texlive[61193] Master: rbt-mathnotes (30nov21)
commits+karl at tug.org
commits+karl at tug.org
Tue Nov 30 23:53:25 CET 2021
Revision: 61193
http://tug.org/svn/texlive?view=revision&revision=61193
Author: karl
Date: 2021-11-30 23:53:25 +0100 (Tue, 30 Nov 2021)
Log Message:
-----------
rbt-mathnotes (30nov21)
Modified Paths:
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trunk/Master/tlpkg/bin/tlpkg-ctan-check
trunk/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc
Added Paths:
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trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/LICENSE.txt
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/README.md
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/cheat-sheet.pdf
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/cheat-sheet.tex
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/multivar.pdf
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/multivar.tex
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/topology-hw-1.pdf
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/topology-hw-1.tex
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/rbt-mathnotes.pdf
trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/rbt-mathnotes.tex
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-formula-sheet.cls
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-hw.cls
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-messages.sty
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-util.sty
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.cls
trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.sty
trunk/Master/tlpkg/tlpsrc/rbt-mathnotes.tlpsrc
Added: trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/LICENSE.txt
===================================================================
--- trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/LICENSE.txt (rev 0)
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@@ -0,0 +1,416 @@
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Property changes on: trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/LICENSE.txt
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+++ trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/README.md 2021-11-30 22:53:25 UTC (rev 61193)
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+# rbt-mathnotes
+
+Rebecca Turner’s personal macros and styles for typesetting mathematics notes.
+
+See `rbt-mathnotes.pdf` for detailed documentation.
+
+Contents:
+
+- `rbt-mathnotes` package
+- `rbt-mathnotes` document class
+- `rbt-mathnotes-hw` document class, containing specialized commands for
+ typesetting homework assignments and solutions (in particular, the `problem`
+ environment and `\prob` command)
+- `rbt-mathnotes-formula-sheet` document class, optimized for stuffing as much
+ text as possible onto an exam “cheat sheet”
+- Examples of each document class in the `examples` directory
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--- trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/cheat-sheet.tex (rev 0)
+++ trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/cheat-sheet.tex 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,227 @@
+%% cheat-sheet.tex
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\documentclass{rbt-mathnotes-formula-sheet}
+\usepackage{nicefrac}
+\ExplSyntaxOn
+\NewDocumentCommand \normalized { m }
+ { \frac { #1 } { \| #1 \| } }
+\let \gr \grad
+\def \ddx { \frac{d}{dx} }
+% VL = vector literal
+\NewDocumentCommand \vl { m } { \left\langle #1 \right\rangle }
+\ExplSyntaxOff
+
+\title{Formula Sheet}
+\author{Rebecca Turner}
+\date{2019-11-12}
+
+% "The most common size for index cards in North America and UK is 3 by 5
+% inches (76.2 by 127.0 mm), hence the common name 3-by-5 card. Other sizes
+% widely available include 4 by 6 inches (101.6 by 152.4 mm), 5 by 8 inches
+% (127.0 by 203.2 mm) and ISO-size A7 (74 by 105 mm or 2.9 by 4.1 in)."
+\mathnotes{
+ height = 4in ,
+ width = 6in ,
+}
+\begin{document}
+\maketitle
+\begin{gather*}
+% 12.2: Vectors
+% 12.3: Dot product
+ \textstyle\vec a \cdot \vec b = \sum_i a_i b_i = |\vec a| |\vec b| \cos \theta. \\
+% 12.4: Cross product
+ \vec a \times \vec b
+ % = \left| \begin{array}{rrr}
+ % \hat{i} & \hat{j} & \hat{k} \\
+ % a_1 & a_2 & a_3 \\
+ % b_1 & b_2 & b_3 \\
+ % \end{array} \right| \\
+ = \langle a_2 b_3 - a_3 b_2,
+ \quad a_3b_1 - a_1b_3, \\
+ a_1b_2 - a_2b_1 \rangle.\quad
+ |\vec a \times \vec b| = |\vec a| |\vec b| \sin \theta.
+% 12.5: Equations of lines and planes.
+\shortintertext{Param.\ eqns.\ of line through $\langle x_0,y_0,z_0 \rangle$
+par.\ to $\langle a,b,c \rangle$:}
+ x = x_0 + at,
+ \quad y = y_0 + bt,
+ \quad z = z_0 + ct. \\
+\text{Symm.\ eqns.: }
+ \frac{x-x_0}{a}
+ = \frac{y-y_0}{b}
+ = \frac{z-z_0}{c}. \\
+\shortintertext{Vec.\ eqn.\ of plane through $\vec r$ with $\vec n$ normal:}
+ \vec n \cdot (\vec r - \vec r_0) = 0,
+ \quad \vec n \cdot \vec r = \vec n \cdot \vec r_0. \\
+% 13.1: Vector functions
+% 13.2: Derivatives/integrals of vector functions
+% 13.3: Arc length and curvature
+\shortintertext{Length along a vec.\ fn.\ $\vec r(t)$:}
+ \textstyle\int_a^b \left|\vec r'(t)\right|\,dt = \int_a^b \sqrt{\sum_i
+ r_i'(t)^2}\,dt, \\
+\shortintertext{Unit tang.\ $\vec T(t) = \vec r'(t)/\left|\vec
+r'(t)\right|$, so curvature of $\vec r(t)$ w/r/t the arc len.\ fn. $s$:}
+ \kappa = \left|\frac{d\vec T}{ds}\right|
+ = \frac{\left| \vec T'(t) \right|}{\left| \vec r'(t) \right|}
+ = \frac{\left| \vec r'(t) \times \vec r''(t) \right|}{\left| \vec r'(t)
+ \right|^3}. \\
+\text{Unit normal:}\quad
+ \vec N(t) = \vec T'(t)\,/\,\left| \vec T'(t) \right| \\
+% 14.1: Functions of several variables
+% 14.2: Limits and continuity
+% 14.3: Partial derivatives
+\text{Clairaut's thm.:}\quad
+ f_{xy}(a,b) = f_{yx}(a,b) \\
+% 14.4: Tangent planes & linear approximations
+\shortintertext{Tan.\ plane to $z = f(x,y)$ at $\langle x_0, y_0,
+z_0\rangle$:}
+ z - z_0 = f_x(x_0, y_0) (x-x_0) \\
+ + f_y(x_0, y_0) (y-y_0). \\
+% Partial derivatives of f for each variable exist near a point and are
+% continuous => f is differentiable at the po\int.
+% 14.6: Directional derivatives and the gradient vector
+\text{Grad.:}\quad
+ \grad f(x,y) = \pd[f]x \hat{i} + \pd[f]y \hat{j}. \\
+\shortintertext{Dir.\ deriv.\ towards $\vec u$ at $\langle x_0, y_0 \rangle$:}
+ D_{\langle a,b\rangle} f(x_0, y_0) = f_x(x,y) a + f_y(x,y) b \\
+ = \grad f(x,y) \cdot \vec u. \\
+\shortintertext{Max of $D_{\vec u} f(\vec x) = \left|\grad f(\vec
+x)\right|$. Tan.\ plane of $f$ at $\vec p$:}
+ 0 =
+ f_x(\vec p)(x-\vec p_x)
+ + f_y(\vec p)(y-\vec p_y) \\
+ + f_z(\vec p)(z-\vec p_z).
+% 14.7: Maximum and minimum values
+\shortintertext{If $f$ has loc.\ extrem.\ at $\vec p$, then $f_x(\vec p) =
+0$ (\& $f_y$, etc). If so, let}
+ D = \left| \begin{array}{ll}
+ f_{xx} & f_{xy} \\
+ f_{yx} & f_{yy}
+ \end{array}\right|
+ = f_{xx} f_{yy} - (f_{xy})^2.
+\shortintertext{%
+ $D = 0$: no information.
+ $D < 0$: saddle pt.
+ $D > 0$: $f_{xx}(\vec p) > 0 \implies$ loc.\ min;
+ $f_{xx}(\vec p) < 0 \implies$ loc.\ max.
+ ($D$ is the \textbf{Hessian mat.})
+\endgraf
+ Set of possible abs. min and max vals of $f$ in reg.\ $D$: $f$ at critical
+ pts.\ and extreme vals.\ on the boundary of $D$.
+% 14.8: Lagrange multipliers
+\endgraf
+ Lagrange mults.: extreme vals of $f(\vec p)$ when $g(\vec p) = k$.
+ Find all $\vec x, \lambda$ s.t.
+}
+ \grad f(\vec x) = \lambda \grad g(\vec x),\quad g(\vec x) = k.
+\shortintertext{i.e.\ $f_x = \lambda g_x$, etc.}
+% 15.1: Double integrals over rectangles
+% 15.2: Iterated integrals
+% 15.3: Double integrals over general regions
+ \iint f(r\cos\theta, r\sin\theta)r\,dr\,d\theta. \\
+ A = \iint_D \left(\sqrt{f_x(x,y)^2 + f_y(x,y)^2 + 1}\right) \,dA. \\
+\shortintertext{Line int.s}
+ \int_C f(x,y)\,ds = \\
+ \int_a^b f(x(t), y(t))\sqrt{\left(\pd[x]t\right)^2 + \left(\pd[y]t\right)^2}\,dt \\
+\shortintertext{If $C$ is a smooth curve given by $\vec r(t)$ from $a \le t
+\le b$,}
+ \int_C \grad f \cdot d\vec r = f(\vec r(b)) - f(\vec r(a)) \\
+\text{Spherical coords:}\quad
+ x = \rho \sin \phi \cos \theta \\
+ y = \rho \sin \phi \sin \theta, z = \rho \cos \phi \\
+ \curl \vec F = \\ \left< \pd[R]y - \pd[Q]z, \pd[P]z - \pd[R]x, \pd[Q]x -
+ \pd[P]y\right>. \\
+ \vec F = \langle P,Q,R \rangle,\quad
+ \curl \vec F = \grad \times \vec F \\
+ \vec F \text{ ``conservative''} \implies \exists f, \vec F = \grad f. \\
+ \dive \vec F = \grad \cdot \vec F = \pd[P]x + \pd[Q]y + \pd[R]z. \\
+ \curl(\grad f) = \vec 0,\quad \dive \curl \vec F = 0 \\
+\shortintertext{If $C$ is a positively-oriented (ccw) closed curve, $D$
+is bounded by $C$, and $\vec n$ represents the normal,}
+ % \int_C P\,dx + Q\,dy = \iint_D\left( \pd[Q]{x} - \pd[P]{y} \right). \\
+ \oint_C \vec F \cdot \vec n\,ds = \iint_D \dive \vec F(x,y)\,dA.
+\end{gather*}
+
+\pagebreak
+\raggedright Common derivs:
+$f(g(x)) \to g'(x) f'(g(x))$,
+$b^x \to b^x \ln b$,
+$f^{-1}(x) \to 1/f'(f^{-1}(x))$,
+$\ln x \to 1/x$,
+$\sin x \to \cos x$, $\cos x \to -\sin x$,
+$\tan x \to \sec^2 x$,
+$\sin^{-1} x \to 1/\sqrt{1-x^2}$,
+$\cos^{-1} x \to -(\sin^{-1}x)'$ (etc.),
+$\tan^{-1} x \to 1/(1+x^2)$,
+$\sec^{-1} x \to 1/(|x|\sqrt{x^2-1})$.
+
+Common ints (don't forget $+C$):
+\begin{gather*}
+ x^n \to \frac{x^{n + 1}}{n + 1} + C \quad \text{when } n \ne -1 \\
+ 1/x \to \ln |x| \\
+ \tan x \to -\ln(\cos x) \\
+ \int uv'\,dx = uv - \int u'v\,dx \quad\text{(Int.\ by parts)} \\
+ \int u\,dv = uv-\int v\,du \\
+ \int_{g(a)}^{g(b)} f(u)\,du = \int_a^b f(g(x))g'(x)\,dx
+ \quad\text{$u$-substitution.}
+\intertext{E.x.\ in $\int 2x \cos x^2\,dx$, let $u=x^2$, find $du/dx=2x
+\implies du = 2x\,dx$, subs.\ $\int \cos u\,du = \sin u + C = \sin x^2 +
+C$.}
+ \iint_R f(x,y)\,dA = \int_\alpha^\beta \int_a^b f(r\cos\theta,
+ r\sin\theta)r\,dr\,d\theta
+\end{gather*}
+\begin{itemize}
+ \item Integrand contains $a^2-x^2$, let $x = a\sin\theta$ and use $1 -
+ \sin^2 \theta = \cos^2 \theta$.
+ \item $a^2 + x^2$, let $x = a\tan\theta$, use $1 + \tan^2 \theta = \sec^2
+ \theta$.
+ \item $x^2 - a^2$, let $x = a\sec\theta$, use $\sec^2\theta - 1 = \tan^2
+ \theta$.
+\end{itemize}
+
+\begin{gather*}
+ \lim_{x \to 0} \sin x/x = 1 \\
+ \lim_{x \to 0} (1-\cos x)/x = 0 \\
+ \lim_{x \to \infty} x \sin(1/x) = 1 \\
+ \lim_{x \to 0} (1+x)^{1/x} = e \\
+ \lim_{x \to 0} (e^{ax}-1)/(bx) = a/b \\
+ \lim_{x \to 0^+} x^x = 1 \\
+ \lim_{x \to 0^+} x^{-n} = \infty \\
+ \text{For $0/0$ or $\pm\infty/\infty$,}\quad
+ \lim_{x \to c} f(x)/g(x) = \lim_{x \to c} f'(x)/g'(x) \\
+ \text{For $g(x)$ cont.\ at $L$,}
+ \lim_{x \to c} f(x) = L \implies \lim_{x \to c} g(L)
+\end{gather*}
+
+\end{document}
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+%% multivar.tex
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\documentclass[knowledge]{rbt-mathnotes}
+\title{Multivariable Calculus}
+\mathnotes{
+ instructor = Prof.~Corey Bregman ,
+ name = Rebecca Turner ,
+ email = rebeccaturner at brandeis.edu ,
+ course = \textsc{math} 20a (multivariable calculus) ,
+ institution = Brandeis University ,
+ semester = Fall 2019 ,
+}
+
+\ExplSyntaxOn
+\NewDocumentCommand \normalized { m }
+ { \frac { #1 } { \| #1 \| } }
+\let \gr \grad
+\def \ddx { \frac{d}{dx} }
+% VL = vector literal
+\NewDocumentCommand \vl { m } { \left\langle #1 \right\rangle }
+\ExplSyntaxOff
+
+% \makeatletter
+% \@ifpackageloaded{knowledge}
+% {
+\knowledge{notion, index={Derivative!Partial}}
+ | partial derivative
+\AtBeginDocument{\index{Partial derivative|see{Derivative, partial}}}
+
+\knowledge{notion, index={Derivative!Directional}}
+ | directional derivative
+\AtBeginDocument{\index{Directional derivative|see{Directional, partial}}}
+
+\knowledge{notion, index=Unit vector}
+ | unit vector
+
+\knowledge{notion, index=Limit}
+ | limit
+
+\knowledge{notion, index={Differentiable functions}}
+ | differentiable
+
+\knowledge{notion, index=Gradient}
+ | gradient
+
+\knowledge{notion, index={Neighborhood (topology)}}
+ | neighborhood
+
+\knowledge{notion, index=Local maximum}
+ | local maximum
+ | local maxima
+
+\knowledge{notion, index=Local minimum}
+ | local minimum
+ | local minima
+
+\knowledge{notion, index=Absolute maximum}
+ | absolute maximum
+ | absolute maxima
+
+\knowledge{notion, index=Absolute minimum}
+ | absolute minimum
+ | absolute minima
+
+\knowledge{notion, index=Local extremum}
+ | local extremum
+ | local extrema
+
+\knowledge{notion, index=Critical point}
+ | critical point
+
+\knowledge{notion, index=Saddle point}
+ | saddle point
+
+\knowledge{notion, index={Lagrange multiplier}}
+ | Lagrange multiplier
+ | Lagrange multipliers
+ | the method of Lagrange multipliers
+
+\knowledge{url={https://en.wikipedia.org/wiki/Joseph-Louis_Lagrange}}
+ | Joseph-Louis Lagrange
+ | Lagrange
+
+\knowledge{url={https://en.wikipedia.org/wiki/Marquis_de_Condorcet}}
+ | Marquis de Condorcet
+
+ \knowledge{url={https://en.wikipedia.org/wiki/Adrien-Marie_Legendre}}
+ | Adrien-Marie Legendre
+% }
+% {}
+% \makeatother
+\date{2019-10-23}
+\begin{document}
+\maketitle
+\tableofcontents
+
+\chapter{Vectors}
+I already know about vectors --- I've been taught them in about five
+different courses so far. I'm skipping this.
