpiZeroN[#1]{1}} - \WithSuffix\def\CpiZeroThree[#1]{\CpiZeroN[#1]{3}} - \WithSuffix\def\CpiZeroTwo[#1]{\CpiZeroN[#1]{2}} + \WithSuffix\def\CpiOneOne[#1]{\CpiOneN[#1]{1}} + \WithSuffix\def\CpiOneThree[#1]{\CpiOneN[#1]{3}} + \WithSuffix\def\CpiOneTwo[#1]{\CpiOneN[#1]{2}} + \WithSuffix\def\CpiZeroN[#1]#2{\Cpi[0,#1]{#2}} + \WithSuffix\def\CpiZeroOne[#1]{\CpiZeroN[#1]{1}} + \WithSuffix\def\CpiZeroThree[#1]{\CpiZeroN[#1]{3}} + \WithSuffix\def\CpiZeroTwo[#1]{\CpiZeroN[#1]{2}} \WithSuffix\def\CdeltaOneN[#1]#2{\Cdelta[1,#1]{#2}} - \WithSuffix\def\CdeltaOneOne[#1]{\CdeltaOneN[#1]{1}} - \WithSuffix\def\CdeltaOneTwo[#1]{\CdeltaOneN[#1]{2}} - \WithSuffix\def\CdeltaOneThree[#1]{\CdeltaOneN[#1]{3}} + \WithSuffix\def\CdeltaOneOne[#1]{\CdeltaOneN[#1]{1}} + \WithSuffix\def\CdeltaOneTwo[#1]{\CdeltaOneN[#1]{2}} + \WithSuffix\def\CdeltaOneThree[#1]{\CdeltaOneN[#1]{3}} \WithSuffix\def\CdeltaZeroZero[#1]{\CdeltaZeroN[#1]{0}} - \WithSuffix\def\CdeltaZeroN[#1]#2{\Cdelta[0,#1]{#2}} + \WithSuffix\def\CdeltaZeroN[#1]#2{\Cdelta[0,#1]{#2}} \WithSuffix\def\CdeltaZeroTwo[#1]{\CdeltaZeroN[#1]{2}} \WithSuffix\def\CdeltaZeroThree[#1]{\CdeltaZeroN[#1]{3}} \WithSuffix\def\CdeltaZeroOne[#1]{\CdeltaZeroN[#1]{1}} - %%%ABREVIATIONS - \newcommand*{\Cdeltaz}{\CdeltaN{0}} - \newcommand*{\Cdeltazn}{\CdeltaZeroN} - \newcommand*{\Cdeltazii}{\CdeltaZeroTwo} - \newcommand*{\Cdeltazi}{\CdeltaZeroOne} - \newcommand*{\Cdeltazz}{\CdeltaZeroZero} - \newcommand*{\Cdeltaziii}{\CdeltaZeroThree} - \newcommand*{\CdeltaIn}{\CdeltaOneN} - \newcommand*{\CdeltaIi}{\CdeltaOneOne} - \newcommand*{\Cdeltaoneone}{\CdeltaOneOne} - \newcommand*{\CdeltaIii}{\CdeltaOneTwo} - \newcommand*{\CdeltaIiii}{\CdeltaOneThree} - \newcommand*{\Csigmazn}{\CsigmaZeroN} - \newcommand*{\Csigmazi}{\CsigmaZeroOne} - \newcommand*{\Csigmazii}{\CsigmaZeroTwo} - \newcommand*{\Csigmaziii}{\CsigmaZeroThree} - \newcommand*{\CsigmaIn}{\CsigmaOneN} - \newcommand*{\CsigmaIi}{\CsigmaOneOne} - \newcommand*{\CsigmaIii}{\CsigmaOneTwo} - \newcommand*{\CsigmaIiii}{\CsigmaOneThree} - \newcommand*{\Cpizn}{\CpiZeroN} - \newcommand*{\Cpizi}{\CpiZeroOne} - \newcommand*{\Cpizii}{\CpiZeroTwo} - \newcommand*{\Cpiziii}{\CpiZeroThree} - \newcommand*{\CpiIn}{\CpiOneN} - \newcommand*{\CpiIi}{\CpiOneOne} - \newcommand*{\CpiIii}{\CpiOneTwo} - \newcommand*{\CpiIiii}{\CpiOneThree} + %%%ABREVIATIONS + \newcommand*{\Cdeltaz}{\CdeltaN{0}} + \newcommand*{\Cdeltazn}{\CdeltaZeroN} + \newcommand*{\Cdeltazii}{\CdeltaZeroTwo} + \newcommand*{\Cdeltazi}{\CdeltaZeroOne} + \newcommand*{\Cdeltazz}{\CdeltaZeroZero} + \newcommand*{\Cdeltaziii}{\CdeltaZeroThree} + \newcommand*{\CdeltaIn}{\CdeltaOneN} + \newcommand*{\CdeltaIi}{\CdeltaOneOne} + \newcommand*{\Cdeltaoneone}{\CdeltaOneOne} + \newcommand*{\CdeltaIii}{\CdeltaOneTwo} + \newcommand*{\CdeltaIiii}{\CdeltaOneThree} + \newcommand*{\Csigmazn}{\CsigmaZeroN} + \newcommand*{\Csigmazi}{\CsigmaZeroOne} + \newcommand*{\Csigmazii}{\CsigmaZeroTwo} + \newcommand*{\Csigmaziii}{\CsigmaZeroThree} + \newcommand*{\CsigmaIn}{\CsigmaOneN} + \newcommand*{\CsigmaIi}{\CsigmaOneOne} + \newcommand*{\CsigmaIii}{\CsigmaOneTwo} + \newcommand*{\CsigmaIiii}{\CsigmaOneThree} + \newcommand*{\Cpizn}{\CpiZeroN} + \newcommand*{\Cpizi}{\CpiZeroOne} + \newcommand*{\Cpizii}{\CpiZeroTwo} + \newcommand*{\Cpiziii}{\CpiZeroThree} + \newcommand*{\CpiIn}{\CpiOneN} + \newcommand*{\CpiIi}{\CpiOneOne} + \newcommand*{\CpiIii}{\CpiOneTwo} + \newcommand*{\CpiIiii}{\CpiOneThree} %%%BOLDFACE - \newcommand*{\Deltan}[1]{\utilde{\mathbf{\Delta}}_{#1}} - \WithSuffix\def\Deltan[#1]#2{\utilde{\mathbf{\Delta}}^{#1}_{#2}} - % \WithSuffix\def\Deltan(#1)#2{\deltan{#2}\!