- Commit
- 9595d4e31fab53935cd5c71226a4008c5fd8466e
- Parent
- a46cb25171de5d9b555da10f203f49a56b2a2fbb
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Moved .tikz files to .tex
Also made it so that tikz_gallery_generator properly handles .tex
tikz-gallery-generator
Custum build of stapix for tikz.pablopie.xyz
Diffstats
77 files changed, 1303 insertions, 1303 deletions
diff --git a/examples/config.yml b/examples/config.yml @@ -1,5 +1,5 @@ # TODO: Differenciate between alt texts and captions -- path: ./images/26-nodes-diagram.tikz +- path: ./images/26-nodes-diagram.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -11,64 +11,64 @@ source: https://commons.wikimedia.org/wiki/File:Calabi-Yau-alternate.png alt: A visual representation of the Calebi-Yau manifold -- path: ./images/complex-lattice.tikz +- path: ./images/complex-lattice.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: A complex lattice with two linearly independent periods -- path: ./images/complex-surreal-venn.tikz +- path: ./images/complex-surreal-venn.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the relationship between the real, complex and surreal numbers -- path: ./images/cube.tikz +- path: ./images/cube.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: A cube -- path: ./images/diamond.tikz +- path: ./images/diamond.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: A domond-like shape -- path: ./images/dihedral-representation-is-irreducible.tikz +- path: ./images/dihedral-representation-is-irreducible.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: An ilustration of the proof that the natural real representation of the Dihidral group is irreducible -- path: ./images/dihedral-representation.tikz +- path: ./images/dihedral-representation.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The action of the dihedral group in the real plain -- path: ./images/elliptic-curve-group-structure.tikz +- path: ./images/elliptic-curve-group-structure.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The group structure of the points of an elliptic curve -- path: ./images/euclidian-plane.tikz +- path: ./images/euclidian-plane.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The Cartesian plane -- path: ./images/finite-topological-plot.tikz +- path: ./images/finite-topological-plot.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: A plot of the number of topological spaces of n points in logarithmic scale -- path: ./images/galois-lattice-antisomorphism.tikz +- path: ./images/galois-lattice-antisomorphism.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -76,14 +76,14 @@ subgroups of the Galois group of a Galois extension and the lattice of intermediary subfields of such extension. -- path: ./images/geodesic.tikz +- path: ./images/geodesic.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the fact that geodesics locally minimize distances -- path: ./images/grothendieck-riemann-roch.tikz +- path: ./images/grothendieck-riemann-roch.tex license: PD author: Alexander Grothendieck author-url: https://grothendieckcircle.org/ @@ -99,7 +99,7 @@ alt: A diagram of the classification of finite simple groups in the format of a periodic table -- path: ./images/hyperbolic-plane-disc.tikz +- path: ./images/hyperbolic-plane-disc.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -119,13 +119,13 @@ source: https://commons.wikimedia.org/wiki/File:KleinInvariantJ.jpg alt: The j-invariant Klein function in the complex plane -- path: ./images/k4.tikz +- path: ./images/k4.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The complete graph of four vertices -- path: ./images/mobius.tikz +- path: ./images/mobius.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -138,19 +138,19 @@ alt: The first columns of the chacter table of the monster simple group in characteristic zero -- path: ./images/natural-number-line.tikz +- path: ./images/natural-number-line.