+
+\chapter{Partial derivatives}
+
+If we have a function of multiple variables, say
+\[f(a_1, a_2, a_3, \dots),\]
+we might care about the change of $f$ with respect to only one variable. By
+picking a fixed value for all but one of the variables, we can determine
+this.
+
+Say that we want to find the "partial derivative" of $f$ with respect to
+$a_2$; then, by constructing $g(a_2) = f(c_1, a_2, c_3, \dots)$, we've
+created a function of \emph{one} variable, which we can differentiate as
+usual.
+\begin{notation}
+ We write the "partial derivative" of a function $f$ at a point $\vec p$
+ with respect to a basis element $a$ of $\vec p$ as \fbox{$f_a(\vec p)$.}
+
+ We may also use much more common notation
+ \[\pd[f]{a},\]
+ using the "partial derivative" symbol $\partial$, a stylized cursive
+ ``d''.\footnote{Introduced by "Marquis de Condorcet" in 1770, who used it
+ to represent a partial \emph{differential}, i.e.~the $dy$ or $dx$ in
+ $dy/dx$, and then adapted in 1786 by "Adrien-Marie Legendre" for use as the
+ partial derivative.}
+
+ In the interest of completeness, I'll exhaustedly note that the book also
+ uses, on occasion, the notation $D_a f$.
+\end{notation}
+
+We can also calculate ""higher partial derivatives"" --- similarly to the
+higher ordinary derivatives. The notation is a fairly clear extension:
+\[(f_x)_x = f_{xx} = \pd x \left( \pd[f]{x} \right) = \pd[^2 f]{x^2}.\]
+
+\begin{thm}[Clairaut's Theorem]
+ Suppose $f$ is defined on a neighborhood $N$ about a point $\vec p$.
+ If $f_{xy}$ and $f_{yx}$ are continuous in $N$, then $f_{xy}(\vec p) =
+ f_{yx}(\vec p)$.
+\end{thm}
+
+\section{Gradients}
+\begin{notation}
+ This ridiculous textbook denotes the "partial derivative" of a function
+ $f(x, y) = z$ with respect to $x$ as $f_x(x, y)$.
+\end{notation}
+
+\begin{defn}
+ The ""directional derivative"" of a function $f$ at $(x_0, y_0)$ in the
+ direction of a "unit vector" $\vec u = \langle a, b \rangle$ is
+ \[D_{\vec u} f(x_0, y_0) = \lim_{h \to 0} \frac{f(x_0 + ha, y_0 + hb) -
+ f(x_0, y_0)}{h},\]
+ if the "limit" exists.
+\end{defn}
+
+If $f : \Re^2 \mapsto \Re$ is a "differentiable" function, then $f$ has a
+"directional derivative" in the direction of any "unit vector" $\vec u =
+\langle a, b \rangle$ of
+\begin{alignat*}{1}
+ D_{\vec u} f(x, y) &= f_x(x, y) a + f_y(x, y) b.
+\intertext{Or, if $\vec u = \langle \cos \theta, \sin \theta \rangle$, then}
+ D_{\vec u} f(x, y) &= f_x(x, y) \cos \theta + f_y(x, y) \sin \theta.
+\end{alignat*}
+
+Noticing that the "directional derivative" of a function can be written as
+the dot product of two vectors,
+\begin{alignat*}{1}
+ D_{\vec u} f(x, y) &= f_x(x, y) a + f_y(x, y) b \\
+ &= \langle f_x(x, y), f_y(x, y) \rangle \cdot \langle a, b \rangle \\
+ &= \langle f_x(x, y), f_y(x, y) \rangle \cdot \vec u,
+\end{alignat*}
+we call the first vector $\langle f_x(x, y), f_y(x, y) \rangle$ the
+""gradient"" of $f$ and denote it as $\grad f$.
+
+\begin{defn}
+ The "gradient" of a function $f$ of two variables is defined as
+ \[\grad f(x, y) = \langle f_x(x, y), f_y(x, y) \rangle
+ = \frac{\partial f}{\partial x} \vec i + \frac{\partial f}{\partial y}
+ \vec j.\]
+\end{defn}
+
+Therefore, we can rewrite the "directional derivative" of a function $f$
+as
+\[D_{\vec u} f(x, y) = \grad f(x, y) \cdot \vec u.\]
+It's intuitive, then, that the maximum value of the "directional derivative"
+is $|\grad f(x, y)|$, when $\vec u$ is parallel to $\grad f(x, y)$.
+
+\section{Maximum and minimum values}
+\begin{defn}
+ $f : A^k \mapsto B$ has a ""local maximum"" at $\vec a$ if for some
+ "neighborhood" $N \subset A$ about $\vec a$, for all $\vec x \in N$,
+ $f(\vec x) \le f(\vec a)$.
+
+ Conversely, if $f(\vec x) \ge f(\vec a)$, then $f(\vec a)$ is a ""local
+ \emph{minimum}@local minimum"".
+
+ If the statement also holds true for $N = A$, then $\vec a$ is an
+ ""absolute maximum"" (or ""absolute minimum"").
+\end{defn}
+
+If $f$ has a "local maximum" or "minimum at local minimum" at $\vec a$ and the
+partials of $f$ exist at $\vec a$, then $\partial f/\partial x (\vec a) = 0$
+and $f_y(a, b) = 0$; geometrically, the tangent plane to a maximum or
+minimum must be horizontal.
+
+\begin{defn}
+ A point $\vec a$ is called a ""critical point"" of $f$ if $f_x(\vec a) =
+ 0$ or $f_x(\vec a)$ doesn't exist for all variables of $f$.
+\end{defn}
+
+\begin{defn}
+ A ""saddle point"" of a function is a "critical point" which is not a
+ "local extremum" of the function.
+\end{defn}
+
+If $(a, b)$ is a critical point of $f$, then let
+\[D = D(a, b) = f_{xx} (a,b) \, f_{yy} (a,b) - (f_{xy}(a,b))^2.\]
+If $D < 0$, then $(a, b)$ is a "saddle point" of $f$.
+
+\section{Lagrange multipliers}
+Often we want to find the "local extrema" of a function subject to
+constraints, i.e.~maximizing the volume of an object while keeping its
+surface area constant. The method of "Lagrange multipliers"\footnote{After
+"Joseph-Louis Lagrange" (1736--1813), ``an Italian Enlightenment Era
+mathematician and astronomer [who] made significant contributions to the
+fields of analysis, number theory, and both classical and celestial
+mechanics.''} is a strategy for doing this.
+
+To find extrema of $f(\vec p)$ constrained with $g(\vec p) = k$,
+we look for extrema of $f$ that are restricted to lie on the level curve
+$g(\vec p) = k$; it happens that the largest $c$ such that $f(\vec p) = c$
+intersects with $g(\vec p) = k$ when the two level curves are tangent with
+each other, i.e.~they have identical normals. In other words, for some
+scalar $\lambda$, $\grad f(\vec p) = \lambda \grad g(\vec p)$.
+
+More formally, suppose $f$ has an extrema at $\vec p_0$. Then, let the level
+surface generated by the constraint $g(\vec p) = k$ be called $S$, where
+$\vec p_0 \in S$. Then, let $C$ be the set of points given by $\vec r(t)$ such
+that $C \subset S$ and $\vec p_0 \in C$. Further, let $t_0$ be a point such
+that $\vec r(t_0) = \vec p_0$.
+
+Then, $f \after \vec r$ gives the values of $f$ on the curve $C$. $f$ has an
+extrema at $\vec p$, so $f \after \vec r$ must also, and $(f \after \vec
+r)'(t_0) = 0$. If $f$ is "differentiable", we can use the chain rule to
+write
+\begin{alignat*}{1}
+ 0 &= (f \after \vec r)'(t_0) \\
+ &= \grad f(\vec p_0) \cdot \vec r'(t_0).
+\end{alignat*}
+Therefore, the gradient of $f$ is orthogonal to the tangent of every such
+curve $C$. We also know that $\grad g(\vec p_0)$ is orthogonal to $\vec
+r'(t_0)$, so the gradients of $f$ and $g$ at $\vec p_0$ must be parallel.
+Therefore, if $\grad g(\vec p_0) \ne 0$, there exists some $\lambda$ such
+that
+\begin{equation}
+ \grad f(\vec p_0) = \lambda \grad g(\vec p_0),
+\end{equation}
+where the constant $\lambda$ is called a "Lagrange multiplier".
+
+Then, the ""method of Lagrange multipliers"" gives us a process to
+find the maximum and minimum values of a function $f(\vec p)$ subject to the
+constraint $g(\vec p) = k$, where $\vec p \in \Re^n$. To use the method of
+Lagrange multipliers, we assume that the extreme values exist and that
+$\grad g \ne 0$ on the level surface $g(\vec p) = k$.
+\begin{enumerate}
+ \item Find all values of $\vec p$ and $\lambda$ such that
+ \begin{alignat*}{1}
+ \grad f(\vec p) &= \lambda \grad g(\vec p) \\
+ \text{and}\qquad g(\vec p) &= k. \\
+ \end{alignat*}
+
+ \item Next, evaluate $f$ at all of the points found in the first step. The
+ largest of these values is the maximum value of $f$, and the smallest of
+ them is the minimum value.
+\end{enumerate}
+
+\chapter{Multiple integrals}
+Single integrals are good for functions of one variable. To integrate
+functions of multiple variables, we use multiple integrals. Straightforward
+enough.
+
+Multiple integrals allow us to calculate things like surface areas and
+volumes of geometric objects.
+
+In general, for some double integral
+\[\underbrace{\int_a^b \overbrace{\int_c^d f(x,y)\,dx}^{\mathclap{\text{We
+treat $y$ as constant while evaluating this.}}}\,dy,}_{\mathclap{\text{We've
+eliminated $x$ from the equation before evaluating this.}}}\]
+we do the opposite of partial differentiation and treat all variables other
+than the one we're integrating for as constant, repeatedly, until we've
+integrated with respect to all variables; each step in this process is
+called, predictably, ""partial integration"".
+
+\section{Double integrals}
+For an axis-aligned rectangle $R$ on the $xy$-plane from $(x_0, y_0)$ to $(x_1,
+y_1)$, the area of a function $f(x, y)$ under $R$ is given by the double
+integral
+\begin{alignat*}{1}
+ \iint_{Y} f(x,y)\,dA &= \underbrace{\int_{x_0}^{x_1} \int_{y_0}^{y_1}
+ f(x,y)\,dy\,dx}_{\mathclap{\text{This is the iterated form of the
+ integral.}}} \\
+ &= \int_{y_0}^{y_1} \int_{x_0}^{x_1} f(x,y)\,dx\,dy, \\
+\end{alignat*}
+where we use $\iint_R$ to mean ``integrating over the area of $R$'' and
+``$dA$'' to mean ``with respect to area.''
+
+The right-hand side of the equation above is called the ""iterated form"",
+or an \reintro*"iterated integral".
+
+We can also iterate over funkier regions if we're willing to play with the
+limits of integration a bit. The easiest regions to integrate over are the
+ones that are easily expressible as the region bounded above and below by
+functions of one variable, e.g. ``the region under the line $y = 2x$ and
+above the line $y = x^2$'' (note that this is bounded on the left at $x = 0$
+and on the right at $x = 2$).
+
+% Area[ImplicitRegion[x^2 < y \[And] y < 2 x, {x, y}
+The area of that region is expressed by the integral
+\begin{alignat*}{1}
+ A &= \int_0^2 \int_{x^2}^{2x}\,dy\,dx \\
+ &= \int_0^2 {\bigg[ x \bigg]}_{x^2}^{2x}\,dx \\
+ &= \int_0^2 {\bigg( 2x-x^2 \bigg)}\,dx \\
+ &= {\left[ x^2 - \frac{x^3}{3} \right]}_0^2 \\
+ &= 4 - \frac{8}{3} = \frac{4}{3}.
+\end{alignat*}
+
+A more complicated region might be ``the region under the paraboloid $z =
+x^2 + y^2$ and above the region in the $xy$-plane bounded by $y = \sqrt{x}$
+and $y=1-\cos x$.''
+
+We can build larger regions out of pieces, by summing smaller integrals.
+
+\section{Polar coordinates}
+Use the conversions
+\begin{alignat*}{1}
+ r &= \sqrt{x^2+y^2} \\
+ x &= r\cos\theta \\
+ y &= r\sin\theta \\
+\intertext{for the coordinates and then we have that if $R$ is a ``polar
+rectangle'' (arc-shaped region bounded by angles and radii) from $r=a$ to
+$r=b$ and $\theta = \alpha$ to $\theta = \beta$, we have}
+ \iint_R f(x,y)\,dA &= \int_\alpha^\beta \int_a^b f(r\cos\theta,
+ r\sin\theta)r\,dr\,d\theta, \\
+\intertext{which makes our lives easier for circly areas and volumes. Don't
+forget to multiply by $r$.
+\endgraf
+For squiggly and varying radii, we can use functions $h_1(\theta)$ and
+$h_2(\theta)$ instead of constants $a$ and $b$:}
+ \iint_D f(x,y)\,dA &= \int_\alpha^\beta \int_{h_1(\theta)}^{h_2(\theta)} f(r\cos\theta,
+ r\sin\theta)r\,dr\,d\theta. \\
+\end{alignat*}
+
+\section{Cylindrical coordinates}
+Just add $z$.
+
+\section{Spherical coordinates}
+I can never remember how these work. If we have a point $P$, and we drop it
+down to the $xy$-plane, the angle between the positive $x$-axis and the
+segment from the origin to $P$ is $\theta$.
+
+Next, the angle between the positive $z$-axis and the segment from the origin
+to $P$ is $\phi$.
+
+Finally, the length of the segment from the origin to $P$ is $\rho$.
+
+The conversions
+\begin{alignat*}{1}
+ x &= \rho \sin \phi \cos \theta \\
+ y &= \rho \sin \phi \sin \theta \\
+ z &= \rho \cos \phi \\
+\intertext{give us the integral-conversion for the spherical wedge bounded
+by $a \le \rho \le b, \alpha \le \theta \le \beta, c \le \phi \le d$ as}
+ \iiint_E f(x,y,z)\,dV &= \int_c^d \int_\alpha^\beta \int_a^b
+ f(\rho \sin\phi \cos\theta,\,
+ \rho \sin\phi \sin\theta,\,
+ \rho \cos \theta)
+ [\rho^2 \sin\phi]
+ \,d\rho\,d\theta\,d\phi. \\
+\end{alignat*}
+Very gross!
+
+\section{Surface area}
+
+For $f(x,y)$ with $f_x$, $f_y$ continuous, the surface area of $f$ within
+a region $D$ is
+\[A = \iint_D \left(\sqrt{f_x(x,y)^2 + f_y(x,y)^2 + 1}\right) \,dA.\]
+
+% Need notes on:
+% - Change of variables (in multiple integrals)
+
+\chapter{Vector calculus}
+A vector field is a mapping $\R^k \mapsto \R^n$; for each point in
+$k$-dimensional Euclidean space, we associate an $n$-dimensional vector.
+These vectors can represent velocity, distance, or anything else, and come
+up in all sorts of applied fields.
+
+We'll be mostly concerned with vector fields $\R^2\mapsto\R^2$ and
+$\R^3\mapsto\R^3$.