\left(#1\right)} - \newcommand*{\DeltaZeroN}[1]{\utilde{\mathbf{\Delta}}^{0}_{#1}} - \WithSuffix\def\DeltaZeroN[#1]#2{\utilde{\mathbf{\Delta}}^{0,#1}_{#2}} - % \WithSuffix\def\DeltaZeroN(#1)#2{\DeltaZeroN{#2}\!\left(#1\right)} - \newcommand*{\DeltaZeroTwo}{\DeltaZeroN{2}} - \WithSuffix\def\DeltaZeroTwo[#1]{\DeltaZeroN[#1]{2}} - % \WithSuffix\def\DeltaZeroTwo(#1){\DeltaZeroN[#1]{2}} - \newcommand*{\DeltaZeroThree}{\DeltaZeroN{3}} - \WithSuffix\def\DeltaZeroThree[#1]{\DeltaZeroN[#1]{3}} - % \WithSuffix\def\DeltaZeroThree(#1){\DeltaZeroN[#1]{3}} - \newcommand*{\DeltaZeroOne}{\DeltaZeroN{1}} - \WithSuffix\def\DeltaZeroOne[#1]{\DeltaZeroN[#1]{1}} - % \WithSuffix\def\DeltaZeroOne(#1){\DeltaZeroN[#1]{1}} - \newcommand*{\DeltaZeroZero}{\DeltaZeroN{0}} - \WithSuffix\def\DeltaZeroZero[#1]{\DeltaZeroN[#1]{0}} - % \WithSuffix\def\DeltaZeroZero(#1){\DeltaZeroN[#1]{0}} - - - \newcommand*{\DeltaOneN}[1]{\Deltan{#1}^1} - \WithSuffix\def\DeltaOneN[#1]#2{\utilde{\mathbf{\Delta}}^{1,#1}_{#2}} - % \WithSuffix\def\DeltaOneN(#1)#2{\DeltaOneN{#2}\!\left(#1\right)} - \newcommand*{\DeltaOneOne}{\DeltaOneN{1}} - \WithSuffix\def\DeltaOneOne[#1]{\DeltaOneN[#1]{1}} - % \WithSuffix\def\DeltaOneOne(#1){\DeltaOneN[#1]{1}} - \newcommand*{\DeltaOneTwo}{\DeltaOneN{2}} - \WithSuffix\def\DeltaOneTwo[#1]{\DeltaOneN[#1]{2}} - % \WithSuffix\def\DeltaOneTwo(#1){\DeltaOneN[#1]{2}} - \newcommand*{\DeltaOneThree}{\DeltaOneN{3}} - \WithSuffix\def\DeltaOneThree[#1]{\DeltaOneN[#1]{3}} - % \WithSuffix\def\DeltaOneThree(#1){\DeltaOneN[#1]{3}} - - - - \newcommand*{\Sigman}[1]{\utilde{\mathbf{\Sigma}}_{#1}} - \WithSuffix\def\Sigman[#1]#2{\utilde{\mathbf{\Sigma}}^{#1}_{#2}} - % \WithSuffix\def\Sigman(#1)#2{\sigman{#2}\!\left(#1\right)} - \newcommand*{\SigmaZeroN}[1]{\utilde{\mathbf{\Sigma}}^{0}_{#1}} - \WithSuffix\def\SigmaZeroN[#1]#2{\utilde{\mathbf{\Sigma}}^{0,#1}_{#2}} - % \WithSuffix\def\SigmaZeroN(#1)#2{\SigmaZeroN{#2}\!\left(#1\right)} - \newcommand*{\SigmaZeroOne}{\SigmaZeroN{1}} - \WithSuffix\def\SigmaZeroOne[#1]{\SigmaZeroN[#1]{1}} - % \WithSuffix\def\SigmaZeroOne(#1){\SigmaZeroN[#1]{1}} - \newcommand*{\SigmaZeroTwo}{\SigmaZeroN{2}} - \WithSuffix\def\SigmaZeroTwo[#1]{\SigmaZeroN[#1]{2}} - % \WithSuffix\def\SigmaZeroTwo(#1){\SigmaZeroN[#1]{2}} - \newcommand*{\SigmaZeroThree}{\SigmaZeroN{3}} - \WithSuffix\def\SigmaZeroThree[#1]{\SigmaZeroN[#1]{3}} - % \WithSuffix\def\SigmaZeroThree(#1){\SigmaZeroN[#1]{3}} - - - - \newcommand*{\SigmaOneN}[1]{\utilde{\mathbf{\Sigma}}^1_{#1}} - \WithSuffix\def\SigmaOneN[#1]#2{\utilde{\mathbf{\Sigma}}^{1,#1}_{#2}} - % \WithSuffix\def\SigmaOneN(#1)#2{\SigmaOneN{#2}\!\left(#1\right)} - \newcommand*{\SigmaOneOne}{\SigmaOneN{1}} - \WithSuffix\def\SigmaOneOne[#1]{\SigmaOneN[#1]{1}} - % \WithSuffix\def\SigmaOneOne(#1){\SigmaOneN[#1]{1}} - \newcommand*{\SigmaOneTwo}{\SigmaOneN{2}} - \WithSuffix\def\SigmaOneTwo[#1]{\SigmaOneN[#1]{2}} - % \WithSuffix\def\SigmaOneTwo(#1){\SigmaOneN[#1]{2}} - \newcommand*{\SigmaOneThree}{\SigmaOneN{3}} - \WithSuffix\def\SigmaOneThree[#1]{\SigmaOneN[#1]{3}} - % \WithSuffix\def\SigmaOneThree(#1){\SigmaOneN[#1]{3}} - - - - \newcommand*{\Pin}[1]{\utilde{\mathbf{\Pi}}_{#1}} - \WithSuffix\def\Pin[#1]#2{\utilde{\mathbf{\Pi}}^{#1}_{#2}} - % \WithSuffix\def\Pin(#1)#2{\pin{#2}\!