Added parameters & text logical operators

nigel.stanger / LaTeX

Browse code Added parameters & text logical operators master
1 parent 4fb2d59 commit 2a34a087c2317b40aa4deb67750311c700139165 Nigel Stanger authored 5 days ago

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\def\packagedate{13 February 2025} \def\packageversion{2.2} \def\packageshortdate{2025/02/13} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Defines various relational algebra symbols. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Version History % v1.0 Initial version. % v2.0 Complete rewrite to support Unicode OpenType fonts and LaTeX3. % v2.1 Plays nicely with other packages that \setmathfont, and only % interpolates join symbols if they aren’t in the current font. % v2.2 Added text versions of logical operators (AND, OR, NOT), and % "parameters" of the form "<x>". Fixed missing \fi. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \NeedsTeXFormat{LaTeX2e}[2001/06/01] \ProvidesPackage{relalg}% [\packageshortdate\space v\packageversion\space Relational algebra notation] \RequirePackage{amsmath} \RequirePackage{expl3} \RequirePackage{iftex} \ExplSyntaxOn \bool_new:N \g__ra_unicode_engine \ifLuaTeX \PackageInfo{relalg}{LuaTeX\space engine\space detected} \bool_set_true:N \g__ra_unicode_engine \fi \ifXeTeX \PackageInfo{relalg}{XeTeX\space engine\space detected} \bool_set_true:N \g__ra_unicode_engine \fi \bool_if:NTF \g__ra_unicode_engine { \RequirePackage[no-math]{fontspec} \RequirePackage{unicode-math} % Stolen from unicode-math.sty as the fallback in unicode-math doesn't % seem to work? Weirdly it seems to work in a bare-bones MWE. \bool_if:NF \g__um_main_font_defined_bool \__um_load_lm: % The various join symbols aren't covered very well by many maths fonts % (including Latin Modern Math, annoyingly), so if necessary let's % Frankenstein them in from fonts that do have them. We need to hack % the scale to get roughly proportional looking sizes. % \iffontchar trick from <https://tex.stackexchange.com/questions/642080/newunicodechar-only-if-undeclared> % Outer joins (left, right, full): \iffontchar\font "27D5\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="027D5, Scale=0.875]\fi \iffontchar\font "27D6\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D6, Scale=0.875]\fi \iffontchar\font "27D7\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D7, Scale=0.875]\fi % \setmathfont{STIXTwoMath-Regular.otf}[range={"027D5-"027D7}, Scale=0.875] % Inner join: (1.143 = 1 / 0.875) \iffontchar\font "2A1D\relax\else\setmathfont{KpMath-Light.otf}[range="2A1D, Scale=1.143]\fi }{ \PackageInfo{relalg}{non-Unicode\space engine\space detected} \RequirePackage{latexsym} % for \Join } \ExplSyntaxOff %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % IDENTIFIERS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % General identifiers. \NewDocumentCommand{\RelIdentifier}{m}{\ensuremath{\mathit{#1}}} % Attribute names. \let\RelAttribute\RelIdentifier \let\RelAttr\RelIdentifier % Relation variable names. \let\RelVariable\RelIdentifier \let\RelVar\RelIdentifier % Attribute sets: \RelAttributeSet{foo,bar,baz}, \RelAttrSet{foo,bar,baz} % <https://tex.stackexchange.com/a/159132>, expl3 manual Section 23 \ExplSyntaxOn \NewDocumentCommand{\RelAttributeSet}{m}{ \clist_clear:N \l_tmpa_clist \clist_map_inline:nn{#1}{ \clist_put_right:Nn \l_tmpa_clist {\RelAttribute{##1}} } \ensuremath{\{\clist_use:Nn \l_tmpa_clist {,}\}} } \let\RelAttrSet\RelAttributeSet \ExplSyntaxOff % "Parameters" of the form "<x>". \NewDocumentCommand{\RelParameter}{m}{\ensuremath{\langle\RelIdentifier{#1}\rangle}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % BASIC OPERATORS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Restrict (select) operator. \NewDocumentCommand{\RelRestrict}{}{\ensuremath{\sigma}} \let\RelSelect\RelRestrict % Project operator. \NewDocumentCommand{\RelProject}{}{\ensuremath{\pi}} % Set union operator. \NewDocumentCommand{\RelUnion}{}{\ensuremath{\cup}} % Set difference operator. \NewDocumentCommand{\RelDifference}{}{\ensuremath{-}} \let\RelMinus\RelDifference % Cartesian product operator. \NewDocumentCommand{\RelCartesianProduct}{}{\ensuremath{\times}} \let\RelProduct\RelCartesianProduct \let\RelTimes\RelCartesianProduct % Rename operator. \NewDocumentCommand{\RelRename}{}{\ensuremath{\rho}} % Extend operator. \NewDocumentCommand{\RelExtend}{}{\ensuremath{\epsilon}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ADDITIONAL OPERATORS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Set intersection operator. \NewDocumentCommand{\RelIntersection}{}{\ensuremath{\cap}} \let\RelIntersect\RelIntersection % Join operator (including natural join). % For some reason XeTeX puts less space in front of the operator than LuaTeX. % Adding +2.5mu for XeTeX looks close enough to LuaTeX's output. This also % applies to the outer join operators below. \NewDocumentCommand{\RelJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\Join}}} \let\RelNaturalJoin\RelJoin \let\RelNatJoin\RelJoin \let\RelNJoin\RelJoin % Division operator (two alternatives). \NewDocumentCommand{\RelDivide}{}{\ensuremath{/}} \NewDocumentCommand{\RelAltDivide}{}{\ensuremath{\div}} % Assignment operator. \NewDocumentCommand{\RelAssign}{}{\ensuremath{\leftarrow}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % EXTENDED OPERATORS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Aggregate functions. \DeclareMathOperator{\AggAvg}{avg} \DeclareMathOperator{\AggCount}{count} \DeclareMathOperator{\AggMin}{min} \DeclareMathOperator{\AggMax}{max} \DeclareMathOperator{\AggSum}{sum} \NewDocumentCommand{\RelAggregrate}{m m}{\ensuremath{\mathcal{G}_{#1}(#2)}} \NewDocumentCommand{\RelAverage}{m}{\RelAggregrate{\AggAverage}{#1}} \let\RelAvg\RelAverage \NewDocumentCommand{\RelCount}{m}{\RelAggregrate{\AggCount}{#1}} \NewDocumentCommand{\RelMaximum}{m}{\RelAggregrate{\AggMax}{#1}} \let\RelMax\RelMaximum \NewDocumentCommand{\RelMinimum}{m}{\RelAggregrate{\AggMin}{#1}} \let\RelMin\RelMinimum \NewDocumentCommand{\RelSum}{m}{\RelAggregrate{\AggSum}{#1}} % Outer join operators. \ExplSyntaxOn \bool_if:NTF \g__ra_unicode_engine { \NewDocumentCommand{\RelLeftOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\leftouterjoin}}} \NewDocumentCommand{\RelRightOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\rightouterjoin}}} \NewDocumentCommand{\RelFullOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\fullouterjoin}}} }{ % Hand-tweaked for non-Unicode engines based on answers at % <https://tex.stackexchange.com/questions/20740/symbols-for-outer-joins> % Weirdly the height of \Join is fractionally shorter than \bowtie, so % we can't use the more