+
+If we have a plane curve given by the vector equation
+\begin{alignat*}{1}
+ \vec r(t) &= \left< x(t), y(t) \right> \qquad a \le t \le b, \\
+\intertext{then the line integral of $f$ along $\vec r(t)$ from $a$ to $b$
+is}
+ & \int_a^b f(x(t), y(t)) \sqrt{{\left(\dd[x]{t}\right)}^2 +
+ {\left(\dd[y]{t}\right)}^2}\,dt,
+\end{alignat*}
+i.e.\ the length of the curve multiplied, at each point, by the value of the
+vector field $f$ at that point.
+
+% Need notes on:
+% 16.1, 16.2, 16.3, 16.4, 16.5,
+% Need to update cheat sheet.
+
+\appendix
+\chapter{Common formulas for derivatives and integrals}
+\backmatter
+\section{Derivatives}
+
+\begin{alignat*}{2}
+ \ddx&\;& (f + g) &= f' + g' \\
+ \ddx&& x^n &= nx^{n - 1} \\
+ \ddx&& (fg) &= fg' + f'g \\
+ \ddx&& \frac{h}{l} &= \frac{l h' - h l'}{l^2} \\
+ \ddx&& f(g(x)) &= f'(g(x)) g'(x) \quad\text{(Chain rule.)} \\
+ \ddx&& b^x &= b^x \ln b \\
+ \ddx&& f^{-1}(x) &= \frac{1}{f'(f^{-1}(x)} \\
+ \ddx&& c &= 0 \\
+ \ddx&& c\,f &= c\,f' \\
+ \ddx&& e^x &= e^x \\
+ \ddx&& e^{f(x)} &= f'(x) e^{f(x)} \quad\text{(By the chain rule.)} \\
+ \ddx&& \ln x &= \frac{1}{x} \\
+ \ddx&& \log_b x &= \frac{1}{x \ln b} \\
+ \ddx&& [\vec u \cdot \vec v] &= \vec u' \cdot \vec v + \vec u \cdot \vec v' \\
+ \ddx&& [\vec u \times \vec v] &= \vec u' \times \vec v + \vec u \times \vec v' \\
+\end{alignat*}
+
+\subsection{Trigenometric}
+\begin{alignat*}{2}
+ \ddx&\;& \sin x &= \cos x \\
+ \ddx&& \cos x &= -\sin x \\
+ \ddx&& \tan x &= \sec^2 x \\
+ \ddx&& \cot x &= -\csc^2 x \\
+ \ddx&& \sec x &= \sec x \tan x \\
+ \ddx&& \csc x &= -\csc x \cot x \\
+ % inverse
+ \ddx&& \sin^{-1} x &= \frac{ 1}{\sqrt{1 - x^2}} \\
+ \ddx&& \cos^{-1} x &= \frac{-1}{\sqrt{1 - x^2}} \\
+ \ddx&& \tan^{-1} x &= \frac{ 1}{1 + x^2} \\
+ \ddx&& \cot^{-1} x &= \frac{-1}{1 + x^2} \\
+ \ddx&& \sec^{-1} x &= \frac{ 1}{|x| \sqrt{x^2 - 1}} \\
+ \ddx&& \csc^{-1} x &= \frac{-1}{|x| \sqrt{x^2 - 1}} \\
+\end{alignat*}
+
+\section{Integrals}
+See also:
+\emph{\href{https://www.whitman.edu/mathematics/calculus/calculus_08_Techniques_of_Integration.pdf}{Techniques
+of Integration}}.
+\begin{alignat*}{1}
+ \int x^n\,dx &= \frac{x^{n + 1}}{n + 1} + C \quad \text{when } n \ne -1 \\
+ \int x^{-1}\,dx &= \ln|x| + C \\
+ \int e^x\,dx &= e^x + C \\
+ \dd{t} \int_{a(t)}^{b(t)} g(s)\,ds &= b'(t) g(b(t)) - a'(t) g(a(t))
+ \quad\text{(Leibniz' rule.)} \\
+ \int uv'\,dx &= uv - \int u'v\,dx \\
+\end{alignat*}
+
+\subsection{Trigenometric}
+\begin{alignat*}{1}
+ \int \sin x\,dx &= -\cos x + C \\
+ \int \cos x\,dx &= \sin x + C \\
+ \int \sec^2 x\,dx &= \tan x + C \\
+ \int \sec x \tan x\,dx &= \sec x + C \\
+ \int \frac{1}{1 + x^2}\,dx &= \tan^{-1} x + C \\
+ \int \frac{1}{\sqrt{1 + x^2}}\,dx &= \sin^{-1} x + C \\
+\end{alignat*}
+
+\printindex
+\end{document}
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+++ trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/examples/topology-hw-1.tex 2021-11-30 22:53:25 UTC (rev 61193)
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+%% topology-hw-1.tex
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\documentclass[twocolumn, noxcolor, maketitle]{rbt-mathnotes-hw}
+\mathnotes{
+ instructor = Prof.~Ruth Charney ,
+ name = Rebecca Turner ,
+ email = rebeccaturner at brandeis.edu ,
+ course = \textsc{math} 104a (Intro to Topology) ,
+ institution = Brandeis University ,
+ semester = Spring 2020 ,
+}
+\title{Homework 1}
+\date{2020-01-18}
+\def\T{\mathcal{T}}
+\def\basis{\mathcal{B}}
+\usepackage[
+ letterpaper,
+ margin = 1in,
+]{geometry}
+\raggedbottom
+\begin{document}
+\maketitle
+
+\section{Topological Spaces}
+\subsection{Open Sets and the Definition of a Topology}
+\begin{problem}[1.7]
+ Define a topology on $\R$ (by listing the open sets within it) that contains
+ the open sets $(0,2)$ and $(1,3)$ that contains as few open sets as possible.
+\end{problem}
+$\T = \{ \emptyset, (0,2), (1,3), (1,2), (0,3), \R \}$.
+
+\subsection{Basis for a Topology}
+\begin{problem}[1.10]
+ Show that $\mathcal{B} = \{[a,b) \subset \R : a < b\}$ is a basis for a
+ topology on $\R$.
+\end{problem}
+\begin{enumerate}
+ \item \textbf{$\emptyset \in \T$, $\R \in \T$.} $\emptyset \in \T$ (by the
+ definition of the completion of a basis to a topology).
+
+ Next, we show $\R \in \T$. For all $n \in \Z_{\ge 0}$, $[n-1, n) \in \basis$
+ and $[-n + 1, -n) \in \basis$. We know that if $b_1, b_2 \in \basis$, $b_1
+ \union b_2 \in \T$, so these short intervals can be gathered together (``unionized'')
+ to produce $\R$:
+ \[ \bigunion_{n=1}^{\infty} \left( [n-1, n) \union [-n + 1, -n] \right) = \R, \]
+ so $\R \in \T$.
+
+ \item \textbf{$\T$ contains all finite intersections of elements of $\T$.}
+ Suppose we have two intervals $[a, b)$ and $[c, d)$. Then, we define
+ \begin{alignat*}{1}
+ a' &= \max(a, c) \\
+ b' &= \min(b, d).
+ \end{alignat*}
+ If $a' > b'$, the intersection $[a, b) \inter [c, d) = \emptyset$, which is
+ in $\T$. Otherwise, the intersection is $[a', b')$, which is an element of
+ $\basis$. All elements of the basis are in $\T$, so the intersection of two
+ elements is in the topology.
+
+ Thankfully, the intersection is itself always a basis element, so we can
+ use the same process to show that finite intersections are in $\T$ by
+ induction.
+
+ \item \textbf{Unions of elements of $\T$ are in $\T$.} By the definition of
+ the completion of a basis to a topology, this is true (all unions of basis
+ elements are included in $\T$).
+\end{enumerate}
+
+\begin{problem}[1.12]
+ % See example 1.9 for defn of \R_l
+ Determine which of the following are open sets in $\R_l$. In each case, prove
+ your assertion.
+ \[ A = [4,5)
+ \quad B = \{3\}
+ \quad C = [1,2]
+ \quad D = (7,8) \]
+\end{problem}
+\begin{enumerate}
+ \item $A$ is open in $\R_l$; $[4,5) \in \basis$.
+ \item $B$ is not an open set in $\R_l$; there is no $[a, b) \subset \R$ where
+ both $b > a$ and $|[a, b)| = 1$ (because $[0,1) \cong \R$, i.e.~all
+ intervals contain infinitely many points).
+
+ (Where $\cong$ means ``is isomorphic to.'')
+ \item $C$ is not open in $\R_l$ because the upper bound of an open set in
+ $\R_l$ is never inclusive. There is no set of intervals $[a_1, b_1), \dots$
+ where the union or intersection of the intervals has an inclusive upper bound.
+ \item $D$ is open because we can take
+ \[ D = \lim_{n\to\infty} \left[7 + \frac{1}{n}, 8\right), \]
+ where $[7 + 1/n, 8) \in \basis$ for any $n \in \R$ with $n \ne 0$.
+\end{enumerate}
+
+\pagebreak
+\begin{problem}[1.15]
+ An arithmetic progression in $\Z$ is a set
+ \[ A_{a,b} = \{\dots, a - 2b, a - b, a, a + b, a + 2b, \dots\} \]
+ with $a,b \in \Z$ and $b \ne 0$. Prove that the collection of arithmetic
+ progressions
+ \[ \mathcal{A} = \{ A_{a,b} : a, b \in \Z \text{ and } b \ne 0 \} \]
+ is a basis for a topology on $\Z$. The resulting topology is called the
+ arithmetic progression topology on $\Z$.
+\end{problem}
+
+\begin{proof}
+ \def\Ar#1#2{A_{#1,#2}}
+ \def\Ars{\mathcal{A}}
+ Let us describe the \emph{minimal form} of an arithmetic progression $\Ar ab$
+ to be the progression $\Ar{a'}{b'} = \Ar ab$ with $a', b' > 0$ and the
+ smallest possible $a'$; in particular, that $a' < b'$.
+
+ We can obtain the minimal form of the progression like so:
+ \begin{alignat*}{1}
+ a' &= a \bmod b \\
+ b' &= |b|, \\
+ \Ar{a'}{b'} &= \Ar ab.
+ \end{alignat*}
+
+ \begin{remark}
+ Two arithmetic progressions have the same elements if their minimal forms are
+ the same; this give an equivalence relation on $\Ars$.
+ \end{remark}
+
+ Now, suppose we have two arithmetic progressions $\Ar ab$ and $\Ar cd$. We
+ assume that the progressions are in minimal form without loss of generality. We
+ also assume that $b \le d$ (by swapping $(a,b)$ with $(c,d)$ if necessary),
+ again without loss of generality.
+
+ If $b \mid d$ and $a = c$, we have $\Ar ab \subset \Ar cd$. In particular, $\Ar
+ ab \inter \Ar cd = \Ar cd$.
+
+ If $b \mid d$ and $a \ne c$, we have $\Ar ab \inter \Ar cd = \emptyset$.
+
+ If $b \nmid d$, we have a different progression. An intersection is generated by
+ an index $(n_1, n_2)$, where
+ \begin{alignat*}{1}
+ a + b n_1 &= c + d n_2. \\
+ \intertext{We can then solve for $n_1$:}
+ t(n) &= c - a + dn \\
+ n_1 &= \frac{t(n_2)}{b}. \\
+ \intertext{Next, we have an infinite \emph{set} of possibilities for $n_2$:}
+ n_2 &\in \left\{n \in \Z : t(n) \mid b \right\}.
+ \intertext{Sorting the possible values of $n_2$ by absolute value, let us call
+ the smallest two values $i_1$ and $i_2$. Then, the difference between
+ adjacent elements in the intersection progression $\Ar ab \inter \Ar cd$
+ is $i_2 - i_1$.
+ \endgraf
+ Let}
+ a' &= a + bi_1 \\
+ b' &= i_2 - i_1 \\
+ \Ar ab \inter \Ar cd &= \Ar{a'}{b'}.
+ \end{alignat*}
+ This isn't super rigorous, admittedly (we're missing some inductive reasoning
+ about the integers to prove that there are an infinite set of valid values of
+ $n_2$, in particular), but I have some fairly convincing Haskell code. And the
+ missing steps are mostly boilerplate, and it's late at night already\dots
+
+ In all cases, the intersection of two arithmetic progressions is either empty or
+ another arithmetic progression (i.e.~either the empty set or another basis
+ element), so the same argument given above for $\R_l$ holds (namely that we can
+ extend this to all finite intersections of elements of $\Ars$ inductively).
+
+ Therefore, finite intersections are in the basis. Unions are in the completion
+ of the basis (again by definition). The special element $\emptyset$ is in the
+ completion (by definition), and $\Z = \Ar01$, so $\Z \in \basis$. Therefore,
+ $\Ars$ forms the basis of a topology on $\Z$.
+\end{proof}
+
+\pagebreak
+\subsection{Closed Sets}
+\begin{problem}[1.27(a)]
+ The infinite comb $C$ is the subset of the plane illustrated in Figure~1.17
+ and defined by
+ \begin{multline*}
+ C = \{(x,0) : 0 \le x \le 1\} \;\union \\
+ \bigg\{ \left( \frac{1}{2^n}, y \right) : n = 0,1,2, \dots \\
+ \text{ and } 0 \le y \le 1 \bigg\}.
+ \end{multline*}
+ Prove that $C$ is not closed in the standard topology on $\R^2$.
+\end{problem}
+\begin{proof}
+ Suppose $C$ is closed in the standard topology on $\R^2$. Then, its complement
+ $C^c = \R^2 \setminus C$ must be an open set.
+
+ The point $(0, 1)$ is not in $C$, so $(0, 1) \in C^c$. Every open ball in $\R^2$
+ containing $(0, 1)$ also contains a smaller open ball centered about $(0, 1)$.
+ (For example, the open ball about $(-1, 1)$ of radius $1.1$ contains the open
+ ball centered about $(0, 1)$ of radius $0.1$.)
+
+ However, every open ball centered about $(0, 1)$ contains infinitely many
+ points of $C$; if the ball has radius $r$, all the comb's ``tines'' at $x =
+ 1/2^n$ for $n > - \log_2 r$ intersect with the ball.
+
+ Therefore, every open ball containing $(0, 1)$ also contains points in $C$. As
+ a result, $C^c$ is not open, which contradicts our assumption. Therefore, $C$
+ is not closed.
+\end{proof}
+
+\begin{problem}[1.32]
+ Prove that intervals of the form $[a, b)$ are closed in the lower limit
+ topology on $\R$.
+\end{problem}
+\begin{proof}
+ Take some interval $[a, b)$. Its complement is given by $(-\infty, a) \union
+ [b, \infty)$. Given that
+ \begin{alignat*}{1}
+ (-\infty, a) &= \bigunion_{n=1}^\infty [a-n, a) \\
+ [b, \infty) &= \bigunion_{n=1}^\infty [b, b+n),
+ \end{alignat*}
+ the complement of $[a, b)$ is the union of a number of lower-limit intervals
+ in $\R$, i.e.~the basis elements. The basis elements and its unions are open
+ sets, so the complement of $[a, b)$ is an open set. Then, by the definition of
+ a closed set, $[a, b)$ is closed in $\R_l$.
+\end{proof}
+
+
+\end{document}
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--- trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/rbt-mathnotes.tex (rev 0)
+++ trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/rbt-mathnotes.tex 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,475 @@
+%% rbt-mathnotes.tex
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\documentclass{ltxguidex}
+
+\errorcontextlines=10
+\usepackage{longtable}
+\usepackage{changepage}
+\usepackage{metalogo}
+\usepackage{changelog}
+\newcommand{\mn}{\ctan{rbt-mathnotes}}
+
+\makeatletter
+\renewcommand{\SX at explpreset}{
+ language=[LaTeX]TeX,
+ numbers=none,
+}
+\makeatother
+
+%\setmainfont{Charter}
+\lstset{basewidth=0.6em}
+
+\usepackage[
+ nomaketitle,
+ notitles,
+ noxcolor,
+ noenumitem,
+ notheorems,
+]{rbt-mathnotes}
+
+\usepackage{FiraSans}
+\usepackage{FiraMono}
+
+\NewDocumentEnvironment{ctandescription}{}
+ {\NewDocumentCommand{\pkg}{m}{\item[\ctan{##1}]}
+ \begin{description}}
+ {\end{description}}
+
+\author{Rebecca Turner\thanks{\email{rbt at sent.as}, \https{becca.ooo}}}
+\title{The \mn\ Package}
+\date{1.0.2 2021/11/29}
+\begin{document}
+\maketitle
+
+\begin{abstract}
+ Rebecca Turner's personal macros and styles for typesetting mathematics
+ notes.