\left(#1\right)} - \newcommand*{\PiZeroN}[1]{\utilde{\mathbf{\Pi}}^0_{#1}} - \WithSuffix\def\PiZeroN[#1]#2{\utilde{\mathbf{\Pi}}^{0,#1}_{#2}} - % \WithSuffix\def\PiZeroN(#1)#2{\PiZeroN{#2}\left(#1\right)} - \newcommand*{\PiZeroOne}{\PiZeroN{1}} - \WithSuffix\def\PiZeroOne[#1]{\PiZeroN[#1]{1}} - % \WithSuffix\def\PiZeroOne(#1){\PiZeroN[#1]{1}} - \newcommand*{\PiZeroTwo}{\PiZeroN{2}} - \WithSuffix\def\PiZeroTwo[#1]{\PiZeroN[#1]{2}} - % \WithSuffix\def\PiZeroTwo(#1){\PiZeroN[#1]{2}} - \newcommand*{\PiZeroThree}{\PiZeroN{3}} - \WithSuffix\def\PiZeroThree[#1]{\PiZeroN[#1]{3}} - % \WithSuffix\def\PiZeroThree(#1){\PiZeroN[#1]{3}} - - \newcommand*{\PiOneN}[1]{\utilde{\mathbf{\Pi}}^1_{#1}} - \WithSuffix\def\PiOneN[#1]#2{\utilde{\mathbf{\Pi}}^{1,#1}_{#2}} - % \WithSuffix\def\PiOneN(#1)#2{\PiOneN{#2}\!\left(#1\right)} - \newcommand*{\PiOneOne}{\PiOneN{1}} - \WithSuffix\def\PiOneOne[#1]{\PiOneN[#1]{1}} - % \WithSuffix\def\PiOneOne(#1){\PiOneN[#1]{1}} - \newcommand*{\PiOneTwo}{\PiOneN{2}} - \WithSuffix\def\PiOneTwo[#1]{\PiOneN[#1]{2}} - % \WithSuffix\def\PiOneTwo(#1){\PiOneN[#1]{2}} - \newcommand*{\PiOneThree}{\PiOneN{3}} - \WithSuffix\def\PiOneThree[#1]{\PiOneN[#1]{3}} - % \WithSuffix\def\PiOneThree(#1){\PiOneN[#1]{3}} - - - - %%%ABREVIATIONS - \newcommand*{\Deltaz}{\deltaN{0}} - \newcommand*{\Deltazn}{\DeltaZeroN} - \newcommand*{\Deltazii}{\DeltaZeroTwo} - \newcommand*{\Deltazi}{\DeltaZeroOne} - \newcommand*{\Deltazz}{\DeltaZeroZero} - \newcommand*{\Deltaziii}{\DeltaZeroThree} - \newcommand*{\DeltaIn}{\DeltaOneN} - \newcommand*{\DeltaIi}{\DeltaOneOne} - \newcommand*{\Deltaoneone}{\DeltaOneOne} - \newcommand*{\DeltaIii}{\DeltaOneTwo} - \newcommand*{\DeltaIiii}{\DeltaOneThree} - \newcommand*{\Sigmazn}{\SigmaZeroN} - \newcommand*{\Sigmazi}{\SigmaZeroOne} - \newcommand*{\Sigmazii}{\SigmaZeroTwo} - \newcommand*{\Sigmaziii}{\SigmaZeroThree} - \newcommand*{\SigmaIn}{\SigmaOneN} - \newcommand*{\SigmaIi}{\SigmaOneOne} - \newcommand*{\SigmaIii}{\SigmaOneTwo} - \newcommand*{\SigmaIiii}{\SigmaOneThree} - \newcommand*{\Pizn}{\PiZeroN} - \newcommand*{\Pizi}{\PiZeroOne} - \newcommand*{\Pizii}{\PiZeroTwo} - \newcommand*{\Piziii}{\PiZeroThree} - \newcommand*{\PiIn}{\PiOneN} - \newcommand*{\PiIi}{\PiOneOne} - \newcommand*{\PiIii}{\PiOneTwo} - \newcommand*{\PiIiii}{\PiOneThree} + \newcommand*{\Deltan}[1]{\utilde{\symbf{\Delta}}_{#1}} + \WithSuffix\def\Deltan[#1]#2{\utilde{\symbf{\Delta}}^{#1}_{#2}} + % \WithSuffix\def\Deltan(#1)#2{\deltan{#2}\!\left(#1\right)} + \newcommand*{\DeltaZeroN}[1]{\utilde{\symbf{\Delta}}^{0}_{#1}} + \WithSuffix\def\DeltaZeroN[#1]#2{\utilde{\symbf{\Delta}}^{0,#1}_{#2}} + % \WithSuffix\def\DeltaZeroN(#1)#2{\DeltaZeroN{#2}\!\left(#1\right)} + \newcommand*{\DeltaZeroTwo}{\DeltaZeroN{2}} + \WithSuffix\def\DeltaZeroTwo[#1]{\DeltaZeroN[#1]{2}} + % \WithSuffix\def\DeltaZeroTwo(#1){\DeltaZeroN[#1]{2}} + \newcommand*{\DeltaZeroThree}{\DeltaZeroN{3}} + \WithSuffix\def\DeltaZeroThree[#1]{\DeltaZeroN[#1]{3}} + % \WithSuffix\def\DeltaZeroThree(#1){\DeltaZeroN[#1]{3}} + \newcommand*{\DeltaZeroOne}{\DeltaZeroN{1}} + \WithSuffix\def\DeltaZeroOne[#1]{\DeltaZeroN[#1]{1}} + % \WithSuffix\def\DeltaZeroOne(#1){\DeltaZeroN[#1]{1}} + \newcommand*{\DeltaZeroZero}{\DeltaZeroN{0}} + \WithSuffix\def\DeltaZeroZero[#1]{\DeltaZeroN[#1]{0}} + % \WithSuffix\def\DeltaZeroZero(#1){\DeltaZeroN[#1]{0}} + + + \newcommand*{\DeltaOneN}[1]{\Deltan{#1}^1} + \WithSuffix\def\DeltaOneN[#1]#2{\utilde{\symbf{\Delta}}^{1,#1}_{#2}} + % \WithSuffix\def\DeltaOneN(#1)#2{\DeltaOneN{#2}\!