sensible solution of measuring off the line % height. Use only font-relative units to ensure proper scaling. \def\__ra_outer_join{\rule[0.11ex]{0.25em}{0.1ex}\llap{\rule[1.41ex]{0.25em}{0.1ex}}} \NewDocumentCommand{\RelLeftOuterJoin}{}{\ensuremath{\mathbin{\__ra_outer_join\mkern-6.4mu\Join}}} \NewDocumentCommand{\RelRightOuterJoin}{}{\ensuremath{\mathbin{\Join\mkern-6.4mu\__ra_outer_join}}} \NewDocumentCommand{\RelFullOuterJoin}{}{\ensuremath{\mathbin{\__ra_outer_join\mkern-6.4mu\Join\mkern-6.4mu\__ra_outer_join}}} } \ExplSyntaxOff \let\RelLOuterJoin\RelLeftOuterJoin \let\RelLeftOuter\RelLeftOuterJoin \let\RelLOJ\RelLeftOuterJoin \let\RelROuterJoin\RelRightOuterJoin \let\RelRightOuter\RelRightOuterJoin \let\RelROJ\RelRightOuterJoin \let\RelFOuterJoin\RelFullOuterJoin \let\RelFullOuter\RelFullOuterJoin \let\RelFOJ\RelFullOuterJoin % Semijoin operator. \NewDocumentCommand{\RelLeftSemiJoin}{}{\ensuremath{\ltimes}} \let\RelSemiJoin\RelLeftSemiJoin \NewDocumentCommand{\RelRightSemiJoin}{}{\ensuremath{\rtimes}} \let\RelReverseSemiJoin\RelRightSemiJoin % Antijoin operator. \NewDocumentCommand{\RelLeftAntiJoin}{}{\ensuremath{\triangleright}} \let\RelAntiJoin\RelLeftAntiJoin \NewDocumentCommand{\RelRightAntiJoin}{}{\ensuremath{\triangleleft}} \let\RelReverseAntiJoin\RelRightAntiJoin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % MISCELLANEOUS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Logical operators. \DeclareMathOperator{\AndText}{AND} \DeclareMathOperator{\OrText}{OR} \DeclareMathOperator{\NotText}{NOT} \ExplSyntaxOn \NewDocumentCommand{\RelLogicalAnd}{O{symbol}}{ \tl_if_eq:nnTF {#1} {text} {\ensuremath{\AndText}} {\ensuremath{\wedge}} } \let\RelLogAnd\RelLogicalAnd \let\RelAnd\RelLogicalAnd \NewDocumentCommand{\RelLogicalOr}{O{symbol}}{ \tl_if_eq:nnTF {#1} {text} {\ensuremath{\OrText}} {\ensuremath{\vee}} } \let\RelLogOr\RelLogicalOr \let\RelOr\RelLogicalOr \NewDocumentCommand{\RelLogicalNot}{O{symbol}}{ \tl_if_eq:nnTF {#1} {text} {\ensuremath{\NotText}} {\ensuremath{\neg}} } \let\RelLogNot\RelLogicalNot \let\RelNot\RelLogicalNot \ExplSyntaxOff \endinput \def\packagedate{15 Jamuary 2025} \def\packageversion{2.1} \def\packageshortdate{2025/01/15} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Defines various relational algebra symbols. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Version History % v1.0 Initial version. % v2.0 Complete rewrite to support Unicode OpenType fonts and LaTeX3. % v2.1 Plays nicely with other packages that \setmathfont, and only % interpolates join symbols if they aren’t in the current font. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \NeedsTeXFormat{LaTeX2e}[2001/06/01] \ProvidesPackage{relalg}% [\packageshortdate\space v\packageversion\space Relational algebra notation] \RequirePackage{amsmath} \RequirePackage{expl3} \RequirePackage{iftex} \ExplSyntaxOn \bool_new:N \g__ra_unicode_engine \ifLuaTeX \PackageInfo{relalg}{LuaTeX\space engine\space detected} \bool_set_true:N \g__ra_unicode_engine \fi \ifXeTeX \PackageInfo{relalg}{XeTeX\space engine\space detected} \bool_set_true:N \g__ra_unicode_engine \fi \bool_if:NTF \g__ra_unicode_engine { \RequirePackage[no-math]{fontspec} \RequirePackage{unicode-math} % Stolen from unicode-math.sty as the fallback in unicode-math doesn't % seem to work? Weirdly it seems to work in a bare-bones