+\end{abstract}
+
+\begin{note}
+ Browse the sources, contribute, or complain at \\
+ \https{github.com/9999years/latex-mathnotes}
+\end{note}
+
+\tableofcontents
+\vfill
+\pagebreak
+
+\begin{note}
+ Copyright 2021 Rebecca B. Turner.
+
+ This work 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
+ \https{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 work has the LPPL maintenance status `maintained'.
+
+ The Current Maintainer of this work is Rebecca B. Turner.
+
+ This work consists of the files:
+ \begin{itemize}
+ \item \texttt{README.md}
+ \item \texttt{rbt-mathnotes.tex}
+ \item \texttt{rbt-mathnotes.sty}
+ \item \texttt{rbt-mathnotes.cls}
+ \item \texttt{rbt-mathnotes-util.sty}
+ \item \texttt{rbt-mathnotes-messages.sty}
+ \item \texttt{rbt-mathnotes-hw.cls}
+ \item \texttt{rbt-mathnotes-formula-sheet.cls}
+ \item \texttt{examples/cheat-sheet.tex}
+ \item \texttt{examples/multivar.tex}
+ \item \texttt{examples/topology-hw-1.tex}
+ \end{itemize}
+ and the derived files:
+ \begin{itemize}
+ \item \texttt{rbt-mathnotes.pdf}
+ \item \texttt{examples/cheat-sheet.pdf}
+ \item \texttt{examples/multivar.pdf}
+ \item \texttt{examples/topology-hw-1.pdf}
+ \end{itemize}
+\end{note}
+
+\vfill
+\pagebreak
+
+\section{Package options}
+
+Some options are enabled by default, and can be disabled by passing
+|no<option>|. The enabled-by-default options are:
+\begin{keys}
+ \key{fonts}[\bool][true]
+ \key{stix}[\bool][true]
+ \begin{itemize}
+ \item In \XeTeX\ or \LuaTeX, loads the \ctan{unicode-math} package, and
+ then, if the \option{stix} option is also given, loads the
+ \texttt{STIX2Text} and \texttt{STIX2Math} \textsc{otf} fonts (available
+ in the \ctan{stix2-otf} package).
+
+ The \texttt{STIX2Math} font is loaded with stylistic sets 1 (roundhand
+ script forms instead of chancery script for |\mathcal| Script
+ Alphanumeric Symbols) and 8 (upright, rather than slanted, forms for
+ integrals); see ``Stylistic Sets'' in
+ \href{http://mirrors.ctan.org/fonts/stix2-otf/STIXTwoMath-Regular.pdf}{the
+ \texttt{stix2-otf} documentation} (pp.~51--53) for more information.
+
+ \item In other engines, if the \option{stix} option is also given, loads
+ the \package{stix2} package from \ctan{stix2-type1}.
+ \end{itemize}
+
+ \key{symbols}[\bool][true]
+
+ Defines a collection of ``natural language'' math-mode symbol commands.
+ Most commands are declared with |\ProvideDocumentCommand| so that they
+ won't overwrite custom commands you've already defined.
+
+ Note that symbols may look different depending on the \option{fonts} and
+ \option{stix} options.
+
+ \begin{longtable}{rl}
+ |\lnot| & $\lnot$ \\
+ |\Rational|, |\Rat|, |\Q| & $\Rational$ \\
+ |\Natural|, |\Nat|, |\N| & $\Natural$ \\
+ |\Integer|, |\Int|, |\Z| & $\Integer$ \\
+ |\Complex|, |\Comp|, |\C| & $\Complex$ \\
+ |\Real|, |\R| & $\R$ \\
+ |\powerset| & $\powerset$ \\
+ |\vec{A}| & $\vec{A}$ \\
+ |\intersection|, |\inter| & $\intersection$ \\
+ |\bigintersection|, |\biginter| & $\bigintersection$ \\
+ |\union| & $\union$ \\
+ |\bigunion| & $\bigunion$ \\
+ |\divisible|, |\div| & $a \divisible b$ \\
+ |\notdivisible|, |\ndivisible|, |\notdiv|, |\ndiv| & $a \notdivisible b$ \\
+ |\floor{A}| & $\floor{A}$ \\
+ |\ceil{A}| & $\ceil{A}$ \\
+ |\emptyset|, |\es| & $\emptyset$ \\
+ |\after| & $g \after f$ \\
+ |\cross| & $a \cross b$ \\
+ |\img| & $\img f$ \\
+ |\pre| & $\pre f$ \\
+ |\Stab| & $\Stab f$ \\
+ |\FixPt| & $\FixPt f$ \\
+ |\id| & $\id$ \\
+ |\injection|, |\inj| & $\injection$ \\
+ |\surjection|, |\surj| & $\surjection$ \\
+ |\bijection|, |\bij| & $\bijection$ \\
+ |\restriction|, |\restr| & $f \restr_{\N}$ \\
+ |\dd[y]{x}| & $\dd[y]{x}$ \\
+ |\pd[y]{x}| & $\pd[y]{x}$ \\
+ |\curl| & $\curl$ \\
+ |\dive| & $\dive$ \\
+ \end{longtable}
+
+ \key{maketitle}[\bool][true]
+ Redefines |\maketitle| and related commands. The provided |\maketitle|
+ command will automatically insert a |\thanks| if any email, course,
+ instructor, institution, or semester is supplied with the |\mathnotes|
+ command.
+
+ \key{titles}[\bool][true]
+ No-op; may set the format of sectioning commands in the future.
+
+ \key{xcolor}[\bool][true]
+ Load the \ctan{xcolor} package and defines several colors with the |MN|
+ prefix.
+
+ \key{theorems}[\bool][true]
+ Set up various theorem environments with the \ctan{ntheorem} and
+ \ctan{mdframed} packages.
+
+ Provides |thm| (Theorem), |lem| (Lemma), |cor| (Corollary), |prop|
+ (Proposition), |defn| (Definition), |notation|, |ex|
+ (Example), |note|, |remark|, |hint|, and |abuse-of-notation| (Abuse of
+ notation) theorem-like environments.
+
+ \key{enumitem}[\bool][true]
+ Loads the \ctan{enumitem} package.
+
+\end{keys}
+
+The other options are not enabled by default, and can be enabled by passing
+|<option>| --- the option name --- as a package option:
+\begin{keys}
+ \key{listings}[\bool]
+ Loads the \ctan{listings} and \ctan{xcolor} packages.
+ Sets default styles for listings, including setting the default language to
+ |Mathematica|.
+
+ \key{knowledge}\bool]
+ Loads the \ctan{knowledge} package and sets up default styles.
+ Patches lists so that manually placing |\AP| and |\itemAP| commands is
+ unecessary.
+
+ \key{index}[\bool]
+ Sets the |knowledge| key and starts indexing with |\makeindex|.
+
+ \key{footnotes}[\bool]
+ Loads the \ctan{footmisc} package and sets up footnotes.
+
+ \key{figures}[\bool]
+ Loads the \ctan{graphicx} and \ctan{caption} packages and sets up figure
+ captions.
+
+ \key{tabu}[\bool]
+ Loads the \ctan{multirow}, \ctan{booktabs}, \ctan{longtable}, and
+ \ctan{tabu} packages.
+
+ Defines the |\Th| command.
+
+ \key{kindle}[\bool]
+ Sets a small page size and tweaks the layout for Kindle devices; designed in
+ particular for whatever generation of Kindle Paperwhite I have.
+ Only compatible with the \ctan{memoir} document class.
+
+\end{keys}
+
+\section{Commands}
+
+\begin{desc}
+|\numberthis|
+\end{desc}
+
+At the end of a line (before the |\\|) in an \ctan{amsmath} starred
+environment, gives an equation a number.
+
+\begin{LTXexample}
+\begin{alignat*}{2}
+ x &= y \\
+ y &= 2z \numberthis \\
+ z &= 1/w
+\end{alignat*}
+\end{LTXexample}
+
+\begin{desc}
+|\labelthis{<label>}|
+\end{desc}
+
+At the end of a line (before the |\\|) in an \ctan{amsmath} starred
+environment, gives an equation a number and label for referencing.
+
+\begin{LTXexample}
+\begin{alignat*}{2}
+ x &= y \\
+ y &= 2z \labelthis{eq:cool} \\
+ z &= 1/w.
+\end{alignat*}
+As we saw in
+Equation~\ref{eq:cool}, \dots
+\end{LTXexample}
+
+\begin{desc}
+|\newacronym[<command>]{<text>}|
+\end{desc}
+
+Defines |\<command>| to be |\textsc{<text>}|; |<command>| defaults to |<text>|
+if ommitted.
+
+\begin{LTXexample}
+\newacronym{nist}
+\newacronym[\seetan]{ctan}
+
+\nist\ is not associated
+with \seetan.
+\end{LTXexample}
+
+\begin{desc}
+|\newacronyms{<acronyms>}|
+\end{desc}
+
+Defines a collection of acronym commands together using |\newacronym|;
+|<acronyms>| is a comma-separated list of acronyms.
+
+\begin{LTXexample}
+\newacronyms{apa, mla}
+
+\apa\ and \mla\ are common
+citation styles.
+\end{LTXexample}
+
+\begin{desc}
+|\mathnotes{<key-value pairs>}|
+\end{desc}
+
+\begin{keys}
+ \key{date}[\m{date}]
+ \key{author}[\m{author}]
+ \key{title}[\m{title}]
+ Sets the date, author, or title; setting these keys are equivalent to using the
+ |\date|, |\author|, and |\title| commands, respectively.
+
+ \key{institution}[\m{institution}]
+ Sets the institution (e.g., Brandeis University) associated with the
+ document.
+ \key{course}[\m{course}]
+ Sets the course (e.g., \textsc{math}~23a) associated with the
+ document.
+ \key{semester}[\m{semester}]
+ Sets the semester (e.g., Fall 2018) associated with the document.
+ \key{instructor}[\m{instructor}]
+ Sets the instructor (e.g., Prof.~Ruth~Charney) associated with the document.
+ \key{email}[\m{email}]
+ Sets the email (e.g., \email{rbt at sent.as}) associated with the author.
+\end{keys}
+
+\begin{desc}
+|\TODO[<item>]|
+\end{desc}
+
+Typesets a to-do marker.
+
+\begin{LTXexample}
+\TODO
+
+\TODO[explain in detail]
+\end{LTXexample}
+
+\begin{desc}
+|\email{<email>}|
+\end{desc}
+Typesets an email address, with a link if the \ctan{hyperref} package is loaded.
+
+\begin{LTXexample}
+\email{rbt at sent.as}
+\end{LTXexample}
+
+\begin{desc}
+|\Th[<column spec>]{<header>}|
+\end{desc}
+Typesets a table column header in bold using |\multicolumn|. Especially useful
+if the column in question is a math or numeric column.
+
+\m{column spec} defaults to |l| (left-aligned).
+
+\section{The \texttt{rbt-mathnotes} document class}
+
+The \mn\ document class is a \ctan{memoir}-based class that automatically loads
+the \mn\ package.
+
+\section{The \texttt{rbt-mathnotes-hw} document class}
+
+The |rbt-mathnotes-hw| document class is based on the |rbt-mathnotes| document
+class, providing additional commands and styles for typesetting homework
+assignments. Theorems are given subtler styling that takes up less space on
+the page. The author name and title are added to the top-left heading.
+
+\begin{desc}
+|problem| \\
+|\begin{problem}[<number or options>]| \\
+|\prob[<number or options>]{<text>}|
+\end{desc}
+
+The |problem| environment (and its matching shorthand |\prob|) typesets a
+homework problem typesets a homework problem. Problems are added to the table of
+contents at the chapter-level, which is the top level if I remember correctly.
+
+\m{number or options} is a list of key-value pairs:
+
+\begin{keys}
+ \key{number}[\m{number}]
+ Sets the problem's number. For brevity, an unrecognized key with no value
+ is also used as the problem number; this allows concise expressions like
+ |\begin{problem}[4.3a] ...| to specify problem numbers (to match textbook
+ problem numbers, for example). Otherwise, problem numbers
+ start at 1 and count up.
+
+ \key{title}[\m{title}]
+ Sets the problem's ``title''.
+
+ \key{label}[\m{label}]
+ Sets the problem's label (e.g., |prob:n-sheeted-covering|), which can be
+ referred to later with |\ref|.
+\end{keys}
+
+If your professor calls them ``exercises'' or something, you can change the
+string used to refer to them with the |\mathnotes| command, which supports an
+additional key in |rbt-mathnotes-hw|:
+\begin{keys}
+ \key{problem string}[\m{problem string}][Problem]
+ The string used to represent a problem in titles and contents entries.
+\end{keys}
+
+\pagebreak
+\section{The \texttt{rbt-mathnotes-formula-sheet} document class}
+
+Sometimes, exams will let you take any formula sheet of a given size as
+reference material. The |rbt-mathnotes-formula-sheet| document class (based on the
+\ctan{article} class) is optimized for getting as much material as possible in
+that area. A tiny |\maketitle| is provided, as well as a tiny |\section|.
+Theorem titles are highly abbreviated (``Thm'' instead of ``Theorem''). Lists
+are rendered without linebreaks between items. Paragraphs are compressed and the
+page margins are set to a tenth of an inch. The entire document is set in
+|\scriptsize|.
+
+Some additional keys are added to the |\mathnotes| command to customize the
+output:
+
+\begin{keys}
+ \key{columns}[\m{column count}][3]
+ The number of text columns to set the formula sheet in; use 1 to turn off
+ columns.
+
+ \key{balance columns}
+ If set, the unstarred |multicols| environment is used instead of |multicols*|,
+ which attempts to spread material between each of the columns evenly, to
+ make their vertical sizes as even as possible.
+
+ It doesn't look great --- you want to know when you've filled up one column
+ --- so it's off by default.
+
+ \key{width}[\m{width}][8.5in]
+ \key{height}[\m{height}][11in]
+ Set the paper width and height. The 0.1 inch margins are not customizable.
+\end{keys}
+
+\begin{changelog}[author=Rebecca Turner]
+ \begin{version}[v=1.0.2, date=2021-11-27, short]
+ Added license notice to all files.
+ \end{version}
+
+ \begin{version}[v=1.0.1, date=2021-11-24, short]
+ Renamed package from \texttt{mathnotes} to \texttt{rbt-mathnotes} to avoid
+ a file name conflict with
+ \href{http://mirrors.ctan.org/fonts/newtx/doc/mathnotes.pdf}{\texttt{CTAN:/fonts/newtx/doc/mathnotes.pdf}}.
+ \end{version}
+
+ \begin{version}[v=1.0.0, date=2021-11-04, short]
+ Initial release as \texttt{mathnotes}, documented package.
+ \end{version}
+\end{changelog}
+
+\end{document}
Property changes on: trunk/Master/texmf-dist/doc/latex/rbt-mathnotes/rbt-mathnotes.tex
___________________________________________________________________
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===================================================================
--- trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-formula-sheet.cls (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-formula-sheet.cls 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,150 @@
+%% rbt-mathnotes-formula-sheet.cls
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\ProvidesExplClass{rbt-mathnotes-formula-sheet}{2021/11/29}{1.0.2}{Styles
+ for mathematical exam formula sheets.}
+
+\LoadClass{article}
+
+\RequirePackage{rbt-mathnotes}
+
+\cs_set:Npn \@maketitle
+ {
+ \textbf{\@title}~
+ (\@author,~\@date)
+ }
+
+\cs_set:Npn \mn__tiny_thm:nn #1#2
+ {
+ \RenewDocumentEnvironment { #1 } { o }
+ {
+ \textbf
+ {
+ #2
+ \IfValueT { ##1 }
+ {
+ :~##1
+ }
+ .