\left(#1\right)} + \newcommand*{\DeltaOneOne}{\DeltaOneN{1}} + \WithSuffix\def\DeltaOneOne[#1]{\DeltaOneN[#1]{1}} + % \WithSuffix\def\DeltaOneOne(#1){\DeltaOneN[#1]{1}} + \newcommand*{\DeltaOneTwo}{\DeltaOneN{2}} + \WithSuffix\def\DeltaOneTwo[#1]{\DeltaOneN[#1]{2}} + % \WithSuffix\def\DeltaOneTwo(#1){\DeltaOneN[#1]{2}} + \newcommand*{\DeltaOneThree}{\DeltaOneN{3}} + \WithSuffix\def\DeltaOneThree[#1]{\DeltaOneN[#1]{3}} + % \WithSuffix\def\DeltaOneThree(#1){\DeltaOneN[#1]{3}} + + + + \newcommand*{\Sigman}[1]{\utilde{\symbf{\Sigma}}_{#1}} + \WithSuffix\def\Sigman[#1]#2{\utilde{\symbf{\Sigma}}^{#1}_{#2}} + % \WithSuffix\def\Sigman(#1)#2{\sigman{#2}\!\left(#1\right)} + \newcommand*{\SigmaZeroN}[1]{\utilde{\symbf{\Sigma}}^{0}_{#1}} + \WithSuffix\def\SigmaZeroN[#1]#2{\utilde{\symbf{\Sigma}}^{0,#1}_{#2}} + % \WithSuffix\def\SigmaZeroN(#1)#2{\SigmaZeroN{#2}\!\left(#1\right)} + \newcommand*{\SigmaZeroOne}{\SigmaZeroN{1}} + \WithSuffix\def\SigmaZeroOne[#1]{\SigmaZeroN[#1]{1}} + % \WithSuffix\def\SigmaZeroOne(#1){\SigmaZeroN[#1]{1}} + \newcommand*{\SigmaZeroTwo}{\SigmaZeroN{2}} + \WithSuffix\def\SigmaZeroTwo[#1]{\SigmaZeroN[#1]{2}} + % \WithSuffix\def\SigmaZeroTwo(#1){\SigmaZeroN[#1]{2}} + \newcommand*{\SigmaZeroThree}{\SigmaZeroN{3}} + \WithSuffix\def\SigmaZeroThree[#1]{\SigmaZeroN[#1]{3}} + % \WithSuffix\def\SigmaZeroThree(#1){\SigmaZeroN[#1]{3}} + + + + \newcommand*{\SigmaOneN}[1]{\utilde{\symbf{\Sigma}}^1_{#1}} + \WithSuffix\def\SigmaOneN[#1]#2{\utilde{\symbf{\Sigma}}^{1,#1}_{#2}} + % \WithSuffix\def\SigmaOneN(#1)#2{\SigmaOneN{#2}\!\left(#1\right)} + \newcommand*{\SigmaOneOne}{\SigmaOneN{1}} + \WithSuffix\def\SigmaOneOne[#1]{\SigmaOneN[#1]{1}} + % \WithSuffix\def\SigmaOneOne(#1){\SigmaOneN[#1]{1}} + \newcommand*{\SigmaOneTwo}{\SigmaOneN{2}} + \WithSuffix\def\SigmaOneTwo[#1]{\SigmaOneN[#1]{2}} + % \WithSuffix\def\SigmaOneTwo(#1){\SigmaOneN[#1]{2}} + \newcommand*{\SigmaOneThree}{\SigmaOneN{3}} + \WithSuffix\def\SigmaOneThree[#1]{\SigmaOneN[#1]{3}} + % \WithSuffix\def\SigmaOneThree(#1){\SigmaOneN[#1]{3}} + + + + \newcommand*{\Pin}[1]{\utilde{\symbf{\Pi}}_{#1}} + \WithSuffix\def\Pin[#1]#2{\utilde{\symbf{\Pi}}^{#1}_{#2}} + % \WithSuffix\def\Pin(#1)#2{\pin{#2}\!\left(#1\right)} + \newcommand*{\PiZeroN}[1]{\utilde{\symbf{\Pi}}^0_{#1}} + \WithSuffix\def\PiZeroN[#1]#2{\utilde{\symbf{\Pi}}^{0,#1}_{#2}} + % \WithSuffix\def\PiZeroN(#1)#2{\PiZeroN{#2}\left(#1\right)} + \newcommand*{\PiZeroOne}{\PiZeroN{1}} + \WithSuffix\def\PiZeroOne[#1]{\PiZeroN[#1]{1}} + % \WithSuffix\def\PiZeroOne(#1){\PiZeroN[#1]{1}} + \newcommand*{\PiZeroTwo}{\PiZeroN{2}} + \WithSuffix\def\PiZeroTwo[#1]{\PiZeroN[#1]{2}} + % \WithSuffix\def\PiZeroTwo(#1){\PiZeroN[#1]{2}} + \newcommand*{\PiZeroThree}{\PiZeroN{3}} + \WithSuffix\def\PiZeroThree[#1]{\PiZeroN[#1]{3}} + % \WithSuffix\def\PiZeroThree(#1){\PiZeroN[#1]{3}} + + \newcommand*{\PiOneN}[1]{\utilde{\symbf{\Pi}}^1_{#1}} + \WithSuffix\def\PiOneN[#1]#2{\utilde{\symbf{\Pi}}^{1,#1}_{#2}} + % \WithSuffix\def\PiOneN(#1)#2{\PiOneN{#2}\!\left(#1\right)} + \newcommand*{\PiOneOne}{\PiOneN{1}} + \WithSuffix\def\PiOneOne[#1]{\PiOneN[#1]{1}} + % \WithSuffix\def\PiOneOne(#1){\PiOneN[#1]{1}} + \newcommand*{\PiOneTwo}{\PiOneN{2}} + \WithSuffix\def\PiOneTwo[#1]{\PiOneN[#1]{2}} + % \WithSuffix\def\PiOneTwo(#1){\PiOneN[#1]{2}} + \newcommand*{\PiOneThree}{\PiOneN{3}} + \WithSuffix\def\PiOneThree[#1]{\PiOneN[#1]{3}} + % \WithSuffix\def\PiOneThree(#1){\PiOneN[#1]{3}} + + + + %%%ABREVIATIONS + \newcommand*{\Deltaz}{\deltaN{0}} + \newcommand*{\Deltazn}{\DeltaZeroN} + \newcommand*{\Deltazii}{\DeltaZeroTwo} + \newcommand*{\Deltazi}{\DeltaZeroOne} + \newcommand*{\Deltazz}{\DeltaZeroZero} + \newcommand*{\Deltaziii}{\DeltaZeroThree} + \newcommand*{\DeltaIn}{\DeltaOneN} + \newcommand*{\DeltaIi}{\DeltaOneOne} + \newcommand*{\Deltaoneone}{\DeltaOneOne} + \newcommand*{\DeltaIii}{\DeltaOneTwo} + \newcommand*{\DeltaIiii}{\DeltaOneThree} + \newcommand*{\Sigmazn}{\SigmaZeroN} + \newcommand*{\Sigmazi}{\SigmaZeroOne} + \newcommand*{\Sigmazii}{\SigmaZeroTwo} + \newcommand*{\Sigmaziii}{\SigmaZeroThree} + \newcommand*{\SigmaIn}{\SigmaOneN} + \newcommand*{\SigmaIi}{\SigmaOneOne} + \newcommand*{\SigmaIii}{\SigmaOneTwo} + \newcommand*{\SigmaIiii}{\SigmaOneThree} + \newcommand*{\Pizn}{\PiZeroN} + \newcommand*{\Pizi}{\PiZeroOne} + \newcommand*{\Pizii}{\PiZeroTwo} + \newcommand*{\Piziii}{\PiZeroThree} + \newcommand*{\PiIn}{\PiOneN} + \newcommand*{\PiIi}{\PiOneOne} + \newcommand*{\PiIii}{\PiOneTwo} + \newcommand*{\PiIiii}{\PiOneThree} @@ -1206,192 +1264,202 @@ %%%ABREVIATIONS - +\DeclareOptionX{recfnlsym}[Phi]{\edef\recfnlSYM{\expandafter\noexpand\csname #1 \endcsname}} +\DeclareOptionX{recfsym}[phi]{\edef\recfSYM{\expandafter\noexpand\csname #1 \endcsname}} %Degree Classes \AtEndOfPackage{ \ifrecthy@nodegclasses - \@packinfo{No degree classes loading.} + \@packinfo{No degree classes loading.} \else - \@packinfo{Degree classes loading.} - \newcommand{\Low}[1][]{\ensuremath{ \text{Low}^{#1} }} - \newcommand{\LowN}[2][]{\ensuremath{ \text{Low}^{#1}_{#2} }} - \newcommand{\lowN}[2][]{\ensuremath{ \mathcal{L}^{#1}_{#2} }} + \@packinfo{Degree classes loading.} + \newcommand{\Low}[1][]{\ensuremath{ \text{Low}^{#1} }} + \newcommand{\LowN}[2][]{\ensuremath{ \text{Low}^{#1}_{#2} }} + \newcommand{\lowN}[2][]{\ensuremath{ \mathcal{L}^{#1}_{#2} }} \fi } \AtEndOfPackage{ \ifrecthy@nocomputations - \@packinfo{No computations loading.} + \@packinfo{No computations loading.} \else %%%%%% - \newcommand*{\murec}[2]{\ensuremath{\mu#1\left( #2 \right) }} - - %\newcommand*{\brecfSYM}{\phi} - \newcommand*{\recfnlSYM}{\Phi} - % \newcommand*{\recf}[3][]{\recfSYM^{#1}_{#2}\ifthenelse{\isempty{#3}}{}{\left(#3\right)}} %If give an empty arg just print function no parens - %\newcommand*{\brecf}[3][]{\brecfSYM^{#1}_{#2}\ifthenelse{\isempty{#3}}{}{\left(#3\right)}} - %\recfnl[d]{i}{Y}{x} gives i-th d-recursive functional operating on set Y and integer x - \newcommand*{\recfnl}[4][]{\recfnlSYM_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% - \ifthenelse{\isempty{#4}}% - {\ifthenelse{\isempty{#3}}% - {}% No args then print no parents - {(#3)} - }%If no oracle we just refer to the functional without any arguments - {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% - }} - - \newcommand*{\thetafnl}[4][]{\Theta_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% - \ifthenelse{\isempty{#4}}% - {\ifthenelse{\isempty{#3}}% - {}% No args then print no parents - {(#3)} - }%If no oracle we just refer to the functional without any arguments - {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% - }} - - \newcommand*{\psifnl}[4][]{\Psi_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% - \ifthenelse{\isempty{#4}}% - {\ifthenelse{\isempty{#3}}% - {}% No args then print no parents - {(#3)} - }%If no oracle we just refer to the functional without any arguments - {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% - }} - - \newcommand*{\phifnl}[4][]{\Phi_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% - \ifthenelse{\isempty{#4}}% - {\ifthenelse{\isempty{#3}}% - {}% No args then print no parents - {(#3)} - }%If no oracle we just refer to the functional without any arguments - {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% - }} - - \newcommand*{\upsilonfnl}[4][]{\Upsilon_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% - \ifthenelse{\isempty{#4}}% - {\ifthenelse{\isempty{#3}}% - {}% No args then print no parents - {(#3)} - }%If no