Правила ISO для набора математики. Пакет mismath

Аннотация

Мы продолжаем описывать средства для упрощения набора математики, соответствующей правилам ISO. В данной статье мы кратко описываем пакет для системы LaTeX mismath.

Полный текст

Mismath package The mismath package provides a set of macros for improving the typesetting of mathematical formulas in accordance with the recommendations of the international standard ISO 80000-2 [1, 2]. Mathematical constants (e, i, π) are typeset in an upright font rather than in italics like variables. Vectors are typeset with arrows above or in bold type. Tensors are typeset in sans-serif bold italic. Uppercase Greek letters are typeset in italics. The package offers: standard operator names; useful aliases for frequently used commands; improved spacing in mathematical expressions; environments for systems of equations and small matrices; two-column display-style math output for long calculations involving short expressions. It is compatible with other packages: amsmath, mathtools: basic mathematical typesetting; esvect: arrows over vectors; mleftright: improves spacing for automatic delimiters. If a command is already defined in previously loaded packages, mismath does not redefine it but issues a warning. If you need to force the use of the mismath definition, you can reset the command using \let\command\relax before loading the package. Recommended package loading order: \usepackage{amsmath} \usepackage{mathtools} \usepackage{amssymb} \usepackage{mismath} \usepackage{unicode-math} The package automatically loads mleftright and mathtools (which, in turn, loads amsmath). If options need to be passed to these packages, they can be specified for mismath, or amsmath or mathtools can be loaded with the desired options before mismath. When using the unicode-math package, mismath should be loaded before unicode-math. © 2026 D. S. Kulyabov, A. V. Korolkova, L. A. Sevastianov, Y. P. Rybakov This work is licensed under a Creative Commons “Attribution-NonCommercial 4.0 International” license. The mismath package combines the functions of other packages. All these features are gathered into a single package and configured in a unified style, in accordance with ISO standards. Alternatives to the mismath package: Upright constants: upgreek (for Greek letters), fixmath; Vectors with arrows: esvect; Tensors: tensor; Improved spacing: mleftright, mathtools; Systems of equations: amsmath (cases and matrix environments); Two columns in displaymath: multicol, IEEEtrantools. Package options Options are specified when loading the package: \usepackage[<options>]{mismath}. nofunction: disables the loading of additional function and operator definitions. classicReIm: retains the standard \Re and \Im (the symbols ℜ and ℑ) without redefining them as Re and Im. lineargroups: loads macros for classical linear groups (\GL, \SL, \Sp, \O, \SO, \U, \SU). textshortcuts: adds text shortcuts for mathematics (e.g., \ale for almost everywhere, \cc for complex conjugate, \st for such that, \wrt for with respect to). ibrackets: loads the ibrackets package for improved handling of square brackets. decimalcomma: loads the decimalcomma package to use a comma as the decimal separator in math mode. nosingleletter: disables all single-letter macros (such as \R, \C, \e, \i), replacing them with two-letter equivalents (e.g., \RR, \CC, \ee, \ii). We prefer using double letters to avoid potential conflicts with the author’s notation or other packages. lineargroups option \(\GL(n,\RR)\), \(\SL(2,\CC)\), ↪ \(\Sp(2n,\FF)\), \(\OO(3)\), ↪ \(\SO(n)\), \(\UU(1)\), ↪ \(\SU(2)\) GL(n, ℝ), SL(2, ℂ), Sp(2n, ), O(3), SO(n), U(1), SU(2) Basic commands Mathematical constants Constants are typeset in an upright font, as required by the ISO standard. Mathematical constants \(\ee\), \(\ii\), \(\jj\) e, i, j Vectors, tensors, norms \vect{argument}: vector with an arrow above. \boldvect: a switch that renders vectors in bold italics throughout the document or the current group. \hvect{<argument>}, \hvec{<argument>}: used to raise the arrows when vectors appear side-by-side (e.g., \hvect{u} + \hvect{v}). \norm{<argument>}: norm (double vertical bars). \abs{<argument>}: absolute value (single vertical bars). \innerprod{<arg1>}{<arg2>}: inner product (angle brackets). \tensor{<argument>} (or \mathbfsfit): tensor (bold sans-serif italics). Vectors #a„, a \(\vect{a}\), { \(\boldvect \vect{a}\) }\\ \(\hvect{u} + \hvect{v}\) \\ \(\norm{a}\), \(\abs{a}\)\\ \(\innerprod{a}{b}\) \\ \(\tensor{F}\) #„ #„ u + v ‖a‖, |a| ⟨a, b⟩ Operators The package defines a set of standard mathematical operators. Common operators \Re, \Im: real and imaginary parts. \id: identity operator; \Var: variance; \Cov: covariance; \rank: rank; \tr: matrix trace; \grad: gradient; \divg: divergence; \rot: curl; \curl: curl; \End: endomorphism; \Aut: automorphism; \di: differential (upright d with a thin space following it), though it is better to use the more general derivative package [2]. Standard operators \(\Re\), \(\Im\) \\ \(\id\), \(\Var\), \(\Cov\) \\ \(\rank\), \(\tr{A}\) \\ \(\grad{a}\), \(\divg{a}\) \\ \(\rot{a}\), \(\curl{a}\) \\ \(\End\), \(\Aut\) \\ \(\di x\), \(\di (x,y)\) Re, Im id, Var, Cov r# a n „k, tr A g# r „ad a#, d „iv a rot a, curl a End, Aut dx, d(x, y) Asymptotic notation Notations for the Bachmann-Landau notation [3, 4]. Asymptotic notation \(n^2 + \bigO (n \log n)\)\\ \(n^2 + \bigo (n \log n)\)\\ \(\ee^{x} = 1 + x + \frac{x^{2}}{2} + \lito n2 + (n log n) n2 + O(n log n) ex = 1 + x + x2 + o(x2) ↪ (x^{2})\) 2 Standard sets Notation for standard sets. We use the decimalcomma option. Following Bourbaki’s notation [5], the package uses boldface for sets. However, double-struck letters can also be used, and this is the convention we follow in our work. Sets {\renewcommand\mathset{\mathbf} \(\RR\), ↪ \(\CC\), \(\ZZ\), \(\NN\), \\ R, C, Z, N, \(\QQ\), \(\HH\), \(\FF\), \(\KK\) } \\ {\renewcommand\mathset{\mathbb} \(\RR\), ↪ \(\CC\), \(\ZZ\), \(\NN\), \\ Q, H, F, K ℝ, ℂ, ℤ, ℕ, ℚ, ℍ, , \(\QQ\), \(\HH\), \(\FF\), \(\KK\) }