+ }
+ }
+ {
+ }
+ }
+
+\mn__tiny_thm:nn { thm } { Thm }
+\mn__tiny_thm:nn { lem } { Lem }
+\mn__tiny_thm:nn { cor } { Cor }
+\mn__tiny_thm:nn { prop } { Prop }
+\mn__tiny_thm:nn { defn } { Defn }
+\mn__tiny_thm:nn { ex } { Ex }
+\mn__tiny_thm:nn { note } { Note }
+\mn__tiny_thm:nn { remark } { Rmrk }
+
+\prg_new_conditional:Npnn \mn__if_should_use_multicols:
+ { T, }
+ {
+ \int_compare:nNnTF
+ { \g__mn_fs_columns_int } = { \c_one_int }
+ { \prg_return_false: }
+ { \prg_return_true: }
+ }
+
+\RequirePackage{multicol}
+\AtBeginDocument
+ {
+ \scriptsize
+ \mn__if_should_use_multicols:T
+ {
+ \begin
+ {
+ multicols
+ \bool_if:NF \g__mn_should_balance_multicols_bool
+ { * }
+ }
+ {
+ \int_use:N \g__mn_fs_columns_int
+ }
+ }
+ \skip_set:Nn \abovedisplayskip { 0pt }
+ \skip_set:Nn \belowdisplayskip { 0pt }
+ }
+
+\AtEndDocument
+ {
+ \mn__if_should_use_multicols:T
+ {
+ \end
+ {
+ multicols
+ \bool_if:NF \g__mn_should_balance_multicols_bool
+ { * }
+ }
+ }
+ }
+
+\bool_new:N \g__mn_should_balance_multicols_bool
+
+\keys_define:nn { mn__main }
+ {
+ columns .int_set:N = \g__mn_fs_columns_int ,
+ columns .initial:x = 3 ,
+
+ balance~columns .default:n = true ,
+ balance~columns .bool_set:N = \g__mn_should_balance_multicols_bool ,
+
+ width .value_required:n = true ,
+ width .code:n = \geometry{ paperwidth = #1 } ,
+
+ height .value_required:n = true ,
+ height .code:n = \geometry{ paperheight = #1 } ,
+ }
+
+\RequirePackage
+ [
+ letterpaper ,
+ margin = 0.1in ,
+ ]
+ { geometry }
+
+\skip_set:Nn \parskip { 0.25em }
+
+\RequirePackage { enumitem }
+\setlist
+ {
+ nosep
+ }
+
+\def\section#1{\hrulefill\\\textbf{#1}\\}
Property changes on: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-formula-sheet.cls
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===================================================================
--- trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-hw.cls (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-hw.cls 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,325 @@
+%% rbt-mathnotes-hw.cls
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\ProvidesExplClass{rbt-mathnotes-hw}{2021/11/29}{1.0.2}{Companion styles
+ to rbt-mathnotes for typeset homework assignments.}
+
+% \PassOptionsToPackage{noxcolor}{rbt-mathnotes}
+
+\RequirePackage{kvoptions}
+\DeclareDefaultOption
+ {
+ \PassOptionsToClass { \CurrentOption } { rbt-mathnotes }
+ }
+\ProcessKeyvalOptions*
+
+\LoadClass { rbt-mathnotes }
+
+\cs_set:Npn \mn__undefine_thm:n #1
+ {
+ \cs_undefine:c { #1 }
+ \cs_undefine:c { end#1 }
+ \cs_undefine:c { #1* }
+ \cs_undefine:c { end#1* }
+ }
+
+\mn__undefine_thm:n { thm }
+\mn__undefine_thm:n { lem }
+\mn__undefine_thm:n { cor }
+\mn__undefine_thm:n { prop }
+\mn__undefine_thm:n { defn }
+\mn__undefine_thm:n { notation }
+\mn__undefine_thm:n { ex }
+
+\cs_undefine:N \mn__undefine_thm:n
+
+\theoremstyle { definition }
+\newtheorem { thm } { Theorem }
+\newtheorem { lem } { Lemma }
+\newtheorem { cor } { Corollary }
+\newtheorem { prop } { Proposition }
+\newtheorem { defn } { Definition }
+\newtheorem { notation } { Notation }
+\newtheorem { ex } { Example }
+
+% The displayed problem number. \g__mn_problems_int isn't incremented if a
+% custom number is given.
+\int_new:N \g__mn_problems_int
+\int_set_eq:NN \g__mn_problems_int \c_one_int
+
+% The internal problem number. \g__mn_all_problems_int is *always*
+% incremented, so it can be used as a unique identifier in hyperref
+% pdf bookmark names.
+\int_new:N \g__mn_all_problems_int
+\int_set_eq:NN \g__mn_all_problems_int \c_one_int
+
+% Label prepended to problem numbers.
+\tl_const:Nn \g__mn_problem_string_tl { Problem }
+
+\skip_const:Nn \g__mn_problem_before_skip { 2em }
+
+% Label appended to problem numbers; omitted from PDF bookmarks.
+\tl_const:Nn \g__mn_problem_after_tl { . }
+
+% A possible custom problem number. If \c_novalue_tl, use
+% \g__mn_problems_int instead.
+\tl_new:N \mn__problem_number_tl
+\tl_set_eq:NN \mn__problem_number_tl \c_novalue_tl
+
+\tl_const:Nn \mn__problem_number_default_tl
+ {
+ \int_to_arabic:n { \g__mn_problems_int }
+ }
+
+% Current problem number, either from \g__mn_problems_int or
+% \mn__problem_number_tl.
+\tl_new:N \mn__problem_number_current_tl
+
+% Current problem display title, including "problem" label, number, and
+% custom title.
+% \tl_new:N \mn__problem_display_title_tl
+
+\keys_define:nn { mn__main }
+ {
+ problem~string .value_required:n = true ,
+ problem~string .tl_set:N = \g__mn_problem_string_tl ,
+ problem~before~skip .skip_set:N = \g__mn_problem_before_skip
+ }
+
+\keys_define:nn { mn__problem }
+ {
+ number .value_required:n = true ,
+ number .tl_set:N = \mn__problem_number_tl ,
+
+ title .value_required:n = true ,
+ title .tl_set:N = \mn__problem_title_tl ,
+ title .initial:n = ,
+
+ label .value_required:n = true ,
+ label .tl_set:N = \mn__problem_label_tl ,
+
+ % Treat unknown keys as the problem number; this lets us avoid having
+ % 2 or more optional arguments.
+ unknown .code:n =
+ \tl_if_empty:nTF { #1 }
+ {
+ % No value; use it for the problem number.
+ \tl_set_eq:NN \mn__problem_number_tl \l_keys_key_tl
+ }
+ {
+ % Non-empty value; give an error.
+ \msg_error:nnx
+ { mathnotes }
+ { no key in problem }
+ { \tl_use:N \l_keys_key_tl }
+ } ,
+ }
+
+\cs_set:Npn \mn__problem_title_pdf:
+ {
+ % A string like "Problem" or "Exercise" or "Question"
+ \tl_use:N \g__mn_problem_string_tl
+ % The problem number.
+ \tl_if_empty:NF \mn__problem_number_current_tl
+ {
+ \ \tl_use:N \mn__problem_number_current_tl
+ }
+ \tl_if_empty:NF \mn__problem_title_tl
+ {
+ :~\tl_use:N \mn__problem_title_tl
+ }
+ }
+
+\cs_set:Npn \mn__problem_title:
+ {
+ \mn__problem_title_pdf:
+ % The text after the problem, nominally a period (".").
+ \tl_use:N \g__mn_problem_after_tl
+ }
+
+% PDF anchor / bookmark name for hyperref.
+\cs_set:Npn \mn__problem_anchor:
+ {
+ problem.\int_to_arabic:n { \g__mn_all_problems_int }
+ }
+
+\NewDocumentEnvironment { problem }
+ {
+ O{} % Problem number or options
+ }
+ {
+ \keys_set:nn { mn__problem } { #1 }
+
+ % Set the problem number
+ \tl_set:Nn \mn__problem_number_current_tl { }
+ \tl_if_eq:NNTF \mn__problem_number_tl \c_novalue_tl
+ {
+ % No number given
+ \tl_set_eq:NN \mn__problem_number_current_tl \mn__problem_number_default_tl
+ }
+ {
+ % Some number given, *maybe* empty
+ \tl_set_eq:NN \mn__problem_number_current_tl \mn__problem_number_tl
+ }
+
+ \vspace { \skip_use:N \g__mn_problem_before_skip }
+
+ \phantomsection
+ \addcontentsline
+ { toc }
+ { chapter }
+ { \mn__problem_title_pdf: }
+ \begin{mdframed}
+ [
+ style = note ,
+ startinnercode =
+ \mn__note_title:n
+ {
+ \cs_gset:Npx \@currentlabel { \tl_use:N \mn__problem_number_current_tl }
+ \cs_gset:Npx \@currentlabelname { \mn__problem_title: }
+ \tl_if_empty:NF \mn__problem_label_tl
+ {
+ \exp_after:wN \label { \tl_use:N \mn__problem_label_tl }
+ }
+ \mn__problem_title:
+ }
+ ,
+ ]
+ }
+ {
+ \end{mdframed}
+ % If we didn't get a custom number, increment the counter.
+ \tl_if_eq:NNT \mn__problem_number_tl \c_novalue_tl
+ {
+ \int_gincr:N \g__mn_problems_int
+ }
+ % But always increment the internal counter.
+ \int_gincr:N \g__mn_all_problems_int
+ }
+
+\NewDocumentCommand \prob
+ {
+ O{} % Problem number or options
+ m % Problem text
+ }
+ {
+ \begin{problem}[#1]
+ #2
+ \end{problem}
+ }
+
+\cs_set:Npn \mn__add_par_arg_to_sectioning_cmd:N #1
+ {
+ \cs_set_eq:cN { mn__\cs_to_str:N #1 _old } #1
+ \cs_set_eq:cc
+ { mn__the\cs_to_str:N #1 _old }
+ { the\cs_to_str:N #1 }
+ \RenewDocumentCommand #1
+ {
+ s % ##1: Numbered / in ToC?
+ d() % ##2: Number override.
+ o % ##3: ToC title.
+ o % ##4: Page header title.
+ m % ##5: Title.
+ }
+ {
+ \group_begin:
+ \cs_set:Npx \mn__current_thesection_cmd
+ { the\cs_to_str:N #1 }
+ % Is there a number override?
+ \IfValueTF { ##2 }
+ {
+ % If yes, *globally* change the number format.
+ \cs_gset:cpn { \mn__current_thesection_cmd } { ##2 }
+ }
+ {
+ % Otherwise, restore the number format from a previous override,
+ % if applicable.
+ \cs_gset_eq:cc
+ { \mn__current_thesection_cmd }
+ { mn__the\cs_to_str:N #1 _old }
+ }
+ % Save the original command so we can use it as a single token.
+ \cs_set_eq:Nc \mn__orig_sectioning_cmd { mn__\cs_to_str:N #1 _old }
+ \exp_last_unbraced:Ne \mn__orig_sectioning_cmd
+ {
+ % Propagate the star.
+ \IfBooleanT { ##1 } { * }
+ % Propogate other arguments.
+ \IfValueT { ##3 } { [##3] }
+ \IfValueT { ##4 } { [##4] }
+ { ##5 }
+ }
+ \group_end:
+ }
+ }
+
+\cs_set:Npn \mn__add_par_arg_to_sectioning_cmds:n #1
+ {
+ \clist_map_function:nN { #1 } \mn__add_par_arg_to_sectioning_cmd:N
+ }
+
+\makeheadstyles { rbt-mathnotes-hw }
+ {
+ \chapterstyle { rbt-mathnotes }
+ \headstyles { rbt-mathnotes }
+
+ % Don't use chapter numbers in sections and beyond:
+ \cs_set:Npn \thesection { \arabic{section} }
+
+ % Add paren-arg to override numbers in sectioning commands.
+ \mn__add_par_arg_to_sectioning_cmds:n
+ {
+ \chapter ,
+ \section ,
+ \subsection ,
+ \subsubsection ,
+ \paragraph ,
+ \subparagraph ,
+ }
+ }
+
+\headstyles { rbt-mathnotes-hw }
+
+\setlength{\columnsep}{3em}
+
+% No chapter numbers for figures.
+\counterwithout{figure}{chapter}
+
+% Put author name, title in headings
+\makeevenfoot { headings } { } { } { }
+\makeoddfoot { headings } { } { } { }
+\makeevenhead { headings } { } { } { \thepage }
+\makeoddhead { headings } { \@author,~\textit{ \@title } } { } { \thepage }
Property changes on: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-hw.cls
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-messages.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-messages.sty (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-messages.sty 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,76 @@
+%% rbt-mathnotes-messages.sty
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\ProvidesExplPackage{rbt-mathnotes-messages}{2021/11/29}{1.0.2}{Messages
+ for mathnotes.}
+
+\msg_new:nnnn { mathnotes }
+ { no name }
+ {
+ No~author~name~given~but~\exp_not:N \maketitle~was~still~used.
+ }
+ {
+ Set~your~name~in~the~preamble: \\
+ \exp_not:N \mathnotes\{~name~=~Your~name~...~,~\}
+ }
+
+\msg_new:nnnn { mathnotes }
+ { acronym already defined }
+ {
+ Command~#1~already~defined;~refusing~to~redefine~as~an~acronym~for~#2.
+ }
+ {
+ Pick~a~different~destination~control~sequence~with~\protect\newacronym's~
+ optional~argument?
+ }
+
+\msg_new:nnnn { mathnotes }
+ { no key in problem }
+ {
+ Key~#1~is~not~defined~for~the~problem~environment.
+ }
+ {
+ If~you~meant~to~set~the~problem~number,~don't~include~a~value.
+ }
+
+
+\msg_new:nnnn { mathnotes }
+ { requires memoir class }
+ {
+ Option~#1~can~only~be~used~with~the~memoir~class!
+ }
+ {
+ Use~the~memoir~document~class~or~one~of~the~rbt-mathnotes~classes~wrapping~it.
+ }
Property changes on: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-messages.sty
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-util.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-util.sty (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-util.sty 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,180 @@
+%% rbt-mathnotes-util.sty
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\ProvidesExplPackage{rbt-mathnotes-util}{2021/11/29}{1.0.2}{Utility commands
+ for rbt-mathnotes.}
+
+\cs_set:Npn \mn__legacy_bool_option:n #1
+ {
+ \bool_new:c { g__mn_#1_bool }
+ \csname if\@currname @#1 \endcsname
+ \bool_gset_true:c { g__mn_#1_bool }
+ \else
+ \bool_gset_false:c { g__mn_#1_bool }
+ \fi
+ }
+
+\keys_define:nn { mn_options }
+ {
+ init .tl_set:N = \l__mn_options_init_tl ,
+ init .default:n = true ,
+ init .initial:x = \tl_use:N \c_novalue_tl ,
+
+ default .tl_set:N = \l__mn_options_default_tl ,
+ default .value_required:n = true ,
+ default .initial:x = \tl_use:N \c_novalue_tl ,
+
+ type .choice: ,
+ type .choices:nn = { bool, str }
+ { \tl_set_eq:NN \l__mn_options_type_tl \l_keys_choice_tl } ,
+ type .value_required:n = true ,
+ type .initial:n = bool ,
+ }
+
+% A hook which executes after \ProcessKeyvalOptions and is used to convert
+% TeX booleans and so on to LaTeX3 booleans and strings.
+\tl_new:N \g__mn_after_options_hook_tl
+% A hook used to define a particular option, allowing keys to be set only in
+% a group.