oracle we just refer to the functional without any arguments - {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% - }} - - - \newcommand*{\cequiv}{\mathrel{\simeq}} - \newcommand*{\ncequiv}{\mathrel{\not\simeq}} - \newcommand*{\conv}[1][]{\mathpunct{\downarrow}_{#1}} - \let\converge=\conv - %\newcommand*{\convs}[1]{\ensuremath{\conv_{#1}}} -% \newcommand*{\nconv}[1][]{\mathpunct{\mkern-4mu{\arrownot\mkern 4mu \downarrow}_{#1}}} - \newcommand*{\nconv}[1][]{\mathpunct{\mkern-4mu{\smallsetminus\mkern 4mu \downarrow}_{#1}}} - \newcommand*{\diverge}{\mathpunct{\uparrow}} - % \newcommand*{\use}[2]{\mathscr{u}(#1\ifthenelse{\isempty{#2}}{}{,#2})} - \newcommand*{\use}[1]{\mathop{\ltx@ifpackageloaded{unicode-math}{\mathbffrak{u}}{\mathfrak{u}}}\!\left[{#1}\right]} - - \newcommand*{\REset}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\@REsetbody} - \newcommand*{\@REsetbody}[1]{W\ifdefined\@PMG@parenarg - ^{\@PMG@parenarg}% - \fi% - \ifdefined\@PMG@braketarg - _{#1, {\@PMG@braketarg}}% - \else - _{#1} - \fi} - \WithSuffix\def\@REsetbody(#1){\def\@PMG@parenarg{#1}\@REsetbody} - \WithSuffix\def\@REsetbody[#1]{\def\@PMG@braketarg{#1}\@REsetbody} - \newcommand*{\alphaREAop}[2][]{\mathcal{J}^{#2}_{#1}} - \let\aREAop=\alphaREAop - \let\reaop=\alphaREAop - \newcommand*{\oneREAop}[1]{J_{#1}} - \let\iREAop=\oneREAop - \WithSuffix\def\reaop*#1{\oneREAop{#1}} - %converges + \newcommand*{\murec}[2]{\ensuremath{\mu#1\left( #2 \right) }} + + %\newcommand*{\brecfSYM}{\phi} + \providecommand*{\recfSYM}{\phi} + \providecommand*{\recfnlSYM}{\Phi} + % \newcommand*{\recf}[3][]{\recfSYM^{#1}_{#2}\ifthenelse{\isempty{#3}}{}{\left(#3\right)}} %If give an empty arg just print function no parens + %\newcommand*{\brecf}[3][]{\brecfSYM^{#1}_{#2}\ifthenelse{\isempty{#3}}{}{\left(#3\right)}} + %\recfnl[d]{i}{Y}{x} gives i-th d-recursive functional operating on set Y and integer x + \newcommand*{\recfnl}[4][]{\recfnlSYM_{#2\ifthenelse{\isempty{#1}}{}{,{#1}} }% + \ifthenelse{\isempty{#4}}% + {\ifthenelse{\isempty{#3}}% + {}% No args then print no parents + {(#3)} + }%If no oracle we just refer to the functional without any arguments + {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% + }} + \NewDocumentCommand{\recf}{omod()}{ + \recfSYM_{#2\IfNoValueTF{#1}{}{, {#1}}}\IfNoValueTF{#3}{}{^{#3}}\IfNoValueTF{#4}{}{(#4)} + } + + + \newcommand*{\thetafnl}[4][]{\Theta_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% + \ifthenelse{\isempty{#4}}% + {\ifthenelse{\isempty{#3}}% + {}% No args then print no parents + {(#3)} + }%If no oracle we just refer to the functional without any arguments + {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% + }} + + \newcommand*{\psifnl}[4][]{\Psi_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% + \ifthenelse{\isempty{#4}}% + {\ifthenelse{\isempty{#3}}% + {}% No args then print no parents + {(#3)} + }%If no oracle we just refer to the functional without any arguments + {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% + }} + + \newcommand*{\phifnl}[4][]{\Phi_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% + \ifthenelse{\isempty{#4}}% + {\ifthenelse{\isempty{#3}}% + {}% No args then print no parents + {(#3)} + }%If no oracle we just refer to the functional without any arguments + {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% + }} + + \newcommand*{\upsilonfnl}[4][]{\Upsilon_{#2\ifthenelse{\isempty{#1}}{}{,#1} }% + \ifthenelse{\isempty{#4}}% + {\ifthenelse{\isempty{#3}}% + {}% No args then print no parents + {(#3)} + }%If no oracle we just refer to the