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The natural number line -- path: ./images/ordinal-number-line.tikz +- path: ./images/ordinal-number-line.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The ordinal number line -- path: ./images/quaternion-rotation.tikz +- path: ./images/quaternion-rotation.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -161,54 +161,54 @@ space, and conjugation by cos t + p sin t acts as rotation by 2 t around this axis." -- path: ./images/real-number-line.tikz +- path: ./images/real-number-line.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The real number line -- path: ./images/real-ordinal-surreal-venn.tikz +- path: ./images/real-ordinal-surreal-venn.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the relationship between the real, ordinal and surreal numbers -- path: ./images/riemannian-metric.tikz +- path: ./images/riemannian-metric.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture is a comparison between the Euclidean distance and the Riemannian distance in a 3-dimensional sphere -- path: ./images/rigid-motion-reflections.tikz +- path: ./images/rigid-motion-reflections.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the fact that reflections are rigid motions -- path: ./images/rigid-motion-rotation.tikz +- path: ./images/rigid-motion-rotation.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the fact that rotations are rigid motions -- path: ./images/smooth-function.tikz +- path: ./images/smooth-function.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the definition of a smooth map between manifolds -- path: ./images/smooth-manifold.tikz +- path: ./images/smooth-manifold.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This picture represents the definition of a smooth manifold -- path: ./images/sphere-quotient.tikz +- path: ./images/sphere-quotient.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -216,7 +216,7 @@ quotient of the (n + 1)-dimensional simple orthogonal group by the n-dimensional simple orthogonal group -- path: ./images/sphere.tikz +- path: ./images/sphere.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -228,20 +228,20 @@ source: https://en.wikipedia.org/wiki/File:SporadicGroups.svg alt: All the Sporadic groups in their subquotient relationship -- path: ./images/square-to-circle-projection.tikz +- path: ./images/square-to-circle-projection.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: "The projection from the square to the circle: we map a point in the square of length √2/2 onto the unit circle by normalizing it" -- path: ./images/standard-sets-venn.tikz +- path: ./images/standard-sets-venn.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: This diagram represents the relationship between standard number sets -- path: ./images/stereographic-projection.tikz +- path: ./images/stereographic-projection.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz @@ -254,30 +254,30 @@ source: https://en.wikipedia.org/wiki/File:Surreal_number_tree.svg alt: Visualization of the surreal number tree -- path: ./images/tangent-space.tikz +- path: ./images/tangent-space.tex license: CC-BY-4 author: Gustavo Mezzovilla alt: The tangent space of a smooth manifold at a point -- path: ./images/topology-mug-donut.tikz +- path: ./images/topology-mug-donut.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: A mug continuously morphing into a donut -- path: ./images/unit-circle-covering.tikz +- path: ./images/unit-circle-covering.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The universal covering of the unit circle -- path: ./images/unit-circle.tikz +- path: ./images/unit-circle.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz alt: The unit complex circle -- path: ./images/upper-central-projection.tikz +- path: ./images/upper-central-projection.tex license: CC-BY-4 author: Pablo author-url: https://pablopie.xyz