MWE. \bool_if:NF \g__um_main_font_defined_bool \__um_load_lm: % The various join symbols aren't covered very well by many maths fonts % (including Latin Modern Math, annoyingly), so if necessary let's % Frankenstein them in from fonts that do have them. We need to hack % the scale to get roughly proportional looking sizes. % \iffontchar trick from <https://tex.stackexchange.com/questions/642080/newunicodechar-only-if-undeclared> % Outer joins (left, right, full): \iffontchar\font "27D5\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="027D5, Scale=0.875] \iffontchar\font "27D6\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D6, Scale=0.875] \iffontchar\font "27D7\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D7, Scale=0.875] % \setmathfont{STIXTwoMath-Regular.otf}[range={"027D5-"027D7}, Scale=0.875] % Inner join: (1.143 = 1 / 0.875) \iffontchar\font "2A1D\relax\else\setmathfont{KpMath-Light.otf}[range="2A1D, Scale=1.143] }{ \PackageInfo{relalg}{non-Unicode\space engine\space detected} \RequirePackage{latexsym} % for \Join } \ExplSyntaxOff %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % IDENTIFIERS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % General identifiers. \NewDocumentCommand{\RelIdentifier}{m}{\ensuremath{\mathit{#1}}} % Attribute names. \let\RelAttribute\RelIdentifier \let\RelAttr\RelIdentifier % Relation variable names. \let\RelVariable\RelIdentifier \let\RelVar\RelIdentifier % Attribute sets: \RelAttributeSet{foo,bar,baz}, \RelAttrSet{foo,bar,baz} % <https://tex.stackexchange.com/a/159132>, expl3 manual Section 23 \ExplSyntaxOn \NewDocumentCommand{\RelAttributeSet}{m}{ \clist_clear:N \l_tmpa_clist \clist_map_inline:nn{#1}{ \clist_put_right:Nn \l_tmpa_clist {\RelAttribute{##1}} } \ensuremath{\{\clist_use:Nn \l_tmpa_clist {,}\}} } \let\RelAttrSet\RelAttributeSet \ExplSyntaxOff %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % BASIC OPERATORS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Restrict (select) operator. \NewDocumentCommand{\RelRestrict}{}{\ensuremath{\sigma}} \let\RelSelect\RelRestrict % Project operator. \NewDocumentCommand{\RelProject}{}{\ensuremath{\pi}} % Set union operator. \NewDocumentCommand{\RelUnion}{}{\ensuremath{\cup}} % Set difference operator. \NewDocumentCommand{\RelDifference}{}{\ensuremath{-}} \let\RelMinus\RelDifference % Cartesian product operator. \NewDocumentCommand{\RelCartesianProduct}{}{\ensuremath{\times}} \let\RelProduct\RelCartesianProduct \let\RelTimes\RelCartesianProduct % Rename operator. \NewDocumentCommand{\RelRename}{}{\ensuremath{\rho}} % Extend operator. \NewDocumentCommand{\RelExtend}{}{\ensuremath{\epsilon}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ADDITIONAL OPERATORS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Set intersection operator. \NewDocumentCommand{\RelIntersection}{}{\ensuremath{\cap}} \let\RelIntersect\RelIntersection % Join operator (including natural join). % For some reason XeTeX puts less space in front of the operator than LuaTeX. % Adding +2.5mu for XeTeX looks close enough to LuaTeX's output. This also % applies to the outer join operators below. \NewDocumentCommand{\RelJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\Join}}} \let\RelNaturalJoin\RelJoin \let\RelNatJoin\RelJoin \let\RelNJoin\RelJoin % Division operator (two