functional without any arguments + {\ifthenelse{\isempty{#3}}{(#4)}{(#3;#4)}% + }} + + + \newcommand*{\cequiv}{\mathrel{\simeq}} + \newcommand*{\ncequiv}{\mathrel{\not\simeq}} + \NewDocumentCommand{\conv}{o}{\mathpunct{\downarrow}_{#1}} + \let\converge=\conv + %\newcommand*{\convs}[1]{\ensuremath{\conv_{#1}}} +% \NewDocumentCommand{\nconv}{o}{\mathpunct{\mkern-4mu{\arrownot\mkern 4mu \downarrow}_{#1}}} + \NewDocumentCommand{\nconv}{o}{\mathpunct{\mkern-4mu{\smallsetminus\mkern 4mu \downarrow}_{#1}}} + \newcommand*{\diverge}{\mathpunct{\uparrow}} + % \newcommand*{\use}[2]{\mathscr{u}(#1\ifthenelse{\isempty{#2}}{}{,#2})} + \newcommand*{\use}[1]{\mathop{\ltx@ifpackageloaded{unicode-math}{\symbffrak{u}}{\mathfrak{u}}}\!\left[{#1}\right]} + + % \NewDocumentCommand{\REset}{omd()}{ + % W_{#2\IfNoValueTF{#1}{}{, #1}}\IfNoValueTF{#3}{}{^{#3}} + % } + + \newcommand*{\REset}{\let\@PMG@parenarg\@PMG@undefined\let\@PMG@braketarg\@PMG@undefined\@REsetbody} + \newcommand*{\@REsetbody}[1]{W\ifdefined\@PMG@parenarg + ^{\@PMG@parenarg}% + \fi% + \ifdefined\@PMG@braketarg + _{#1, {\@PMG@braketarg}}% + \else + _{#1} + \fi} + \WithSuffix\def\@REsetbody(#1){\def\@PMG@parenarg{#1}\@REsetbody} + \WithSuffix\def\@REsetbody[#1]{\def\@PMG@braketarg{#1}\@REsetbody} + \newcommand*{\alphaREAop}[2][]{\mathcal{J}^{#2}_{#1}} + \let\aREAop=\alphaREAop + \let\reaop=\alphaREAop + \newcommand*{\oneREAop}[1]{J_{#1}} + \let\iREAop=\oneREAop + \WithSuffix\def\reaop*#1{\oneREAop{#1}} + %converges \fi \ifrecthy@nodegrees - \@packinfo{No degrees loading.} + \@packinfo{No degrees loading.} \else - %%%%%%Turing Degrees - \def\firsttokof@pmg#1{\first@pmg@rdmxs(#1)} - \def\first@pmg@rdmxs(#1#2){#1} - - \newcommand*{\Tdegvar}[1]{\mathbf{#1}} - \newcommand*{\Tdegof}[1]{\utilde{#1}} - \newcommand*{\Tdeg}[1]{\ifthenelse{ - %\equal{\detokenize{\Tzero}}{\futurelet\next@pmg\discard#1\@nil\expandafter\detokenize{\next@pmg}} - \equal{\detokenize{\Tzero}}{\detokenize{#1}} \OR - \equal{\detokenize{\Tzero}}{\detokenize{#1}} \OR - \equal{\detokenize{\zeroj}}{\detokenize{#1}} \OR - \equal{\detokenize{\zerojj}}{\detokenize{#1}} \OR - \equal{\detokenize{\zerojjj}}{\detokenize{#1}} \OR - \equal{\string \zeron }{\expandafter\string \first@pmg@rdmxs(#1)} - }{\Tdegof{#1}}{\Tdegvar{#1}}} - - \newcommand*{\Tjump}[1]{#1'} - \let\jump=\Tjump - \newcommand*{\jumpn}[2]{#1^{(#2)}} - \newcommand*{\jjump}[1]{#1''} - % \newcommand*{\Tzerosym}{\MVZero} - \newcommand*{\Tzerosym}{\mathbb{0}} - \newcommand*{\Tzero}{{\Tzerosym}} - \newcommand*{\zeron}[1]{{\Tzerosym}^{(#1)}} - \newcommand*{\zeroj}{\jump{{\Tzerosym}}} - \let\Tzeroj=\zeroj - \newcommand*{\zerojj}{\jump{\jump{{\Tzerosym}}}} - \newcommand*{\zerojjj}{\jump{\jump{\jump{{\Tzerosym}}}}} - \let\Tzerojj=\zerojj - \let\Tzerojjj=\zerojjj - - %%Misc Recursion theory stuff - %turing equivalent - \newcommand*{\@recthy@TSYM}{\mathbf{T}} - \newcommand*{\Tequiv}{\mathrel{\equiv_{\@recthy@TSYM}}} - \newcommand*{\Teq}{\Tequiv} - \newcommand*{\nTequiv}{\mathrel{\ncong_{\@recthy@TSYM}}} - \newcommand*{\nTeq}{\nTequiv} - %turing below - - \newcommand*{\Tlneq}{\lneq_{\@recthy@TSYM}} - \newcommand*{\Tleq}{\leq_{\@recthy@TSYM}} - \newcommand*{\Tgneq}{\gneq_{\@recthy@TSYM}} - \newcommand*{\Tgeq}{\geq_{\@recthy@TSYM}} - \newcommand*{\Tgtr}{>_{\@recthy@TSYM}} - \newcommand*{\Tless}{<_{\@recthy@TSYM}} - \newcommand*{\nTleq}{\nleq_{\@recthy@TSYM}} - \newcommand*{\nTgeq}{\ngeq_{\@recthy@TSYM}} - - \newcommand*{\Tdegjoin}{\mathbin{\vee_{\@recthy@TSYM}}} - \newcommand*{\Tdegmeet}{\mathbin{\wedge_{\@recthy@TSYM}}} - \newcommand*{\Tmeet}{\Tdegmeet} - \newcommand*{\Tsetjoin}{\mathbin{\oplus}} - \newcommand*{\TsetJoin}{\mathop{\bigoplus}} - \newcommand*{\Tplus}{\Tsetjoin} - \newcommand*{\TPlus}{\TsetJoin} - \newcommand*{\Tjoin}{\Tsetjoin} - \newcommand*{\TJoin}{\TsetJoin} - - - - - - - \newcommand*{\@recthy@ttSYM}{\ensuremath{\text{\tiny