+\tl_new:N \g__mn_define_option_tl
+% Initializes complementary #1 and no#1 package options.
+\NewDocumentCommand \mn__option_new { o m }
+ {
+ \tl_gclear:N \g__mn_define_option_tl
+ \group_begin:
+ \tl_if_novalue:nF { #1 }
+ { \keys_set:nn { mn_options } { #1 } }
+
+ \tl_set:Nn \l_tmpa_tl { bool }
+ \tl_if_eq:NNT \l__mn_options_type_tl \l_tmpa_tl
+ {
+ % If no default was given, use `false` for bools.
+ \tl_if_eq:NNT \l__mn_options_init_tl \c_novalue_tl
+ { \tl_set:Nn \l__mn_options_init_tl { false } }
+
+ \tl_gput_right:Nx \g__mn_define_option_tl
+ {
+ \exp_not:N \DeclareBoolOption [\l__mn_options_init_tl]{#2}
+ \exp_not:N \DeclareComplementaryOption {no#2}{#2}
+ }
+
+ % After we process options, convert to an expl3 bool.
+ \tl_gput_right:Nn \g__mn_after_options_hook_tl
+ {
+ % Adapt the legacy bool into an expl3 bool.
+ \mn__legacy_bool_option:n { #2 }
+ % Then, delete the legacy bool.
+ \mn__legacy_bool_undefine:n { \@currname @#2 }
+ }
+ }
+
+ % For a string option:
+ \tl_set:Nn \l_tmpa_tl { str }
+ \tl_if_eq:NNT \l__mn_options_type_tl \l_tmpa_tl
+ {
+ \tl_gput_right:No \g__mn_define_option_tl
+ {
+ \exp_not:N \DeclareStringOption
+ \tl_if_eq:NNF \l__mn_options_init_tl \c_novalue_tl
+ { [\l__mn_options_init_tl] }
+ { #2 }
+ \tl_if_eq:NNF \l__mn_options_default_tl \c_novalue_tl
+ { [\l__mn_options_default_tl] }
+ }
+
+ \tl_gput_right:Nn \g__mn_after_options_hook_tl
+ {
+ % Create the new tl for this option.
+ \tl_new:c { g__mn_#2_tl }
+ % Set it to the command kvoptions created.
+ \tl_set:co { g__mn_#2_tl } { \cs:w \@currname @#2 \cs_end: }
+ % Delete the old command.
+ \cs_undefine:c { \@currname @#2 }
+ }
+ }
+ \group_end:
+ \tl_use:N \g__mn_define_option_tl
+ }
+
+\cs_set:Npn \mn__process_options:n #1
+ {
+ \ProcessKeyvalOptions { #1 }
+ \tl_use:N \g__mn_after_options_hook_tl
+ }
+
+\cs_set:Npn \mn__legacy_bool_undefine:n #1
+ {
+ \cs_undefine:c { if#1 }
+ \cs_undefine:c { #1true }
+ \cs_undefine:c { #1false }
+ }
+
+% Package configuration string values.
+% {< module >}{< family >}{< key name >}
+\cs_set:Npn \mn__key_new:nnn #1#2#3
+ {
+ \tl_set_eq:cN { l__#1_#3_tl } \c_novalue_tl
+ \keys_define:nn { #2 }
+ {
+ #1 .value_required:n = true,
+ #1 .tl_set:c = l__#1_#3_tl,
+ }
+ }
+
+\cs_set:Npn \mn__mathnotes_key_new:n #1
+ {
+ \mn__key_new:nnn { mn } { mathnotes } { #1 }
+ }
+
+\cs_set:Npn \mn__keys_new:n #1 { \clist_map_function:nN { #1 } \mn__mathnotes_key_new:n }
+
+\prg_new_conditional:Npnn \mn__if_package_loaded:n #1
+ { p, T, F, TF }
+ {
+ \@ifpackageloaded { #1 }
+ { \prg_return_true: }
+ { \prg_return_false: }
+ }
+
+\prg_new_conditional:Npnn \mn__if_novalue:N #1
+ { p, T, F, TF }
+ {
+ \tl_if_eq:NNTF \c_novalue_tl #1
+ { \prg_return_true: }
+ { \prg_return_false: }
+ }
+\prg_generate_conditional_variant:Nnn \mn__if_novalue:N
+ { c }
+ { p, T, F, TF }
Property changes on: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes-util.sty
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.cls
===================================================================
--- trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.cls (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.cls 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,202 @@
+%% rbt-mathnotes.cls
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\ProvidesExplClass{rbt-mathnotes}{2021/11/29}{1.0.2}{Styles for mathematical
+ note taking.}
+
+\PassOptionsToClass { openany, oneside } { memoir }
+
+\LoadClass{memoir}
+\setsecnumdepth{subsubsection}
+\settocdepth{subsubsection}
+\nouppercaseheads
+\makeevenfoot { plain } { } { } { }
+\makeoddfoot { plain } { } { } { }
+\makeevenhead { plain } { } { } { \thepage }
+\makeoddhead { plain } { } { } { \thepage }
+
+\RequirePackage{etoolbox}
+\RequirePackage{xparse}
+\AtBeginDocument{
+ \patchcmd { \@tocmaketitle }
+ { \thispagestyle { chapter } }
+ { }
+ { }
+ { }
+ }
+
+\makechapterstyle { rbt-mathnotes }
+ {
+ % allow for 99 chapters!
+ \settowidth{\chapindent}{\chapnumfont 999}
+
+ \RenewDocumentCommand \chapnumfont { }
+ {
+ \normalfont
+ \huge
+ \exp:w \mn__color:n {MNsecnum}
+ }
+ \RenewDocumentCommand \chapterheadstart { } { }
+ \RenewDocumentCommand \printchaptername { } { }
+ \RenewDocumentCommand \chapternamenum { } { }
+ \RenewDocumentCommand \printchapternum { }
+ {
+ \noindent
+ \llap
+ {
+ \makebox [ \chapindent ]
+ { \chapnumfont \thechapter }
+ }
+ }
+ \RenewDocumentCommand \afterchapternum { } { }
+ \RenewDocumentCommand \printchaptertitle { m }
+ {
+ \raggedright
+ \huge
+ ##1
+ }
+ \RenewDocumentCommand \afterchaptertitle { }
+ {
+ \vskip \onelineskip
+ \hrule
+ \vskip \onelineskip
+ }
+ }
+
+\makeheadstyles { rbt-mathnotes }
+ {
+ \chapterstyle { rbt-mathnotes }
+
+ \setsecnumformat
+ {
+ \group_begin:
+ \exp:w \mn__color:n {MNsecnum}
+ \cs:w the##1 \cs_end:
+ \quad
+ \group_end:
+ }
+
+ % Sections.
+ \setbeforesecskip
+ {
+ -1\onelineskip plus -0.5\onelineskip minus -0.5\onelineskip
+ }
+ \setaftersecskip
+ {
+ 1\onelineskip plus 0.1\onelineskip
+ }
+ \setsecheadstyle
+ {
+ \normalfont
+ \memRTLraggedright
+ \bfseries
+ \LARGE
+ % \scshape
+ % \MakeTextLowercase
+ }
+
+ % Subsections.
+ \setbeforesubsecskip
+ {
+ -1.0\onelineskip plus -0.25\onelineskip minus -0.25\onelineskip
+ }
+ \setaftersubsecskip
+ {
+ 1.0\onelineskip plus 0.1\onelineskip
+ }
+ \setsubsecheadstyle
+ {
+ \sethangfrom { \noindent ####1 }
+ \normalfont
+ \bfseries
+ \memRTLraggedright
+ }
+
+ % Subsubsections.
+ \setbeforesubsubsecskip
+ {
+ 1.0\onelineskip plus 0.5\onelineskip minus 0.2\onelineskip
+ }
+ \setaftersubsubsecskip
+ {
+ 1.0\onelineskip plus 0.1\onelineskip
+ }
+ \setsubsubsecheadstyle
+ {
+ \normalfont
+ \normalsize
+ \bfseries
+ \memRTLraggedright
+ }
+
+ % Paragraphs.
+ \setbeforeparaskip
+ {
+ 1.0\onelineskip plus 0.5\onelineskip minus 0.2\onelineskip
+ }
+ \setafterparaskip { -1em }
+ \setparaheadstyle
+ {
+ \normalfont
+ \normalsize
+ \bfseries
+ }
+
+ % Subparagraphs.
+ \setsubparaindent { \parindent }
+ \setbeforesubparaskip
+ {
+ 1.0\onelineskip plus 0.5\onelineskip minus 0.2\onelineskip
+ }
+ \setaftersubparaskip { -1em }
+ \setsubparaheadstyle
+ {
+ \normalfont
+ \normalsize
+ \itshape
+ \addperiod
+ }
+ }
+
+\headstyles { rbt-mathnotes }
+
+% \chapterstyle{hangnum}
+% \cs_set:Npn \chapnumfont
+ % {
+ % \HUGE \bfseries
+ % \exp:w \mn__color:n {MNsecnum}
+ % }
+
+\RequirePackage { rbt-mathnotes }
Property changes on: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.cls
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.sty (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.sty 2021-11-30 22:53:25 UTC (rev 61193)
@@ -0,0 +1,1122 @@
+%% rbt-mathnotes.sty
+%% Copyright 2021 Rebecca B. Turner.
+%
+% This work 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 work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Rebecca B. Turner.
+%
+% This work consists of the files:
+% README.md
+% rbt-mathnotes.tex
+% rbt-mathnotes.sty
+% rbt-mathnotes.cls
+% rbt-mathnotes-util.sty
+% rbt-mathnotes-messages.sty
+% rbt-mathnotes-hw.cls
+% rbt-mathnotes-formula-sheet.cls
+% examples/cheat-sheet.tex
+% examples/multivar.tex
+% examples/topology-hw-1.tex
+% and the derived files:
+% rbt-mathnotes.pdf
+% examples/cheat-sheet.pdf
+% examples/multivar.pdf
+% examples/topology-hw-1.pdf
+
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\ProvidesExplPackage{rbt-mathnotes}{2021/11/29}{1.0.2}{Styles for
+ mathematical note taking.}
+\errorcontextlines 20
+% Module 'mn'
+
+% Load some utility packages.
+\RequirePackage{xparse} % Better command declarations.
+\RequirePackage{xkeyval} % Better keyval parsing.
+% {{{ Package options
+\RequirePackage{kvoptions} % More flexible package options.
+\RequirePackage{rbt-mathnotes-util}
+
+\SetupKeyvalOptions
+ {
+ family = mn__package_options ,
+ }
+
+\mn__option_new[init = true]{fonts}
+\mn__option_new[init = true]{stix}
+\mn__option_new[init = true]{symbols}
+\mn__option_new[init = true]{maketitle}
+\mn__option_new[init = true]{titles}
+\mn__option_new[init = true]{xcolor}
+\mn__option_new[init = true]{theorems}
+\mn__option_new[init = true]{enumitem}
+\mn__option_new{listings}
+\mn__option_new{knowledge}
+\mn__option_new{index}
+\mn__option_new{footnotes}
+\mn__option_new{figures}
+\mn__option_new{tabu}
+\mn__option_new{kindle}
+
+\mn__process_options:n { mn__package_options } % }}}
+
+\RequirePackage{rbt-mathnotes-messages}
+
+% {{{ Load fonts.
+% Check if we can load fontspec; this is taken from fontspec.sty.
+\bool_new:N \c__mn_fontspec_bool
+\bool_set:Nn \c__mn_fontspec_bool
+ {
+ \sys_if_engine_xetex_p: || \sys_if_engine_luatex_p:
+ }
+
+% NOTE: The order these packages are loaded in is very important.
+% - mathtools has to be loaded before these or overbrackets and such get
+% messed up
+% - unicode-math overwrites a bunch of commands, so should be loaded after
+% amsmath and others
+% - amsmath should be loaded after stix2 (not sure why, but the stix2
+% documentation specifies this) -- however, if we can use fontspec, we
+% just load the stix2 fonts without the stix2 package itself, so we load
+% amsmath before unicode-math (and the stix2 fonts)
+\RequirePackage{mathtools}
+\bool_if:NTF \g__mn_fonts_bool
+ {
+ \bool_if:NTF \c__mn_fontspec_bool
+ {
+ \RequirePackage{amsmath}[2013/01/14]
+ % unicode-math makes equations copy/pastable in PDF output.
+ % Note that unicode-math encapsulates the functionality of fontspec.
+ \RequirePackage[
+ warnings-off={mathtools-colon,mathtools-overbracket}
+ ]{unicode-math}
+ \bool_if:NT \g__mn_stix_bool
+ {
+ \setmainfont
+ [
+ UprightFont = *-Regular ,
+ ItalicFont = *-Italic ,
+ BoldFont = *-Bold ,
+ BoldItalicFont = *-BoldItalic ,
+ Extension = .otf ,
+ ]
+ { STIX2Text }
+
+ \setmathfont
+ [
+ StylisticSet =
+ {
+ 1 , % better caligraphic forms
+ 8 , % upright integrals
+ } ,
+ Extension = .otf ,
+ ]
+ { STIX2Math }
+ }
+ }
+ {
+ % Otherwise, load non-XeTeX fallbacks.
+ \bool_if:NT \g__mn_stix_bool
+ {
+ \RequirePackage[upint]{stix2}
+ }
+ \RequirePackage{amsmath}[2013/01/14]
+ }
+ }
+ {
+ % No fonts
+ \RequirePackage{amsmath}[2013/01/14]
+ } % }}}
+
+\bool_if:NT \g__mn_symbols_bool % {{{ Define math symbol commands
+ {
+ % Logical not
+ \mn__if_package_loaded:nTF { unicode-math }
+ { \DeclareDocumentCommand \lnot {} { \char "AC } } % 0xAC = ¬
+ { \mathchardef \Not = "1218 }
+
+ % Blackboard bold set symbols
+ \NewDocumentCommand \Rational {}{\mathbb{Q}}
+ \ProvideDocumentCommand \Rat {}{\Rational}
+ \ProvideDocumentCommand \Q {}{\Rational}
+
+ % \NewDocumentCommand \Irrational {}{\mathbb{I}}
+ % \ProvideDocumentCommand \Irrat {}{\Irrational}
+ % \ProvideDocumentCommand \I {}{\Irrational}
+
+ \NewDocumentCommand \Natural {}{\mathbb{N}}
+ \ProvideDocumentCommand \Nat {}{\Natural}
+ \ProvideDocumentCommand \N {}{\Natural}
+
+ \NewDocumentCommand \Integer {}{\mathbb{Z}}
+ \ProvideDocumentCommand \Int {}{\Integer}
+ \ProvideDocumentCommand \Z {}{\Integer}
+
+ \NewDocumentCommand \Complex {}{\mathbb{C}}
+ \ProvideDocumentCommand \Comp {}{\Complex}
+ % Renew \C to mean \Complex in math-mode; normally, \C just gives an
+ % error in math-mode.
+ % ...if \C isn't defined, just define it normally.
+ \AtBeginDocument
+ {
+ \cs_if_free:NTF \C
+ { \NewDocumentCommand }
+ {
+ \cs_set_eq:NN \mn__C_old \C
+ \RenewDocumentCommand
+ }
+ \C {}{
+ \mode_if_math:TF
+ { \Complex } % Complex set
+ { \mn__C_old } % Copyright sign
+ }
+ }
+
+ \NewDocumentCommand \Real {}{\mathbb{R}}
+ \ProvideDocumentCommand \R {}{\Real}
+
+ % Using the Weierstrass p here is probably a bit controversial, but I like
+ % it. I'm open to change, though...
+ \ProvideDocumentCommand \powerset {}{\wp}
+
+ \RenewDocumentCommand \vec {m}{\mathbf{#1}}
+
+ % Operator synonyms.
+ % Set intersect.
+ \ProvideDocumentCommand \intersection {}{\cap}
+ \ProvideDocumentCommand \inter {}{\cap}
+ \ProvideDocumentCommand \bigintersection {}{\bigcap}
+ \ProvideDocumentCommand \biginter {}{\bigcap}
+
+ % Set union.