diff --git /dev/null b/examples/images/26-nodes-diagram.tex @@ -0,0 +1,15 @@ +% This picture represents the 26-nodes diagram +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % Draw the nodes + \foreach \i in {1,2,3,4,5,6,7,8,9,10,11,12,13} + \foreach \offset in {0,1} + \filldraw ({(360/26) * (2 * (\i - 1) + \offset}:3) circle (2pt); + + % Draw the ralations between nodes + \foreach \i in {1,2,3,4,5,6,7,8,9,10,11,12,13} + \draw ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 1) + 1)}:3) + ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 2) + 1)}:3) + ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 5) + 1)}:3) + ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 7) + 1)}:3); +\end{tikzpicture}
diff --git a/examples/images/26-nodes-diagram.tikz /dev/null @@ -1,15 +0,0 @@ -% This picture represents the 26-nodes diagram -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % Draw the nodes - \foreach \i in {1,2,3,4,5,6,7,8,9,10,11,12,13} - \foreach \offset in {0,1} - \filldraw ({(360/26) * (2 * (\i - 1) + \offset}:3) circle (2pt); - - % Draw the ralations between nodes - \foreach \i in {1,2,3,4,5,6,7,8,9,10,11,12,13} - \draw ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 1) + 1)}:3) - ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 2) + 1)}:3) - ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 5) + 1)}:3) - ({(360/26) * 2 * (\i - 1)}:3) -- ({(360/26) * (2 * (\i - 7) + 1)}:3); -\end{tikzpicture}
diff --git /dev/null b/examples/images/complex-lattice.tex @@ -0,0 +1,36 @@ +% This picture represents a complex lattice with two linearly independent +% periods +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[>=triangle 45, scale=0.7] + % The axis + \draw[line width=0.6pt] (0, -1) -- (0, 4); + \draw[line width=0.6pt] (-1, 0) -- (6, 0); + + % The background grid + \foreach \x in {-1,,1,2,3,4,5,6} + \draw[dotted, line width=0.6pt] (\x, -1) -- (\x, 4); + \foreach \y in {-1,,1,2,3,4} + \draw[dotted, line width=0.6pt] (-1, \y) -- (6, \y); + + % The lattice + \begin{scope} + \clip(-1, -1) rectangle (6, 4); + + \foreach \i in {-1,0,1,2} + { + \begin{scope}[shift={({\i * (3 - 1/2)}, 0)}] + \draw[line width=0.6pt, color=cyan] (-.5, -1) -- (2, 4); + \end{scope} + + \begin{scope}[shift={(0, {\i * (2 - 1/3)})}] + \draw[line width=0.6pt, color=cyan] (-1, {-1/3}) -- (6, 2); + \end{scope} + } + \end{scope} + + % The generators of the lattice + \draw[->, >=stealth, line width=0.8pt, color=blue] (0, 0) -- (1, 2); + \draw[->, >=stealth, line width=0.8pt, color=blue] (0, 0) -- (3, 1); + \draw[line width=0.8pt, color=blue] (4, 3)-- (3, 1); + \draw[line width=0.8pt, color=blue] (4, 3)-- (1, 2); +\end{tikzpicture}
diff --git a/examples/images/complex-lattice.tikz /dev/null @@ -1,36 +0,0 @@ -% This picture represents a complex lattice with two linearly independent -% periods -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[>=triangle 45, scale=0.7] - % The axis - \draw[line width=0.6pt] (0, -1) -- (0, 4); - \draw[line width=0.6pt] (-1, 0) -- (6, 0); - - % The background grid - \foreach \x in {-1,,1,2,3,4,5,6} - \draw[dotted, line width=0.6pt] (\x, -1) -- (\x, 4); - \foreach \y in {-1,,1,2,3,4} - \draw[dotted, line width=0.6pt] (-1, \y) -- (6, \y); - - % The lattice - \begin{scope} - \clip(-1, -1) rectangle (6, 4); - - \foreach \i in {-1,0,1,2} - { - \begin{scope}[shift={({\i * (3 - 1/2)}, 0)}] - \draw[line width=0.6pt, color=cyan] (-.5, -1) -- (2, 4); - \end{scope} - - \begin{scope}[shift={(0, {\i * (2 - 1/3)})}] - \draw[line width=0.6pt, color=cyan] (-1, {-1/3}) -- (6, 2); - \end{scope} - } - \end{scope} - - % The generators of the lattice - \draw[->, >=stealth, line width=0.8pt, color=blue] (0, 0) -- (1, 2); - \draw[->, >=stealth, line width=0.8pt, color=blue] (0, 0) -- (3, 1); - \draw[line width=0.8pt, color=blue] (4, 3)-- (3, 1); - \draw[line width=0.8pt, color=blue] (4, 3)-- (1, 2); -\end{tikzpicture}