alternatives). \NewDocumentCommand{\RelDivide}{}{\ensuremath{/}} \NewDocumentCommand{\RelAltDivide}{}{\ensuremath{\div}} % Assignment operator. \NewDocumentCommand{\RelAssign}{}{\ensuremath{\leftarrow}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % EXTENDED OPERATORS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Aggregate functions. \DeclareMathOperator{\AggAvg}{avg} \DeclareMathOperator{\AggCount}{count} \DeclareMathOperator{\AggMin}{min} \DeclareMathOperator{\AggMax}{max} \DeclareMathOperator{\AggSum}{sum} \NewDocumentCommand{\RelAggregrate}{m m}{\ensuremath{\mathcal{G}_{#1}(#2)}} \NewDocumentCommand{\RelAverage}{m}{\RelAggregrate{\AggAverage}{#1}} \let\RelAvg\RelAverage \NewDocumentCommand{\RelCount}{m}{\RelAggregrate{\AggCount}{#1}} \NewDocumentCommand{\RelMaximum}{m}{\RelAggregrate{\AggMax}{#1}} \let\RelMax\RelMaximum \NewDocumentCommand{\RelMinimum}{m}{\RelAggregrate{\AggMin}{#1}} \let\RelMin\RelMinimum \NewDocumentCommand{\RelSum}{m}{\RelAggregrate{\AggSum}{#1}} % Outer join operators. \ExplSyntaxOn \bool_if:NTF \g__ra_unicode_engine { \NewDocumentCommand{\RelLeftOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\leftouterjoin}}} \NewDocumentCommand{\RelRightOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\rightouterjoin}}} \NewDocumentCommand{\RelFullOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\fullouterjoin}}} }{ % Hand-tweaked for non-Unicode engines based on answers at % <https://tex.stackexchange.com/questions/20740/symbols-for-outer-joins> % Weirdly the height of \Join is fractionally shorter than \bowtie, so % we can't use the more sensible solution of measuring off the line % height. Use only font-relative units to ensure proper scaling. \def\__ra_outer_join{\rule[0.11ex]{0.25em}{0.1ex}\llap{\rule[1.41ex]{0.25em}{0.1ex}}} \NewDocumentCommand{\RelLeftOuterJoin}{}{\ensuremath{\mathbin{\__ra_outer_join\mkern-6.4mu\Join}}} \NewDocumentCommand{\RelRightOuterJoin}{}{\ensuremath{\mathbin{\Join\mkern-6.4mu\__ra_outer_join}}} \NewDocumentCommand{\RelFullOuterJoin}{}{\ensuremath{\mathbin{\__ra_outer_join\mkern-6.4mu\Join\mkern-6.4mu\__ra_outer_join}}} } \ExplSyntaxOff \let\RelLOuterJoin\RelLeftOuterJoin \let\RelLeftOuter\RelLeftOuterJoin \let\RelLOJ\RelLeftOuterJoin \let\RelROuterJoin\RelRightOuterJoin \let\RelRightOuter\RelRightOuterJoin \let\RelROJ\RelRightOuterJoin \let\RelFOuterJoin\RelFullOuterJoin \let\RelFullOuter\RelFullOuterJoin \let\RelFOJ\RelFullOuterJoin % Semijoin operator. \NewDocumentCommand{\RelLeftSemiJoin}{}{\ensuremath{\ltimes}} \let\RelSemiJoin\RelLeftSemiJoin \NewDocumentCommand{\RelRightSemiJoin}{}{\ensuremath{\rtimes}} \let\RelReverseSemiJoin\RelRightSemiJoin % Antijoin operator. \NewDocumentCommand{\RelLeftAntiJoin}{}{\ensuremath{\triangleright}} \let\RelAntiJoin\RelLeftAntiJoin \NewDocumentCommand{\RelRightAntiJoin}{}{\ensuremath{\triangleleft}} \let\RelReverseAntiJoin\RelRightAntiJoin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % MISCELLANEOUS % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Logical operators. \NewDocumentCommand{\RelLogicalAnd}{}{\ensuremath{\wedge}} \let\RelLogAnd\RelLogicalAnd \let\RelAnd\RelLogicalAnd \NewDocumentCommand{\RelLogicalOr}{}{\ensuremath{\vee}} \let\RelLogOr\RelLogicalOr \let\RelOr\RelLogicalOr \NewDocumentCommand{\RelLogicalNot}{}{\ensuremath{\neg}} \let\RelLogNot\RelLogicalNot \let\RelNot\RelLogicalNot \endinput

