%===================================================================================================================================== % Package akkmathset by Igor Akkerman (c) 2000, 2001, 2002, 2003, 2004, 2005 % Package providing utilities for typesetting mathematical sets. % % This work may be distributed and/or modified under the % conditions of the LaTeX Project Public License (latest version). % % The latest version of this license can be found at % http://www.latex-project.org/lppl.txt % % This file may only be distributed together with the full 'AkkTeX' bundle. %===================================================================================================================================== \NeedsTeXFormat{LaTeX2e}[1995/12/01] \ProvidesPackage{akkmathset}[2005/04/30 1.0.0 by Igor Akkerman (c) 2000, 2001, 2002, 2003, 2004 Package providing utilities for typesetting mathematical sets] %===================================================================================================================================== \RequirePackage{amsmath} \RequirePackage{amssymb} \RequirePackage{amstext} \RequirePackage{latexsym} %----------------------------------------------------------------------------------------------------------------------------------------------------------------------- \newcommand \NN {{\mathbb N}} \newcommand \NNN {{\NN\minuszero}} \newcommand \RR {{\mathbb R}} \newcommand \RRm {\RR^m} \newcommand \RRn {\RR^n} \newcommand \QQ {{\mathbb Q}} \newcommand \ZZ {{\mathbb Z}} \newcommand \CC {{\mathbb C}} \newcommand \CCm {\CC^m} \newcommand \CCn {\CC^n} \newcommand \KK {{\mathbb K}} \newcommand \KKm {\KK^m} \newcommand \KKn {\KK^n} \newcommand \LL {{\mathbb L}} \newcommand \BB {{\mathcal B}} \newcommand \PP {{\mathcal P}} \newcommand \VV {{\mathcal V}} \newcommand \CCC {{\mathcal C}} \newcommand \set[1] {\{#1\}} \newcommand \Set[1] {\openSet #1 \closeSet} \newcommand \openSet {\!\left\{\left.} \newcommand \closeSet {\right.\right\}\!} \newcommand \setcard[1] {{\left| #1 \right|}} % `such that' bar \newcommand \sth {\,|\,} \newcommand \Sth {\right| \left.} \newcommand \sm \setminus \newcommand \setcomp[1] {{\overline{{#1}}}} \newcommand \C[1] {{\setcomp{#1}}} \newcommand \zeroset {{\set 0}} \newcommand \minuszero {{\setminus\zeroset}} \newcommand \Minuszero {{\!\setminus\!\zeroset}} \newcommand \mz \minuszero \newcommand \Mz \Minuszero \newcommand \pset[1] {{\PP({#1})}} \newcommand \Pset[1] {{\PP\({#1}\)}} \newcommand \Abb {{\operatorname{Abb}}} \newcommand \mker {{\operatorname{ker}}} \newcommand \Ker {{\operatorname{Ker}}} \newcommand \Kern {{\operatorname{Kern}}} \newcommand \Bild {{\operatorname{Bild}}} \renewcommand \Im {{\operatorname{Im}}} \newcommand \End {{\operatorname{End}}} \newcommand \Eig {{\operatorname{Eig}}} \newcommand \Hom {{\operatorname{Hom}}} \newcommand \Mat {{\operatorname{Mat}}} \newcommand \gl {{\operatorname{GL}}} \newcommand \GL {{\operatorname{GL}}} \newcommand \mspan[1][] {{\operatorname{span}\ifset{#1}{\Set{#1}}}} \newcommand \Span [1][] {{\operatorname{Span}\ifset{#1}{\Set{#1}}}} \newcommand \erz[1] {\bigl[#1\bigr]} \newcommand \Erz[1] {\left[#1\right]} \newcommand \closure[1] {{\overline{{#1}}}} \newcommand \jset {{\set{1,\dots,j}}} \newcommand \kset {{\set{1,\dots,k}}} \newcommand \nset {{\set{1,\dots,n}}} \newcommand \mset {{\set{1,\dots,m}}} % big set union with limits \newcommand \Bigcup[1] {{\bigcup\limits_{#1}}} % big set intersection with limits \newcommand \Bigcap[1] {{\bigcap\limits_{#1}}} % equivalence class \newcommand \equivclass[2][] {{[{#2}]_{{#1}}}} \newcommand \eqclass[2][] {{\equivclass{1}{2}}} % quotient set \newcommand \quot[2] {{{#1}/\!\raisebox{-.575ex}{\ensuremath{#2}}}} % square set MxM \newcommand \sqset[1] {#1 \times #1} \newcommand \sqseta {\sqset A} \newcommand \sqsetb {\sqset B} \newcommand \sqsetc {\sqset C} \newcommand \sqsetcc {\sqset \CC} \newcommand \sqseti {\sqset I} \newcommand \sqsetkk {\sqset \KK} \newcommand \sqsetm {\sqset M} \newcommand \sqsetnn {\sqset \NN} \newcommand \sqsetqq {\sqset \QQ} \newcommand \sqsetr {\sqset R} \newcommand \sqsetrr {\sqset \RR} \newcommand \sqsets {\sqset S} \newcommand \sqsett {\sqset T} \newcommand \sqsetu {\sqset U} \newcommand \sqsetv {\sqset V} \newcommand \sqsetw {\sqset W} \newcommand \sqsetx {\sqset X} \newcommand \sqsety {\sqset Y} \newcommand \sqsetz {\sqset Z} \newcommand \sqsetzz {\sqset \ZZ} %------------------------------------------------------------------------------ % families %------------------------------------------------------------------------------ \newcommand \family[3] {{{\({{#1}_{#2}}\)}_{{#2} \in {#3}}}} \newcommand \ifam[1] {{\family{#1} i I}} %------------------------------------------------------------------------------ % elements %------------------------------------------------------------------------------ \newcommand \nin {{n\in\NN}} \newcommand \ninn {{n\in\NNN}} \newcommand \kin {{k\in\NN}} \newcommand \kinn {{k\in\NNN}} \newcommand \ini {{i\in I}}