diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/mathfont/mathfont_example.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/mathfont/mathfont_example.tex | 11 |
1 files changed, 4 insertions, 7 deletions
diff --git a/Master/texmf-dist/doc/latex/mathfont/mathfont_example.tex b/Master/texmf-dist/doc/latex/mathfont/mathfont_example.tex index efb26fe250c..d69aace431e 100644 --- a/Master/texmf-dist/doc/latex/mathfont/mathfont_example.tex +++ b/Master/texmf-dist/doc/latex/mathfont/mathfont_example.tex @@ -6,7 +6,7 @@ %% %% mathfont.dtx (with options: `example') %% -%% Copyright 2018 by Conrad Kosowsky +%% Copyright 2018-2019 by Conrad Kosowsky %% %% This file may be distributed and modified under the terms %% of the LaTeX Public Project License, version 1.3c or any later version. @@ -25,13 +25,10 @@ \documentclass[12pt]{article} \usepackage[margin=72.27pt]{geometry} \usepackage[factor=600,stretch=14,shrink=14,step=1]{microtype} -\usepackage{selnolig} -\usepackage[no-operators]{mathfont} -\mathfont{Times New Roman} +\usepackage{mathfont} +\setfont{Times New Roman} \mathfont[bb]{Symbola} \restoremathinternals -\setmainfont{Times New Roman} -\nolig{Th}{T|h} \hyphenpenalty=10 \exhyphenpenalty=5 \pretolerance=30 @@ -68,7 +65,7 @@ A smooth manifold consists of a topological space $M$ equipped with a smooth max \[ \psi_j^{}\circ f\circ\phi_i^{-1} \] -is itself smooth, where $\leftbrace\psi_i\rightbrace$ is a smooth atlas for $N$. Differentiating $f$ produces the associated tangent map $Df$. The function $Df$ maps the tangent space $TM$ to the tangent space $TN$ and is linear when restricted to individual tangent spaces $T_pM$. If $M$ can be written as a product $M_1\times M_2$, we can consider the partial tangent maps $\partial_1f$ and $\partial_2f$ by considering the compositions $f\circ\iota_1$ and $f\circ\iota_2$, where $\iota_1$ and $\iota_2$ are inclusion maps with respect to a particular point. Combining both maps, we have the equation +is itself smooth, where $\leftbrace\psi_i\rightbrace$ is a smooth atlas for $N$. Differentiating $f$ produces the associated tangent map $Df$. The function $Df$ maps the tangent bundle $TM$ to the tangent bundle $TN$ and is linear when restricted to individual tangent spaces $T_pM$. If $M$ can be written as a product $M_1\times M_2$, we can consider the partial tangent maps $\partial_1f$ and $\partial_2f$ by considering the compositions $f\circ\iota_1$ and $f\circ\iota_2$, where $\iota_1$ and $\iota_2$ are inclusion maps with respect to a particular point. Combining both maps, we have the equation \[ Df(u,v)=\partial_1f(u)+\partial_2f(v), \] |