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relalg.sty

\def\packagedate{13 February 2025}
\def\packageversion{2.2}
\def\packageshortdate{2025/02/13}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Defines various relational algebra symbols.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Version History
% v1.0    Initial version.
% v2.0    Complete rewrite to support Unicode OpenType fonts and LaTeX3.
% v2.1    Plays nicely with other packages that \setmathfont, and only
%         interpolates join symbols if they aren’t in the current font.
% v2.2    Added text versions of logical operators (AND, OR, NOT), and
%         "parameters" of the form "<x>". Fixed missing \fi.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\NeedsTeXFormat{LaTeX2e}[2001/06/01]
\ProvidesPackage{relalg}%
        [\packageshortdate\space v\packageversion\space Relational algebra notation]

\RequirePackage{amsmath}
\RequirePackage{expl3}
\RequirePackage{iftex}

\ExplSyntaxOn
    \bool_new:N \g__ra_unicode_engine

\ifLuaTeX
        \PackageInfo{relalg}{LuaTeX\space engine\space detected}
        \bool_set_true:N \g__ra_unicode_engine
    \fi

\ifXeTeX
        \PackageInfo{relalg}{XeTeX\space engine\space detected}
        \bool_set_true:N \g__ra_unicode_engine
    \fi

\bool_if:NTF \g__ra_unicode_engine {
        \RequirePackage[no-math]{fontspec}
        \RequirePackage{unicode-math}

% Stolen from unicode-math.sty as the fallback in unicode-math doesn't
        % seem to work? Weirdly it seems to work in a bare-bones MWE.
        \bool_if:NF \g__um_main_font_defined_bool \__um_load_lm:

% The various join symbols aren't covered very well by many maths fonts
        % (including Latin Modern Math, annoyingly), so if necessary let's
        % Frankenstein them in from fonts that do have them. We need to hack
        % the scale to get roughly proportional looking sizes.
        % \iffontchar trick from <https://tex.stackexchange.com/questions/642080/newunicodechar-only-if-undeclared>
        % Outer joins (left, right, full):
        \iffontchar\font "27D5\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="027D5, Scale=0.875]\fi
        \iffontchar\font "27D6\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D6, Scale=0.875]\fi
        \iffontchar\font "27D7\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D7, Scale=0.875]\fi
        % \setmathfont{STIXTwoMath-Regular.otf}[range={"027D5-"027D7}, Scale=0.875]
        % Inner join: (1.143 = 1 / 0.875)
        \iffontchar\font "2A1D\relax\else\setmathfont{KpMath-Light.otf}[range="2A1D, Scale=1.143]\fi
    }{
        \PackageInfo{relalg}{non-Unicode\space engine\space detected}
        \RequirePackage{latexsym} % for \Join
    }
\ExplSyntaxOff

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% IDENTIFIERS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% General identifiers.
\NewDocumentCommand{\RelIdentifier}{m}{\ensuremath{\mathit{#1}}}

% Attribute names.
\let\RelAttribute\RelIdentifier
\let\RelAttr\RelIdentifier

% Relation variable names.
\let\RelVariable\RelIdentifier
\let\RelVar\RelIdentifier

% Attribute sets: \RelAttributeSet{foo,bar,baz}, \RelAttrSet{foo,bar,baz}
% <https://tex.stackexchange.com/a/159132>, expl3 manual Section 23
\ExplSyntaxOn
    \NewDocumentCommand{\RelAttributeSet}{m}{
        \clist_clear:N \l_tmpa_clist
        \clist_map_inline:nn{#1}{
            \clist_put_right:Nn \l_tmpa_clist {\RelAttribute{##1}}
        }
        \ensuremath{\{\clist_use:Nn \l_tmpa_clist {,}\}}
    }
    \let\RelAttrSet\RelAttributeSet
\ExplSyntaxOff

% "Parameters" of the form "<x>".
\NewDocumentCommand{\RelParameter}{m}{\ensuremath{\langle\RelIdentifier{#1}\rangle}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% BASIC OPERATORS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Restrict (select) operator.
\NewDocumentCommand{\RelRestrict}{}{\ensuremath{\sigma}}
\let\RelSelect\RelRestrict

% Project operator.
\NewDocumentCommand{\RelProject}{}{\ensuremath{\pi}}

% Set union operator.
\NewDocumentCommand{\RelUnion}{}{\ensuremath{\cup}}

% Set difference operator.
\NewDocumentCommand{\RelDifference}{}{\ensuremath{-}}
\let\RelMinus\RelDifference

% Cartesian product operator.
\NewDocumentCommand{\RelCartesianProduct}{}{\ensuremath{\times}}
\let\RelProduct\RelCartesianProduct
\let\RelTimes\RelCartesianProduct

% Rename operator.
\NewDocumentCommand{\RelRename}{}{\ensuremath{\rho}}

% Extend operator.
\NewDocumentCommand{\RelExtend}{}{\ensuremath{\epsilon}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ADDITIONAL OPERATORS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Set intersection operator.
\NewDocumentCommand{\RelIntersection}{}{\ensuremath{\cap}}
\let\RelIntersect\RelIntersection