diff --git /dev/null b/examples/images/complex-surreal-venn.tex @@ -0,0 +1,16 @@ +% This picture represents the relationshipt between the real, complex and +% surreal numbers +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The reals + \draw (0.75, 0) node{$\mathbb{R}$} + ( 0, 0) circle (1.5); + + % The complex numbers + \draw (-1.5, 0) node[left]{$\mathbb{C}$} + ( 1.5, 0) circle (1.5); + + % The surreal numbers + \draw (3,0) node[right]{$\mathbf{No}$}; +\end{tikzpicture} +
diff --git a/examples/images/complex-surreal-venn.tikz /dev/null @@ -1,16 +0,0 @@ -% This picture represents the relationshipt between the real, complex and -% surreal numbers -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The reals - \draw (0.75, 0) node{$\mathbb{R}$} - ( 0, 0) circle (1.5); - - % The complex numbers - \draw (-1.5, 0) node[left]{$\mathbb{C}$} - ( 1.5, 0) circle (1.5); - - % The surreal numbers - \draw (3,0) node[right]{$\mathbf{No}$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/coxerter-group-reflections.tex @@ -0,0 +1,20 @@ +% This picture represents the action of the action of the generators of the +% Coxerter group of the complete graph of four vertices corresponding to the +% nodes in a maximal free 3-gon +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=.85] + \draw (-1.17265, 0) -- (4, 0) node[above]{$a$}; + + % The action of b in the plane (reflection by this line) + \draw[shift={(-0.57735, -1)}] (0, 0) node[left]{$b$} -- ( 60:3.5); + + % The action of bab^(-1) in the plane (reflection by this line) + \draw[shift={( 0.57735, -1)}] (0, 0) node[right]{$bab^{-1}$} -- (120:3.5); + + % The action of c in the plane (reflection by this line) + \draw[shift={( 2.42265, -1)}] (0, 0) node[right]{$c$} -- (120:3.5); + + % The action of cbab^(-1) in the plane (translation in this direction) + \draw[thick, ->] (0, 0) -- (30:3) node[right]{$\tau = cbab^{-1}$}; +\end{tikzpicture} +
diff --git a/examples/images/coxerter-group-reflections.tikz /dev/null @@ -1,20 +0,0 @@ -% This picture represents the action of the action of the generators of the -% Coxerter group of the complete graph of four vertices corresponding to the -% nodes in a maximal free 3-gon -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=.85] - \draw (-1.17265, 0) -- (4, 0) node[above]{$a$}; - - % The action of b in the plane (reflection by this line) - \draw[shift={(-0.57735, -1)}] (0, 0) node[left]{$b$} -- ( 60:3.5); - - % The action of bab^(-1) in the plane (reflection by this line) - \draw[shift={( 0.57735, -1)}] (0, 0) node[right]{$bab^{-1}$} -- (120:3.5); - - % The action of c in the plane (reflection by this line) - \draw[shift={( 2.42265, -1)}] (0, 0) node[right]{$c$} -- (120:3.5); - - % The action of cbab^(-1) in the plane (translation in this direction) - \draw[thick, ->] (0, 0) -- (30:3) node[right]{$\tau = cbab^{-1}$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/cube.tex @@ -0,0 +1,9 @@ +% This picture represents a cube +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + \draw (0,0,0) -- ++(-1,0,0) -- ++(0,-1,0) -- ++(1,0,0) -- cycle; + \draw (0,0,0) -- ++(0,0,-1) -- ++(0,-1,0) -- ++(0,0,1) -- cycle; + \draw[dotted, shift={(-1, 0)}] (0,0,-1) -- ++(0,-1,0) -- ++(0,0,1); + \draw (0,0,0) -- ++(-1,0,0) -- ++(0,0,-1) -- ++(1,0,0) -- cycle; + \draw[dotted, shift={(0, -1)}] (-1,0,-1) -- ++(1,0,0); +\end{tikzpicture}
diff --git a/examples/images/cube.tikz /dev/null @@ -1,9 +0,0 @@ -% This picture represents a cube -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - \draw (0,0,0) -- ++(-1,0,0) -- ++(0,-1,0) -- ++(1,0,0) -- cycle; - \draw (0,0,0) -- ++(0,0,-1) -- ++(0,-1,0) -- ++(0,0,1) -- cycle; - \draw[dotted, shift={(-1, 0)}] (0,0,-1) -- ++(0,-1,0) -- ++(0,0,1); - \draw (0,0,0) -- ++(-1,0,0) -- ++(0,0,-1) -- ++(1,0,0) -- cycle; - \draw[dotted, shift={(0, -1)}] (-1,0,-1) -- ++(1,0,0); -\end{tikzpicture}