tt}}} - \newcommand*{\ttSYM}{\@recthy@ttSYM} - \newcommand*{\ttlneq}{\lneq_{\@recthy@ttSYM}} - \newcommand*{\ttleq}{\leq_{\@recthy@ttSYM}} - \newcommand*{\ttgneq}{\gneq_{\@recthy@ttSYM}} - \newcommand*{\ttgeq}{\geq_{\@recthy@ttSYM}} - \newcommand*{\ttgtr}{>_{\@recthy@ttSYM}} - \newcommand*{\ttless}{<_{\@recthy@ttSYM}} - \newcommand*{\ttnleq}{\nleq_{\@recthy@ttSYM}} - \newcommand*{\ttngeq}{\ngeq_{\@recthy@ttSYM}} + %%%%%%Turing Degrees + \def\firsttokof@pmg#1{\first@pmg@rdmxs(#1)} + \def\first@pmg@rdmxs(#1#2){#1} + + \providecommand*{\Tdegvar}[1]{\symbf{#1}} + \providecommand*{\Tdegof}[1]{\utilde{#1}} + \providecommand*{\Tdeg}[1]{\ifthenelse{ + %\equal{\detokenize{\Tzero}}{\futurelet\next@pmg\discard#1\@nil\expandafter\detokenize{\next@pmg}} + \equal{\detokenize{\Tzero}}{\detokenize{#1}} \OR + \equal{\detokenize{\Tzero}}{\detokenize{#1}} \OR + \equal{\detokenize{\zeroj}}{\detokenize{#1}} \OR + \equal{\detokenize{\zerojj}}{\detokenize{#1}} \OR + \equal{\detokenize{\zerojjj}}{\detokenize{#1}} \OR + \equal{\string \zeron }{\expandafter\string \first@pmg@rdmxs(#1)} + }{\Tdegof{#1}}{\Tdegvar{#1}}} + + \providecommand*{\Tjump}[1]{#1'} + \let\jump=\Tjump + \providecommand*{\jumpn}[2]{#1^{(#2)}} + \providecommand*{\jjump}[1]{#1''} + % \newcommand*{\Tzerosym}{\MVZero} + \newcommand*{\Tzerosym}{\mathbb{0}} + \providecommand*{\Tzero}{{\Tzerosym}} + \providecommand*{\zeron}[1]{{\Tzerosym}^{(#1)}} + \providecommand*{\zeroj}{\jump{{\Tzerosym}}} + \let\Tzeroj=\zeroj + \providecommand*{\zerojj}{\jump{\jump{{\Tzerosym}}}} + \providecommand*{\zerojjj}{\jump{\jump{\jump{{\Tzerosym}}}}} + \let\Tzerojj=\zerojj + \let\Tzerojjj=\zerojjj + + %%Misc Recursion theory stuff + %turing equivalent + \newcommand*{\@recthy@TSYM}{\symbf{T}} + \providecommand*{\Tequiv}{\mathrel{\equiv_{\@recthy@TSYM}}} + \providecommand*{\Teq}{\Tequiv} + \providecommand*{\nTequiv}{\mathrel{\ncong_{\@recthy@TSYM}}} + \providecommand*{\nTeq}{\nTequiv} + %turing below + + \providecommand*{\Tlneq}{\lneq_{\@recthy@TSYM}} + \providecommand*{\Tleq}{\leq_{\@recthy@TSYM}} + \providecommand*{\Tgneq}{\gneq_{\@recthy@TSYM}} + \providecommand*{\Tgeq}{\geq_{\@recthy@TSYM}} + \providecommand*{\Tgtr}{>_{\@recthy@TSYM}} + \providecommand*{\Tless}{<_{\@recthy@TSYM}} + \providecommand*{\nTleq}{\nleq_{\@recthy@TSYM}} + \providecommand*{\nTgeq}{\ngeq_{\@recthy@TSYM}} + + \providecommand*{\Tdegjoin}{\mathbin{\vee_{\@recthy@TSYM}}} + \providecommand*{\Tdegmeet}{\mathbin{\wedge_{\@recthy@TSYM}}} + \providecommand*{\Tmeet}{\Tdegmeet} + \providecommand*{\Tsetjoin}{\mathbin{\oplus}} + \providecommand*{\TsetJoin}{\mathop{\bigoplus}} + \providecommand*{\Tplus}{\Tsetjoin} + \providecommand*{\TPlus}{\TsetJoin} + \providecommand*{\Tjoin}{\Tsetjoin} + \providecommand*{\TJoin}{\TsetJoin} + + + + + + + \newcommand*{\@recthy@ttSYM}{\ensuremath{\text{\tiny tt}}} + \newcommand*{\ttSYM}{\@recthy@ttSYM} + \newcommand*{\ttlneq}{\lneq_{\@recthy@ttSYM}} + \newcommand*{\ttleq}{\leq_{\@recthy@ttSYM}} + \newcommand*{\ttgneq}{\gneq_{\@recthy@ttSYM}} + \newcommand*{\ttgeq}{\geq_{\@recthy@ttSYM}} + \newcommand*{\ttgtr}{>_{\@recthy@ttSYM}} + \newcommand*{\ttless}{<_{\@recthy@ttSYM}} + \newcommand*{\ttnleq}{\nleq_{\@recthy@ttSYM}} + \newcommand*{\ttngeq}{\ngeq_{\@recthy@ttSYM}} \fi } |