% Join operator (including natural join).
% For some reason XeTeX puts less space in front of the operator than LuaTeX.
% Adding +2.5mu for XeTeX looks close enough to LuaTeX's output. This also
% applies to the outer join operators below.
\NewDocumentCommand{\RelJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\Join}}}
\let\RelNaturalJoin\RelJoin
\let\RelNatJoin\RelJoin
\let\RelNJoin\RelJoin

% Division operator (two alternatives).
\NewDocumentCommand{\RelDivide}{}{\ensuremath{/}}
\NewDocumentCommand{\RelAltDivide}{}{\ensuremath{\div}}

% Assignment operator.
\NewDocumentCommand{\RelAssign}{}{\ensuremath{\leftarrow}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% EXTENDED OPERATORS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Aggregate functions.
\DeclareMathOperator{\AggAvg}{avg}
\DeclareMathOperator{\AggCount}{count}
\DeclareMathOperator{\AggMin}{min}
\DeclareMathOperator{\AggMax}{max}
\DeclareMathOperator{\AggSum}{sum}

\NewDocumentCommand{\RelAggregrate}{m m}{\ensuremath{\mathcal{G}_{#1}(#2)}}

\NewDocumentCommand{\RelAverage}{m}{\RelAggregrate{\AggAverage}{#1}}
\let\RelAvg\RelAverage

\NewDocumentCommand{\RelCount}{m}{\RelAggregrate{\AggCount}{#1}}

\NewDocumentCommand{\RelMaximum}{m}{\RelAggregrate{\AggMax}{#1}}
\let\RelMax\RelMaximum

\NewDocumentCommand{\RelMinimum}{m}{\RelAggregrate{\AggMin}{#1}}
\let\RelMin\RelMinimum

\NewDocumentCommand{\RelSum}{m}{\RelAggregrate{\AggSum}{#1}}

% Outer join operators.
\ExplSyntaxOn
    \bool_if:NTF \g__ra_unicode_engine {
        \NewDocumentCommand{\RelLeftOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\leftouterjoin}}}
        \NewDocumentCommand{\RelRightOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\rightouterjoin}}}
        \NewDocumentCommand{\RelFullOuterJoin}{}{\ensuremath{\ifXeTeX\mkern2.5mu\fi\mathbin{\fullouterjoin}}}
    }{
        % Hand-tweaked for non-Unicode engines based on answers at
        % <https://tex.stackexchange.com/questions/20740/symbols-for-outer-joins>
        % Weirdly the height of \Join is fractionally shorter than \bowtie, so
        % we can't use the more sensible solution of measuring off the line
        % height. Use only font-relative units to ensure proper scaling.
        \def\__ra_outer_join{\rule[0.11ex]{0.25em}{0.1ex}\llap{\rule[1.41ex]{0.25em}{0.1ex}}}
        \NewDocumentCommand{\RelLeftOuterJoin}{}{\ensuremath{\mathbin{\__ra_outer_join\mkern-6.4mu\Join}}}
        \NewDocumentCommand{\RelRightOuterJoin}{}{\ensuremath{\mathbin{\Join\mkern-6.4mu\__ra_outer_join}}}
        \NewDocumentCommand{\RelFullOuterJoin}{}{\ensuremath{\mathbin{\__ra_outer_join\mkern-6.4mu\Join\mkern-6.4mu\__ra_outer_join}}}
    }
\ExplSyntaxOff

\let\RelLOuterJoin\RelLeftOuterJoin
\let\RelLeftOuter\RelLeftOuterJoin
\let\RelLOJ\RelLeftOuterJoin

\let\RelROuterJoin\RelRightOuterJoin
\let\RelRightOuter\RelRightOuterJoin
\let\RelROJ\RelRightOuterJoin

\let\RelFOuterJoin\RelFullOuterJoin
\let\RelFullOuter\RelFullOuterJoin
\let\RelFOJ\RelFullOuterJoin

% Semijoin operator.
\NewDocumentCommand{\RelLeftSemiJoin}{}{\ensuremath{\ltimes}}
\let\RelSemiJoin\RelLeftSemiJoin