+ \ProvideDocumentCommand \union {}{\cup}
+ \ProvideDocumentCommand \bigunion {}{\bigcup}
+ % Disjoint union.
+ \ProvideDocumentCommand \disjointunion {}{\sqcup}
+ \ProvideDocumentCommand \disunion {}{\sqcup}
+
+ % Divisiblity.
+ \ProvideDocumentCommand \divisible {}{\mid}
+ \ProvideDocumentCommand \div {}{\mid}
+ % Negation.
+ \ProvideDocumentCommand \notdivisible {}{\nmid}
+ \ProvideDocumentCommand \ndivisible {}{\nmid}
+ \ProvideDocumentCommand \notdiv {}{\nmid}
+ \ProvideDocumentCommand \ndiv {}{\nmid}
+
+ % Wrappers around floor and ceil.
+ \ProvideDocumentCommand \floor {m}{\lfloor #1\rfloor}
+ \ProvideDocumentCommand \ceil {m}{\lceil #1\rceil}
+
+ % The default empty set symbol is very ugly. Use \varnothing instead,
+ % which is less ugly.
+ \AtBeginDocument{\RenewDocumentCommand \emptyset {}{\varnothing}}
+ \ProvideDocumentCommand \es {}{\emptyset}
+
+ % Function composition. The notation g \after f helps internalize the
+ % order of operations. :)
+ \ProvideDocumentCommand \after {}{\circ}
+
+ % Cross product.
+ \ProvideDocumentCommand \cross {}{\times}
+
+ % Operators.
+ % Function image.
+ \cs_if_free:NT \img
+ { \DeclareMathOperator \img {img} }
+ % Function pre-image.
+ \cs_if_free:NT \pre
+ { \DeclareMathOperator \pre {pre} }
+ % Function stabilizer.
+ \cs_if_free:NT \Stab
+ { \DeclareMathOperator \Stab {Stab} }
+ % Set of a function's fixed points.
+ \cs_if_free:NT \FixPt
+ { \DeclareMathOperator \FixPt {FixPt} }
+ % Identity function
+ \cs_if_free:NT \id
+ { \DeclareMathOperator \id {id} }
+
+ % Injective function.
+ \ProvideDocumentCommand \injection {}{\hookrightarrow}
+ \ProvideDocumentCommand \inj {}{\hookrightarrow}
+ % Surjective function.
+ \ProvideDocumentCommand \surjection {}{\twoheadrightarrow}
+ \ProvideDocumentCommand \surj {}{\twoheadrightarrow}
+ % Bijective function.
+ \ProvideDocumentCommand \bijection {}{\twoheadrightarrowtail}
+ \ProvideDocumentCommand \bijective {}{\twoheadrightarrowtail}
+ \ProvideDocumentCommand \bij {}{\twoheadrightarrowtail}
+ % Function restriction.
+ \cs_if_free:NT \restriction
+ { \DeclareMathOperator \restriction {|} }
+ \ProvideDocumentCommand \restr {}{\restriction}
+
+ % d/dx
+ \ProvideDocumentCommand \dd { O{} m }{\frac{d#1}{d#2}}
+ \ProvideDocumentCommand \pd { O{} m }{\frac{\partial#1}{\partial#2}}
+ \ProvideDocumentCommand \gradient {}{\nabla}
+ \ProvideDocumentCommand \grad {}{\nabla}
+ \cs_if_free:NT \curl
+ { \DeclareMathOperator \curl {curl} }
+ \cs_if_free:NT \dive
+ { \DeclareMathOperator \dive {div} }
+ } % }}}
+
+% Gives this an equation a number in an amsmath starred environment.
+\ProvideDocumentCommand \numberthis { } % {{{
+ {
+ \tag { \theequation }
+ \refstepcounter { equation }
+ } % }}}
+
+% Gives this equation a number and label in an amsmath starred environment.
+\ProvideDocumentCommand \labelthis { m } % {{{
+ {
+ \numberthis
+ \IfValueT { #1 }
+ { \label { #1 } }
+ } % }}}
+
+\bool_if:NT \g__mn_enumitem_bool
+ { \RequirePackage{enumitem} }
+
+\bool_if:NT \g__mn_listings_bool
+ { \RequirePackage{listings} }
+
+\bool_if:NT \g__mn_xcolor_bool % {{{ Load xcolor and define MN colors
+ {
+ \PassOptionsToPackage { rgb } { xcolor }
+ \RequirePackage { xcolor }
+ \providecolorset { HTML }
+ % Prefix/postfix of all color names
+ { } { }
+ {
+ \use_none:n
+ ; MNthmtitle , 0F0066
+ ; MNthmbg , EBFEFF
+ ; MNthmline , 4836B3
+ ; MNextitle , 692219
+ ; MNexbg , FFF0EB
+ ; MNexline , CC7468
+ ; MNdefntitle , 00540B
+ ; MNdefnline , 196924
+ ; MNdefnbg , EBFFED
+ ; MNnotetitle , 6B0019
+ ; MNnoteline , CC3F60
+ ; MNnotebg , FFF5F7
+
+ ; MNsecnum , 8015A1
+
+ ; MNlink , 113DB8
+ }
+ } % }}}
+
+\bool_if:NT \g__mn_listings_bool % {{{ Better default styles
+ {
+ \RequirePackage { xcolor }
+ \lstset
+ {
+ % Use a monospace font for code listings.
+ basicstyle = \ttfamily ,
+ language = Mathematica ,
+ % Tab size of 4, but you should probably use spaces.
+ tabsize = 4 ,
+ % Keywords in blue.
+ keywordstyle = \bfseries\ttfamily\color[rgb]{0,.3,.7} ,
+ % Comments in green.
+ commentstyle = \color[rgb]{0.133,0.545,0.133} ,
+ % Strings in orange.
+ stringstyle = \color[rgb]{0.75,0.49,0.07} ,
+ % The default listings characters are too widely-spaced.
+ % 0.55em/character makes things look a lot better.
+ basewidth = 0.55em ,
+ % Wrap lines if they're too long, and wrap at whitespace.
+ breaklines ,
+ breakatwhitespace = true ,
+ }
+ } % }}}
+
+% Creates an acronym-command.
+% \newacronym[<\command>]{<text>} defines \command to be \textsc{text}.
+% \newacronym{<text>} defines \text to be \textsc{text}.
+\ProvideDocumentCommand \newacronym { o m } % {{{
+ {
+ \group_begin:
+ % If we have #1, then #1 is the cs we're going to define; #1 is a cs.
+ % Otherwise, we define \#2.
+ \IfValueTF { #1 }
+ { \cs_set:Npn \mn__acronym_cs: { \cs_to_str:N #1 } }
+ { \cs_set:Npn \mn__acronym_cs: { #2 } }
+
+ % Ensure that the cs is undefined.
+ \cs_if_exist:cT { \mn__acronym_cs: }
+ {
+ \msg_error:nnxx
+ { mathnotes }
+ { acronym already defined }
+ { \exp_not:c { \mn__acronym_cs: } }
+ { #2 }
+ }
+
+ % Finally, define the acronym command.
+ \cs_new:cpn { \mn__acronym_cs: }
+ { \textsc { #2 } }
+ \group_end:
+ } % }}}
+
+% \newacronyms takes a comma-separated list as its argument and defines them
+% all as acronyms.
+\ProvideDocumentCommand \newacronyms { m }
+ { \clist_map_function:nN { #1 } \newacronym }
+
+% {{{ Package configuration string values; \mathnotes command
+\keys_define:nn { mn__main }
+ {
+ date .value_required:n = true ,
+ date .code:n = \date{#1} ,
+ author .value_required:n = true ,
+ author .code:n = \author{#1} ,
+ title .value_required:n = true ,
+ title .code:n = \title{#1} ,
+
+ generate~thanks .value_required:n = false ,
+ generate~thanks .bool_set:N = \g__mn_should_make_thanks ,
+ generate~thanks .default:n = true ,
+ generate~thanks .initial:n = true ,
+ }
+
+\cs_set:Npn \mn__key_new:n #1
+ {
+ \keys_define:nn { mn__main }
+ {
+ #1 .value_required:n = true ,
+ #1 .tl_gset:c = g__mn_#1_tl ,
+ #1 .initial:x = ,
+ }
+ }
+
+\cs_set:Npn \mn__keys_new:n #1 { \clist_map_function:nN { #1 } \mn__key_new:n }
+
+\mn__keys_new:n
+ {
+ instructor, course, name, email, institution, semester,
+ }
+
+\NewDocumentCommand \mathnotes { m }
+ {
+ \keys_set:nn { mn__main } { #1 }
+ }
+% }}}
+
+\bool_if:NT \g__mn_maketitle_bool % {{{ \author, \title, \maketitle, \thanks, etc.
+ {
+ \bool_new:N \g__mn_author_set
+ \cs_set:Npn \author #1
+ {
+ \bool_gset_true:N \g__mn_author_set
+ \cs_gset:Npn \@author { #1 }
+ }
+
+ \bool_new:N \g__mn_title_set
+ \cs_set:Npn \title #1
+ {
+ \bool_gset_true:N \g__mn_title_set
+ \cs_gset:Npn \@title { #1 }
+ }
+
+ \prg_new_conditional:Npnn \mn__if_should_make_thanks: % {{{
+ { T, }
+ {
+ \bool_if:NTF \g__mn_should_make_thanks
+ {
+ \bool_lazy_all:nTF
+ {
+ { \tl_if_empty_p:N \g__mn_email_tl }
+ { \tl_if_empty_p:N \g__mn_course_tl }
+ { \tl_if_empty_p:N \g__mn_instructor_tl }
+ { \tl_if_empty_p:N \g__mn_institution_tl }
+ { \tl_if_empty_p:N \g__mn_semester_tl }
+ }
+ { \prg_return_false: }
+ { \prg_return_true: }
+ }
+ { \prg_return_false: }
+ } % }}}
+
+ \cs_set:Npn \mn__make_thanks_text % {{{
+ {
+ \tl_if_empty:NF \g__mn_email_tl
+ {
+ \email { \tl_use:N { \g__mn_email_tl } }
+ \bool_lazy_all:nF
+ {
+ { \tl_if_empty_p:N \g__mn_course_tl }
+ { \tl_if_empty_p:N \g__mn_instructor_tl }
+ { \tl_if_empty_p:N \g__mn_institution_tl }
+ { \tl_if_empty_p:N \g__mn_semester_tl }
+ }
+ { ;~ }
+ }
+ \tl_if_empty:NF \g__mn_course_tl
+ {
+ \tl_use:N \g__mn_course_tl
+ \bool_lazy_all:nF
+ {
+ { \tl_if_empty_p:N \g__mn_instructor_tl }
+ { \tl_if_empty_p:N \g__mn_institution_tl }
+ { \tl_if_empty_p:N \g__mn_semester_tl }
+ }
+ { ~ }
+ }
+ \tl_if_empty:NF \g__mn_instructor_tl
+ {
+ \bool_lazy_all:nTF
+ {
+ { \tl_if_empty_p:N \g__mn_email_tl }
+ { \tl_if_empty_p:N \g__mn_course_tl }
+ }
+ { Taught~by~ }
+ { taught~by~ }
+ \tl_use:N \g__mn_instructor_tl
+ }
+ \tl_if_empty:NF \g__mn_institution_tl
+ {
+ \bool_lazy_all:nTF
+ {
+ { \tl_if_empty_p:N \g__mn_email_tl }
+ { \tl_if_empty_p:N \g__mn_course_tl }
+ { \tl_if_empty_p:N \g__mn_instructor_tl }
+ }
+ { At~ }
+ { ~at~ }
+ \tl_use:N \g__mn_institution_tl
+ }
+ \tl_if_empty:NF \g__mn_semester_tl
+ {
+ \bool_lazy_all:nF
+ {
+ { \tl_if_empty_p:N \g__mn_email_tl }
+ { \tl_if_empty_p:N \g__mn_course_tl }
+ { \tl_if_empty_p:N \g__mn_instructor_tl }
+ { \tl_if_empty_p:N \g__mn_institution_tl }
+ }
+ { ,~ }
+ \tl_use:N \g__mn_semester_tl
+ }
+ .
+ } % }}}
+
+ \cs_set:Npn \@author % {{{
+ {
+ % If the author hasn't been set, we provide this (complicated, PITA)
+ % default; however, if we don't have any information to put in it, we
+ % still give a warning.
+ \tl_if_eq:NNTF \g__mn_name_tl \c_novalue_tl
+ {
+ \msg_warning:nn { mathnotes } { no name }
+ }
+ {
+ \tl_use:N \g__mn_name_tl
+ % Do we have any information to put in a \thanks?
+ \mn__if_should_make_thanks:T
+ {
+ \thanks { \mn__make_thanks_text }
+ }
+ }
+ } % }}}
+
+ % {{{ \@maketitle and \maketitle
+ \skip_const:Nn \g__mn_maketitle_after_title { 1em }
+ \skip_const:Nn \g__mn_maketitle_after_author { 0.5em }
+ \skip_const:Nn \g__mn_maketitle_after { 1.5em }
+
+ \RenewDocumentCommand \@maketitle {}
+ {
+ \begin{center}
+ \let \footnote \thanks
+
+ % Set the title, if it exists.
+ \bool_if:NT \g__mn_title_set
+ {
+ \group_begin:
+ \HUGE
+ \bfseries
+ \@title
+ \par
+ \group_end:
+ }
+ \skip_vertical:N \g__mn_maketitle_after_title
+
+ % Set the author.
+ \group_begin:
+ \LARGE
+ \lineskip 0.5em
+ \begin{tabular}[t]{c}
+ \@author
+ \end{tabular}
+ \par
+ \group_end:
+ \skip_vertical:N \g__mn_maketitle_after_author
+
+ % Set the date.
+ \large
+ \@date
+
+ \end{center}
+ \par
+ \skip_vertical:N \g__mn_maketitle_after
+ }
+
+ \RenewDocumentCommand \maketitle {}
+ {
+ \par
+ \group_begin:
+ \cs_set:Npn \thefootnote
+ {
+ \@fnsymbol
+ \c at footnote
+ }
+ \cs_set:Npn \@makefnmark
+ {
+ \rlap
+ {
+ \@textsuperscript { \normalfont \@thefnmark }
+ }
+ }
+ \cs_set:Npn \@makefntext ##1
+ {
+ \parindent 1em
+ \noindent
+ \hbox_to_wd:nn
+ { 1.8em }
+ {
+ \hss
+ \@textsuperscript { \normalfont \@thefnmark }
+ }
+ ##1
+ }
+ \legacy_if:nTF { @twocolumn }
+ {
+ \if_int_compare:w \col at number = \@ne
+ \@maketitle
+ \else:
+ \twocolumn [ \@maketitle ]
+ \fi:
+ }
+ {
+ \newpage
+ \global\@topnum\z@
+ \@maketitle
+ }
+ \thispagestyle{empty}
+ \@thanks
+ \group_end:
+ \setcounter{footnote}{0}
+ \cs_set:Npn \thanks ##1 { }
+ % NOTE: we don't erase the definitions of \@title, etc.