diff --git /dev/null b/examples/images/diamond.tex @@ -0,0 +1,11 @@ +% This picture represents a domond-like thingy +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-.4,xscale=.4] + % Polygon + \draw (244.52,138.11) -- (129.96,172.23) -- (170.52,46.11) -- cycle; + \draw (129.96,172.23) -- (133.33,118.95) -- (170.52,46.11); + \draw[dotted] (133.33,118.95) -- (244.52,138.11) ; + \draw (244.52,138.11) -- (170.62,210.9) -- (129.96,172.23) -- cycle; + \draw[dotted] (133.33,118.95) -- (170.62,210.9) ; +\end{tikzpicture} +
diff --git a/examples/images/diamond.tikz /dev/null @@ -1,11 +0,0 @@ -% This picture represents a domond-like thingy -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-.4,xscale=.4] - % Polygon - \draw (244.52,138.11) -- (129.96,172.23) -- (170.52,46.11) -- cycle; - \draw (129.96,172.23) -- (133.33,118.95) -- (170.52,46.11); - \draw[dotted] (133.33,118.95) -- (244.52,138.11) ; - \draw (244.52,138.11) -- (170.62,210.9) -- (129.96,172.23) -- cycle; - \draw[dotted] (133.33,118.95) -- (170.62,210.9) ; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/dihedral-representation-is-irreducible.tex @@ -0,0 +1,22 @@ +% An ilustration of the proof that the representation of the Dihidral group is +% irreducible +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=1.2] + % The axis + \draw[->] (-1,0)--(3,0) node[right]{$x$}; + \draw[->] (0,-0.5)--(0,1.5) node[above]{$y$}; + + % sigma + \draw[->] (1.5,0.3) arc (0:50:1cm) node at (1.7,0.85) {$\sigma$}; + + % A non-zero vector v + \filldraw[black] (1.5, 0.3) circle (1pt); + \node[right] at (1.5, 0.3) {$v$}; + + % sigma(v) + \filldraw[black] (1, 1.15) circle (1pt); + \node[left] at (1, 1.15) {$\sigma \cdot v$}; + + % The subspace spaned by v + \draw[dotted] (-1, -0.2)--(3, 0.6); +\end{tikzpicture}
diff --git a/examples/images/dihedral-representation-is-irreducible.tikz /dev/null @@ -1,22 +0,0 @@ -% An ilustration of the proof that the representation of the Dihidral group is -% irreducible -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=1.2] - % The axis - \draw[->] (-1,0)--(3,0) node[right]{$x$}; - \draw[->] (0,-0.5)--(0,1.5) node[above]{$y$}; - - % sigma - \draw[->] (1.5,0.3) arc (0:50:1cm) node at (1.7,0.85) {$\sigma$}; - - % A non-zero vector v - \filldraw[black] (1.5, 0.3) circle (1pt); - \node[right] at (1.5, 0.3) {$v$}; - - % sigma(v) - \filldraw[black] (1, 1.15) circle (1pt); - \node[left] at (1, 1.15) {$\sigma \cdot v$}; - - % The subspace spaned by v - \draw[dotted] (-1, -0.2)--(3, 0.6); -\end{tikzpicture}
diff --git /dev/null b/examples/images/dihedral-representation.tex @@ -0,0 +1,18 @@ +% This picture represents the action of the dihedral group in the real plain +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The axis + \draw[->] (-3,0)--(3,0) node[right]{$x$}; + \draw[->] (0,-2)--(0,2) node[above]{$y$}; + + % The triangle + \node[draw, regular polygon, regular polygon sides=3, minimum height=2cm]{}; + + % The action of sigma + \draw[->] (1.5, 0.5) arc (0:90:1cm) + node at (1.5, 1.4) {$\sigma$}; + + % The action of tau + \draw[<->] (-1, -1)--(1, -1) node[right]{$\tau$}; +\end{tikzpicture} +
diff --git a/examples/images/dihedral-representation.tikz /dev/null @@ -1,18 +0,0 @@ -% This picture represents the action of the dihedral group in the real plain -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The axis - \draw[->] (-3,0)--(3,0) node[right]{$x$}; - \draw[->] (0,-2)--(0,2) node[above]{$y$}; - - % The triangle - \node[draw, regular polygon, regular polygon sides=3, minimum height=2cm]{}; - - % The action of sigma - \draw[->] (1.5, 0.5) arc (0:90:1cm) - node at (1.5, 1.4) {$\sigma$}; - - % The action of tau - \draw[<->] (-1, -1)--(1, -1) node[right]{$\tau$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/elliptic-curve-group-structure.tex @@ -0,0 +1,34 @@ +% This picture represents the group structure of the points of an elliptic +% curve +\begin{tikzpicture}[yscale=.7] + % The axis + \draw[->] (-3, 0) -- (3.5, 0); + \draw[->] ( 0, -3.2) -- ( 0, 3.2); + + \clip(-3., -3.2) rectangle (3.5, 3.2); + + % The