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author | Karl Berry <karl@freefriends.org> | 2021-08-08 21:00:57 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2021-08-08 21:00:57 +0000 |
commit | eec3a67f3a57872862cf4adee13eeddc981d5442 (patch) | |
tree | cb82517f4d28e8f9d61ab18d1993595d6fc23ebc /Master/texmf-dist/source/latex/nchairx/chairxmathAlgebraDoc.dtx | |
parent | 3de8aad561c3a6fb16971dc6c7f68c189e8c4dc1 (diff) |
nchairx (8aug21)
git-svn-id: svn://tug.org/texlive/trunk@60196 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/latex/nchairx/chairxmathAlgebraDoc.dtx')
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diff --git a/Master/texmf-dist/source/latex/nchairx/chairxmathAlgebraDoc.dtx b/Master/texmf-dist/source/latex/nchairx/chairxmathAlgebraDoc.dtx new file mode 100644 index 00000000000..f43cb7ae445 --- /dev/null +++ b/Master/texmf-dist/source/latex/nchairx/chairxmathAlgebraDoc.dtx @@ -0,0 +1,270 @@ +% \iffalse meta-comment +% +% Copyright (C) 2018 - 2021 by ChairX +% +% This file may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either +% version 1.3 of this license or (at your option) any later +% version. The latest version of this license is in: +% +% http://www.latex-project.org/lppl.txt +% +% and version 1.3 or later is part of all distributions of +% LaTeX version 2005/12/01 or later. +% +% This file contains the documentation of all algebra related macros. +% +% Macros have to be described by (delete the first %) +% \DescribeMacro{\macro} +% Description and usage of the macro. +% +% The description will appear in the usage +% part of the documentation. Use \subsubsection{} etc. for structuring. +% +% The implementation of the macros defined here has to be written in +% chairxmathAlgebra.dtx +%\fi +% +%\subsubsection{Fonts for Rings and Things} +% +%\DescribeMacro{\field} +% Font for rings |\field{R}|: $\field{R}$\\ +% Uses |fieldfont|. +% +%\DescribeMacro{\ring} +% Font for rings |\ring{C}|: $\ring{C}$\\ +% Uses |ringfont|. +% +%\DescribeMacro{\group} +% Font for particular (matrix) groups |\group{SO}(3)|: $\group{SO}(3)$\\ +% Uses |groupfont|. +% +%\DescribeMacro{\algebra} +% Font for algebras |\algebra{A}|: $\algebra{A}$\\ +% Uses |algebrafont|. +% +%\DescribeMacro{\module} +% Font for modules |\module{M}|: $\module{M}$\\ +% Uses |modulefont|. +% +%\DescribeMacro{\liealg} +% Font for Lie algebras |\liealg{g}|: $\liealg{g}$\\ +% Uses |liealgfont|. +% +%\DescribeMacro{\MC} +% MC for Maurer-Cartan as a tiny index |\mu_\MC \in \liealg{g}^1|: $\mu_\MC \in \liealg{g}^1$\\ +% Uses |scriptfont|. +% +%\DescribeMacro{\gerstenhaber} +% Font for Gerstenhaber algebras |\gerstenhaber{G}|: $\gerstenhaber{G}$\\ +% Uses |gerstenhaberfont|. +% +%\subsubsection{Some Symbols needed in Algebra} +% +%\DescribeMacro{\Pol} +% Polynomials and polynomial functions |\Pol(T^*Q)|: $\Pol(T^*Q)$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\lmult} +% Left multiplications |\lmult_a|: $\lmult_a$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\rmult} +% Right multiplications |\rmult_b|: $\rmult_b$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\Lmult} +% Left multiplications |\Lmult_a|: $\Lmult_a$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\Rmult} +% Right multiplications |\Rmult_b|: $\Rmult_b$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\Center} +% Center |\Center(\algebra{A})|: $\Center(\algebra{A})$ +% +%\DescribeMacro{\ad} +% Adjoint action (infinitesimal) |\ad(a)|: $\ad(a)$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\Ad} +% Adjoint action |\Ad_g|: $\Ad_g$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\Conj} +% Conjugation |\Conj_g|: $\Conj_g$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\acts} +% A generic (left) action map |g \acts a|: $g \acts a$ +% +%\DescribeMacro{\racts} +% A generic right action map |a \racts g|: $a \racts g$ +% +%\DescribeMacro{\Char} +% Characteristics of a field |\Char(\mathbb{k})|: $\Char(\mathbb{k})$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\modulo} +% Yet another modulo |n \modulo 2|: $n \modulo 2$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\Clifford} +% Clifford algebra generated by a vector space and a bilinear form: +% |\Clifford(V, h)|: $\Clifford(V, h)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\cClifford} +% Complex Clifford algebra |\cClifford(V, h)|: $\cClifford(V, h)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\Der} +% ($*$-)Derivations |\Der(\algebra{A})|: $\Der(\algebra{A})$\\ +% |\Der*(\algebra{A})|: $\Der*(\algebra{A})$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\InnDer} +% Inner ($*$-)derivations |\InnDer(\algebra{A})|: $\InnDer(\algebra{A})$\\ +% |\InnDer*(\algebra{A})|: $\InnDer*(\algebra{A})$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\OutDer} +% Outer ($*$-)derivations |\OutDer(\algebra{A})|: $\OutDer(\algebra{A})$\\ +% |\OutDer*(\algebra{A})|: $\OutDer*(\algebra{A})$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\InnAut} +% Inner ($*$-)automorphisms |\InnAut(\algebra{A})|: $\InnAut(\algebra{A})$\\ +% |\InnAut*(\algebra{A})|: $\InnAut*(\algebra{A})$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\OutAut} +% Outer ($*$-)automorphisms |\OutAut(\algebra{A})|: $\OutAut(\algebra{A})$\\ +% |\OutAut*(\algebra{A})|: $\OutAut*(\algebra{A})$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\formal} +% Formal power series in some variables |V\formal{\lambda}|: +% $V \formal{\lambda}$ +% +% \DescribeMacro{\laurent} +% Formal Laurent series in some variables |V\laurent{\lambda}|: +% $V \laurent{\lambda}$ +% +% \DescribeMacro{\sweedler} +% Smaller index for Sweedler notation in Hopf algebra theory \\ +% |\Delta(a) = a_\sweedler{1} \tensor a_\sweedler{2}|: +% $\Delta(a) = a_\sweedler{1} \tensor a_\sweedler{2}$ +% +%\subsubsection{Categories from Algebra} +% +%\DescribeMacro{\algebras} +% Category of algebras |\algebras|: $\algebras$ \\ +% Category of $*$-algebras |\algebras*|: $\algebras*$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Algebras} +% Category of unital algebras |\Algebras|: $\Algebras$ \\ +% Category of unital $*$-algebras |\Algebras*|: $\Algebras*$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\reps} +% Category of ($*$-)representations +% |\reps_\algebra{C}(\algebra{B})|: $\reps_\algebra{C}(\algebra{B})$ \\ +% |\reps*_\algebra{C}(\algebra{B})|: $\reps*_\algebra{C}(\algebra{B})$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Reps} +% Category of strongly non-degenerate ($^*$)-representations +% |\Reps_\algebra{A}(\algebra{B})|:$\Reps_\algebra{A}(\algebra{B})$ \\ +% |\Reps*_\algebra{A}(\algebra{B})|:$\Reps*_\algebra{A}(\algebra{B})$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\PoissonAlg} +% Category of ($*$-)Poisson algebras |\PoissonAlg|: $\PoissonAlg$ \\ +% |\PoissonAlg*|: $\PoissonAlg*$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\modules} +% Category of (inner product) modules +% |\modules_\algebra{A}(\algebra{B})|: $\modules_\algebra{A}(\algebra{B})$ \\ +% |\modules*_\algebra{A}(\algebra{B})|: $\modules*_\algebra{A}(\algebra{B})$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Leftmodules} +% Category of left modules +% |\Leftmodules{\algebra{A}}|: $\Leftmodules{\algebra{A}}$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Rightmodules} +% Category of right modules with optional subscript +% |\Rightmodules[\category{C}]{\algebra{A}}|: $\Rightmodules[\category{C}]{\algebra{A}}$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Modules} +% Category of strongly non-degenerate (inner product) modules +% |\Modules_\algebra{A}(\algebra{B})|: $\Modules_\algebra{A}(\algebra{B})$ \\ +% |\Modules*_\algebra{A}(\algebra{B})|: $\Modules*_\algebra{A}(\algebra{B})$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\LeftModules} +% Category of strongly non-degenerate left modules +% |\LeftModules{\algebra{A}}|: $\LeftModules{\algebra{A}}$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\RightModules} +% Category of strongly non-degenerate right modules with optional subscript +% |\RightModules{\algebra{A}}|: $\RightModules{\algebra{A}}$ or +% |\RightModules[\category{C}]{\algebra{A}}|: $\RightModules[\category{C}]{\algebra{A}}$\\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Bimodules} +% Category of (inner product) bimodules +% |\Bimodules(\algebra{A},\algebra{B})|: $\Bimodules(\algebra{A},\algebra{B})$ \\ +% |\Bimodules*(\algebra{A},\algebra{B})|: $\Bimodules*(\algebra{A},\algebra{B})$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Rings} +% Category of unital rings (meant to be associative) |\Rings|: $\Rings$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Groups} +% Category of groups |\Groups|: $\Groups$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Ab} +% Category of abelian groups |\Ab|: $\Ab$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Lattices} +% Category of lattices |\Lattices|: $\Lattices$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Sets} +% Category of sets |\Sets|: $\Sets$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Vect} +% Category of vector spaces |\Vect|: $\Vect$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\LieAlgs} +% Category of Lie algebras |\LieAlgs|: $\LieAlgs$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Posets} +% Category of partially ordered sets |\Posets|: $\Posets$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Directed} +% Category of directed sets |\Directed|: $\Directed$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\GSets} +% Category of $G$-Sets |\GSets|: $\GSets$ and |\Gsets[H]|: $\GSets[H]$ \\ +% Uses |categorynamefont|. +% +%\DescribeMacro{\Groupoids} +% Category of groupoids |\Groupoids|: $\Groupoids$ \\ +% Uses |categorynamefont|.
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