+ }
+ % }}} \@maketitle and \maketitle
+ } % }}}
+
+\bool_if:NT \g__mn_kindle_bool % {{{
+ {
+ \keys_set:nn { mn__main }
+ {
+ generate~thanks = false ,
+ }
+ \skip_gset:Nn \g__mn_maketitle_after_title { 0em }
+ \skip_gset:Nn \g__mn_maketitle_after_author { 0em }
+ \skip_gset:Nn \g__mn_maketitle_after { 0em }
+ \@ifclassloaded { memoir }
+ {
+ \pagestyle { empty }
+
+ \setstocksize{12.2cm}{9cm}
+ \settrimmedsize{12.2cm}{9cm}{*}
+ \settypeblocksize{12.2cm}{9cm}{*}
+
+ \setlrmargins{0cm}{*}{*}
+ \setulmargins{0cm}{*}{*}
+
+ \setlength{\headheight}{0cm}
+ \setlength{\headsep}{0cm}
+ \setlength{\footskip}{0cm}
+
+ \checkandfixthelayout
+ }
+ {
+ \msg_error:nnx
+ { mathnotes }
+ { requires memoir class }
+ { kindle }
+ }
+ } % }}}
+
+% e.g. `\exp:w \mn__color:n { MNnotetitle }`
+\cs_set:Npn \mn__color:n #1 % {{{
+ {
+ \bool_if:NTF \g__mn_xcolor_bool
+ {
+ \exp_end:
+ \color{#1}
+ }
+ {
+ \exp_end:
+ }
+ } % }}}
+
+\bool_if:NT \g__mn_theorems_bool % {{{ mdtheorem setup
+ {
+ \RequirePackage[thmmarks, amsmath, amsthm]{ntheorem}
+
+ \RequirePackage{mdframed}
+
+ \mdfdefinestyle { theorem }
+ {
+ linewidth = 1.5pt ,
+ }
+
+ \bool_if:NT \g__mn_xcolor_bool
+ {
+ \mdfapptodefinestyle { theorem }
+ {
+ frametitlefont = \normalfont\bfseries\color{MNthmtitle} ,
+ linecolor = MNthmline ,
+ backgroundcolor = MNthmbg ,
+ }
+ }
+
+ \mdfdefinestyle { minor-theorem }
+ {
+ style = theorem ,
+ linewidth = 0.75pt ,
+ }
+
+ \mdfdefinestyle { example }
+ {
+ theoremtitlefont = \normalfont ,
+ }
+
+ \bool_if:NT \g__mn_xcolor_bool
+ {
+ \mdfapptodefinestyle { example }
+ {
+ frametitlefont = \normalfont\bfseries\color{MNextitle} ,
+ linecolor = MNexline ,
+ backgroundcolor = MNexbg ,
+ }
+ }
+
+ \mdfdefinestyle { definition }
+ {
+ }
+
+ \bool_if:NT \g__mn_xcolor_bool
+ {
+ \mdfapptodefinestyle { definition }
+ {
+ frametitlefont = \normalfont\bfseries\color{MNdefntitle} ,
+ linecolor = MNdefnline ,
+ backgroundcolor = MNdefnbg ,
+ }
+ }
+
+ \mdfdefinestyle { note }
+ {
+ topline = false ,
+ rightline = false ,
+ bottomline = false ,
+ linewidth = 2pt ,
+ }
+
+ \bool_if:NT \g__mn_xcolor_bool
+ {
+ \mdfapptodefinestyle { note }
+ {
+ frametitlefont = \normalfont\bfseries\color{MNnotetitle} ,
+ linecolor = MNnoteline ,
+ backgroundcolor = MNnotebg ,
+ }
+ }
+
+ \mdfdefinestyle { example }
+ {
+ theoremtitlefont = \normalfont ,
+ }
+
+ \bool_if:NT \g__mn_xcolor_bool
+ {
+ \mdfapptodefinestyle { example }
+ {
+ frametitlefont = \normalfont\bfseries\color{MNextitle} ,
+ linecolor = MNexline ,
+ backgroundcolor = MNexbg ,
+ }
+ }
+
+ \mdtheorem
+ [ style = theorem ]
+ { thm }
+ { Theorem }
+ % \newtheorem{shortthm}[thm]{Theorem}
+ \mdtheorem
+ [ style = minor-theorem ]
+ { lem }
+ { Lemma }
+ \mdtheorem
+ [ style = minor-theorem ]
+ { cor }
+ { Corollary }
+ \mdtheorem
+ [ style = minor-theorem ]
+ { prop }
+ { Proposition }
+
+ % \theoremstyle{definition}
+ \mdtheorem
+ [ style = definition ]
+ { defn }
+ { Definition }
+ \mdtheorem
+ [ style = definition ]
+ { notation }
+ { Notation }
+
+ % \theoremstyle{remark}
+ \mdtheorem
+ [ style = example ]
+ { ex }
+ { Example }
+
+ \skip_new:N \mn__note_title_after_skip
+ \skip_set:Nn \mn__note_title_after_skip { 1em plus 0.25em minus 0.75em }
+ \cs_set:Npn \mn__note_title:n #1
+ {
+ \textbf
+ {
+ \exp:w \mn__color:n { MNnotetitle }
+ #1
+ }
+ \skip_horizontal:N \mn__note_title_after_skip
+ }
+
+ \newmdenv
+ [
+ style = note ,
+ startinnercode = \mn__note_title:n { Note: } ,
+ ]
+ { note }
+
+ \newmdenv
+ [
+ style = note ,
+ startinnercode = \mn__note_title:n { Remark: } ,
+ ]
+ { remark }
+
+ \newmdenv
+ [
+ style = note ,
+ startinnercode = \mn__note_title:n { Hint: } ,
+ ]
+ { hint }
+
+ \newmdenv
+ [
+ style = note ,
+ startinnercode = \mn__note_title:n { Abuse of notation: } ,
+ ]
+ { abuse-of-notation }
+
+ % % reset for future defn.s
+ % \theoremstyle{plain}
+ } % }}}
+
+\NewDocumentCommand \TODO { o } % {{{
+ {
+ \framebox
+ {
+ \textbf{ TODO \IfValueT { #1 } { :~} }
+ \IfValueT { #1 } { #1 }
+ }
+ } % }}}
+
+% \bool_if:NT \g__mn_titles_bool % {{{
+ % {
+ % \RequirePackage{titlesec}
+ % % \titleformat { \command } [ shape ] { format } { label } { sep } { before-code } [ after-code ]
+ % % before-code can be a command
+ % \titleformat { \chapter }
+ % [ block ]
+ % { \bfseries \HUGE }
+ % { { \exp:w \mn__color:n {MNsecnum} \thechapter} }
+ % { 20pt }
+ % { }
+ % [ ]
+
+ % \titleformat { \section }
+ % [ hang ]
+ % { \bfseries \LARGE }
+ % { { \exp:w \mn__color:n {MNsecnum} \thesection} }
+ % { 16pt }
+ % { }
+ % [ ]
+
+ % \titleformat { \subsection }
+ % [ hang ]
+ % { \bfseries \Large }
+ % { { \exp:w \mn__color:n {MNsecnum} \thesubsection} }
+ % { 16pt }
+ % { }
+ % [ ]
+
+ % % \titlespacing* { \command } { left } { before } { after } [ right ]
+ % \titlespacing* { \chapter } { 0em } { 0em } { 2em } [ 0em ]
+ % \titlespacing* { \section } { 0em } { 2em } { 0.5em } [ 0em ]
+ % \titlespacing* { \subsection } { 0em } { 1em } { 0em } [ 0em ]
+ % \titlespacing* { \subsubsection } { 0em } { 1em } { 0em } [ 0em ]
+ % } % }}}
+
+\bool_if:NT \g__mn_xcolor_bool % {{{
+ {
+ \RequirePackage[hidelinks]{hyperref}
+ \hypersetup
+ {
+ colorlinks = true ,
+ allcolors = MNlink ,
+ }
+ } % }}}
+
+\bool_if:NT \g__mn_index_bool
+ {
+ \bool_set_true:N \g__mn_knowledge_bool
+ }
+
+\bool_if:NTF \g__mn_knowledge_bool % {{{
+ {
+ \bool_if:NT \g__mn_xcolor_bool
+ {
+ \PassOptionsToPackage{xcolor}{knowledge}
+ \providecolorset { HTML }
+ % Prefix/postfix of all color names
+ { } { }
+ {
+ \use_none:n
+ ; MNunknown , DE0B0F
+ ; MNunknowncont , AD483E
+ ; MNintro , 051338
+ }
+ }
+ \RequirePackage[quotation, notion, makeidx]{knowledge}
+
+ % Disable the redefined \label command; this fixes some documents.
+ \KnowledgeConfigureBooleanOption[\knowledge_configuration_label_autoscope_bool]{patch~label}
+
+ % {{{ Patch in the automatic-AP feature
+ \bool_new:N \g__mn_noAP_bool
+ \NewDocumentCommand \noAP { }
+ { \bool_gset_true:N \g__mn_noAP_bool }
+ \cs_set:Npn \mn__maybe_AP:N #1
+ {
+ \bool_if:NTF \g__mn_noAP_bool
+ { \bool_gset_false:N \g__mn_noAP_bool }
+ { #1 }
+ }
+
+ \RequirePackage{etoolbox}
+ \pretocmd { \intro }
+ { \mn__maybe_AP:N \AP }
+ { } { }
+
+ \bool_new:N \l__mn_using_itemAP
+ \cs_set:Npn \mn__use_itemAP:
+ {
+ \bool_if:NF \l__mn_using_itemAP
+ {
+ \let \mn__item_orig: \item
+ \bool_set_true:N \l__mn_using_itemAP
+ \RenewDocumentCommand \item { o }
+ {
+ \IfNoValueTF { ##1 }
+ {
+ \mn__item_orig:
+ \mn__maybe_AP:N \AP
+ }
+ {
+ \mn__item_orig:
+ [
+ \mn__maybe_AP:N \knowledge_itemAP:
+ % NOTE: this isn't expandable, which fucks up
+ % everything.
+ \cs_set_eq:NN \AP \prg_do_nothing:
+ ##1
+ ]
+ }
+ }
+ }
+ }
+ \apptocmd { \enumerate } { \mn__use_itemAP: } { } { }
+ \apptocmd { \itemize } { \mn__use_itemAP: } { } { }
+ \apptocmd { \description } { \mn__use_itemAP: } { } { }
+ % }}}
+
+ % {{{ Make some better styles.
+ \knowledgeconfigure
+ {
+ visible~anchor~points = false
+ }
+ \cs_set:Npn \mn__knowledgestyles:nn #1#2
+ {
+ \clist_map_inline:nn { #1 }
+ { \knowledgestyle* { ##1 } { #2 } }
+ }
+ % List of default styles
+ % notion, intro notion
+ % intro, intro unknown, intro unknown cont
+ % kl unknown, kl unknown cont
+ \bool_if:NTF \g__mn_xcolor_bool
+ {
+ \mn__knowledgestyles:nn
+ { notion , intro~notion }
+ {
+ color = MNlink ,
+ }
+ \mn__knowledgestyles:nn
+ { intro , intro~notion , intro~unknown, intro~unknown~cont , }
+ {
+ boldface ,
+ color = MNintro ,
+ }
+ \mn__knowledgestyles:nn
+ { intro~unknown , intro~unknown~cont , kl~unknown , kl~unknown~cont , }
+ {
+ underline = false ,
+ color = MNunknown ,
+ }
+ \mn__knowledgestyles:nn
+ { intro~unknown~cont , kl~unknown~cont , }
+ {
+ color = MNunknowncont ,
+ }
+ }
+ {
+ % These blank definitions are important for erasing some very poorly
+ % typeset decisions.
+ \mn__knowledgestyles:nn
+ { notion , intro~notion }
+ {
+ }
+ \mn__knowledgestyles:nn
+ { intro , intro~notion , intro~unknown, intro~unknown~cont , }
+ {
+ boldface ,
+ }
+ \mn__knowledgestyles:nn
+ { intro~unknown , intro~unknown~cont , kl~unknown , kl~unknown~cont , }
+ {
+ }
+ \mn__knowledgestyles:nn
+ { intro~unknown~cont , kl~unknown~cont , }
+ {
+ }
+ }
+ % }}}
+ }
+ {
+ % If we don't load the knowledge package, provide a *similar* interface
+ % to make writing commands that *optionally* use the knowledge interface
+ % easier.
+ \ProvideDocumentCommand \itemAP { O{} } { \item[#1] }
+ \ProvideDocumentCommand \AP { } { }
+ \ProvideDocumentCommand \phantomintro { d() m } { }
+ \ProvideDocumentCommand \nointro { m } { }
+ \ProvideDocumentCommand \reintro { s o m } { #3 }
+ \ProvideDocumentCommand \intro { d() o d() m } { #4 }
+ \ProvideDocumentCommand \kl { d() o d() m } { #4 }
+ } % }}}
+
+\bool_if:NT \g__mn_index_bool
+ {
+ \makeindex
+ }
+
+% The \emailstyle command gives the style of an email; by default, we
+% initialize it to \texttt.
+\ProvideDocumentCommand \emailstyle { m } { \texttt{#1} }
+% The \email command typesets an email; if the user has loaded the
+% hyperref package, we can add a link as well.
+\mn__if_package_loaded:nTF { hyperref } % {{{
+ {
+ \ProvideDocumentCommand \email { m }
+ { \href{mailto:#1}{\emailstyle{#1}} }
+ }
+ {
+ \ProvideDocumentCommand \email { m }
+ { \emailstyle{#1} }
+ } % }}}
+
+\bool_if:NT \g__mn_tabu_bool % {{{
+ {
+ \RequirePackage{multirow}
+ \RequirePackage{booktabs}
+ \RequirePackage{longtable}
+ \RequirePackage{tabu}
+ \ProvideExpandableDocumentCommand \Th { O{l} m }
+ {
+ \multicolumn
+ { 1 } % For 1 column...
+ { #1 } % ...with column-spec #1...
+ { \textbf{#2} } % Typeset #2 in bold.
+ }
+ } % }}}
+
+\bool_if:NT \g__mn_figures_bool % {{{
+ {
+ % figure captions
+ \RequirePackage{graphicx}
+ \RequirePackage{caption}
+ \captionsetup
+ {
+ format = hang,
+ font = { sf, footnotesize },
+ margin = 1in
+ }
+ } % }}}
+
+% {{{ Footnotes
+\bool_if:NT \g__mn_footnotes_bool
+ {
+ \PassOptionsToPackage{bottom, hang}{footmisc}
+ \RequirePackage{footmisc}
+ }
+\setlength { \footnotesep } { \baselineskip }
+% }}}
+
+% Document style.
+\setlength { \parindent } { 0em }
+\setlength { \parskip } { 1em }
+% {{{ Set \parskip=0 around \tableofcontents
+\RequirePackage{etoolbox}
+\pretocmd { \tableofcontents }
+ {
+ \group_begin:
+ \setlength{\parskip}{0pt}
+ }
+ { } { }
+\apptocmd { \tableofcontents }
+ { \group_end: }
+ { } { }
+% }}}
+
+% This has to be hooked so that it doesn't break the other bools undefined
+% with it first.
+\AtEndOfPackage { \cs_undefine:N \mn__legacy_bool_undefine:n }
Property changes on: trunk/Master/texmf-dist/tex/latex/rbt-mathnotes/rbt-mathnotes.sty
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Modified: trunk/Master/tlpkg/bin/tlpkg-ctan-check
===================================================================
--- trunk/Master/tlpkg/bin/tlpkg-ctan-check 2021-11-30 22:51:41 UTC (rev 61192)
+++ trunk/Master/tlpkg/bin/tlpkg-ctan-check 2021-11-30 22:53:25 UTC (rev 61193)
@@ -669,7 +669,7 @@
quran quran-bn quran-de quran-ur qyxf-book
r_und_s ragged2e raleway ran_toks randbild
random randomlist randomwalk randtext
- rank-2-roots rccol rcs rcs-multi rcsinfo
+ rank-2-roots rbt-mathnotes rccol rcs rcs-multi rcsinfo
readablecv readarray realboxes realhats realscripts realtranspose rec-thy
recipe recipebook recipecard recycle rectopma
refcheck refcount refenums reflectgraphics refman refstyle
Modified: trunk/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc
===================================================================
--- trunk/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc 2021-11-30 22:51:41 UTC (rev 61192)
+++ trunk/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc 2021-11-30 22:53:25 UTC (rev 61193)
@@ -172,6 +172,7 @@
depend pythonhighlight
depend qsharp
depend rank-2-roots
+depend rbt-mathnotes
depend rec-thy
depend rest-api
depend revquantum
Added: trunk/Master/tlpkg/tlpsrc/rbt-mathnotes.tlpsrc
===================================================================
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