\NewDocumentCommand{\RelRightSemiJoin}{}{\ensuremath{\rtimes}}
\let\RelReverseSemiJoin\RelRightSemiJoin

% Antijoin operator.
\NewDocumentCommand{\RelLeftAntiJoin}{}{\ensuremath{\triangleright}}
\let\RelAntiJoin\RelLeftAntiJoin

\NewDocumentCommand{\RelRightAntiJoin}{}{\ensuremath{\triangleleft}}
\let\RelReverseAntiJoin\RelRightAntiJoin

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% MISCELLANEOUS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Logical operators.
\DeclareMathOperator{\AndText}{AND}
\DeclareMathOperator{\OrText}{OR}
\DeclareMathOperator{\NotText}{NOT}

\ExplSyntaxOn
    \NewDocumentCommand{\RelLogicalAnd}{O{symbol}}{
        \tl_if_eq:nnTF {#1} {text}
            {\ensuremath{\AndText}}
            {\ensuremath{\wedge}}
    }
    \let\RelLogAnd\RelLogicalAnd
    \let\RelAnd\RelLogicalAnd

\NewDocumentCommand{\RelLogicalOr}{O{symbol}}{
        \tl_if_eq:nnTF {#1} {text}
            {\ensuremath{\OrText}}
            {\ensuremath{\vee}}
    }
    \let\RelLogOr\RelLogicalOr
    \let\RelOr\RelLogicalOr

\NewDocumentCommand{\RelLogicalNot}{O{symbol}}{
        \tl_if_eq:nnTF {#1} {text}
            {\ensuremath{\NotText}}
            {\ensuremath{\neg}}
    }
    \let\RelLogNot\RelLogicalNot
    \let\RelNot\RelLogicalNot
\ExplSyntaxOff

\endinput

\def\packagedate{15 Jamuary 2025}
\def\packageversion{2.1}
\def\packageshortdate{2025/01/15}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Defines various relational algebra symbols.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Version History
% v1.0    Initial version.
% v2.0    Complete rewrite to support Unicode OpenType fonts and LaTeX3.
% v2.1    Plays nicely with other packages that \setmathfont, and only
%         interpolates join symbols if they aren’t in the current font.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\NeedsTeXFormat{LaTeX2e}[2001/06/01]
\ProvidesPackage{relalg}%
        [\packageshortdate\space v\packageversion\space Relational algebra notation]

\RequirePackage{amsmath}
\RequirePackage{expl3}
\RequirePackage{iftex}

\ExplSyntaxOn
    \bool_new:N \g__ra_unicode_engine

\ifLuaTeX
        \PackageInfo{relalg}{LuaTeX\space engine\space detected}
        \bool_set_true:N \g__ra_unicode_engine
    \fi

\ifXeTeX
        \PackageInfo{relalg}{XeTeX\space engine\space detected}
        \bool_set_true:N \g__ra_unicode_engine
    \fi

\bool_if:NTF \g__ra_unicode_engine {
        \RequirePackage[no-math]{fontspec}
        \RequirePackage{unicode-math}

% The various join symbols aren't covered very well by many maths fonts
        % (including Latin Modern Math, annoyingly), so if necessary let's
        % Frankenstein them in from fonts that do have them. We need to hack
        % the scale to get roughly proportional looking sizes.
        % \iffontchar trick from <https://tex.stackexchange.com/questions/642080/newunicodechar-only-if-undeclared>
        % Outer joins (left, right, full):
        \iffontchar\font "27D5\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="027D5, Scale=0.875]
        \iffontchar\font "27D6\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D6, Scale=0.875]
        \iffontchar\font "27D7\relax\else\setmathfont{STIXTwoMath-Regular.otf}[range="27D7, Scale=0.875]
        % \setmathfont{STIXTwoMath-Regular.otf}[range={"027D5-"027D7}, Scale=0.875]
        % Inner join: (1.143 = 1 / 0.875)
        \iffontchar\font "2A1D\relax\else\setmathfont{KpMath-Light.otf}[range="2A1D, Scale=1.143]
    }{
        \PackageInfo{relalg}{non-Unicode\space engine\space detected}
        \RequirePackage{latexsym} % for \Join
    }
\ExplSyntaxOff