curve + \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] + plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)}); + \draw[thick, smooth, samples=100, domain=2.0762:3.5] + plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)}); + \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] + plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)}); + \draw[thick, smooth, samples=100, domain=2.0762:3.5] + plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)}); + + % The intersection lines + \draw[thick, color=violet] ( -3, 1.2218) -- ( 3.5, 2.5105); + \draw[thick, color=violet] (-2.5534, -3.2) -- (-2.5534, 3.2); + + % The intersection points + \filldraw ( 0, 1.8165902124584950) circle (1.0pt); + \filldraw ( 2.5927223574355067, 2.3306137033629240) circle (1.0pt); + \filldraw (-2.5534168046838945, 1.3103592942448403) circle (1.0pt); + \filldraw (-2.5534168046838945, -1.3103592942526257) circle (1.0pt); + + % The labels + \draw ( 0, 2.2346057845515620) node[right]{$P$}; + \draw ( 3, 2.6354835353265860) node {$Q$}; + \draw (-2, -1.0195783099751021) node {$P+Q$}; +\end{tikzpicture}
diff --git a/examples/images/elliptic-curve-group-structure.tikz /dev/null @@ -1,34 +0,0 @@ -% This picture represents the group structure of the points of an elliptic -% curve -\begin{tikzpicture}[yscale=.7] - % The axis - \draw[->] (-3, 0) -- (3.5, 0); - \draw[->] ( 0, -3.2) -- ( 0, 3.2); - - \clip(-3., -3.2) rectangle (3.5, 3.2); - - % The curve - \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] - plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)}); - \draw[thick, smooth, samples=100, domain=2.0762:3.5] - plot(\x, {sqrt((\x)^(3)-5.9*(\x)+3.3)}); - \draw[thick, smooth, samples=100, domain=-2.6712:0.5950] - plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)}); - \draw[thick, smooth, samples=100, domain=2.0762:3.5] - plot(\x, {0-sqrt((\x)^(3)-5.9*(\x)+3.3)}); - - % The intersection lines - \draw[thick, color=violet] ( -3, 1.2218) -- ( 3.5, 2.5105); - \draw[thick, color=violet] (-2.5534, -3.2) -- (-2.5534, 3.2); - - % The intersection points - \filldraw ( 0, 1.8165902124584950) circle (1.0pt); - \filldraw ( 2.5927223574355067, 2.3306137033629240) circle (1.0pt); - \filldraw (-2.5534168046838945, 1.3103592942448403) circle (1.0pt); - \filldraw (-2.5534168046838945, -1.3103592942526257) circle (1.0pt); - - % The labels - \draw ( 0, 2.2346057845515620) node[right]{$P$}; - \draw ( 3, 2.6354835353265860) node {$Q$}; - \draw (-2, -1.0195783099751021) node {$P+Q$}; -\end{tikzpicture}
diff --git /dev/null b/examples/images/euclidian-plane.tex @@ -0,0 +1,9 @@ +% This picture represents the cartesian plain +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + \draw (0, 0) node[left]{$\mathbb{R}^2$} -- + (2, 0) -- + (3, 1) -- + (1, 1) -- cycle; +\end{tikzpicture} +
diff --git a/examples/images/euclidian-plane.tikz /dev/null @@ -1,9 +0,0 @@ -% This picture represents the cartesian plain -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - \draw (0, 0) node[left]{$\mathbb{R}^2$} -- - (2, 0) -- - (3, 1) -- - (1, 1) -- cycle; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/finite-topological-plot.tex @@ -0,0 +1,28 @@ +% A plot of the number of topological spaces of n points in logarithmic scale +% Copyright Pablo (C) 2023 +\begin{tikzpicture} + \begin{axis}[ + xlabel={$n$}, + ylabel={$\log(\text{\# topological spaces of $n$ points})$}, + xmin=0, xmax=20, + ymin=0, ymax=85, + legend pos=north west, + ymajorgrids=true, + grid style=dashed, + title={Finite Topological Spaces}, + ] + + \addplot[ycomb, mark=*, color=blue] + coordinates { + (1, 0.0) (2, 0.0) (3, 1.3862943611198906) + (4, 3.367295829986474) (5, 5.872117789475416) + (6, 8.845345196421732) (7, 12.25260788832186) + (8, 16.070505071998763) (9, 20.2813120724568) + (10, 24.870523629947815) (11, 29.825692867915237) + (12, 35.135878446962565) (13, 40.79136515152374) + (14, 46.783499368150814) (15, 53.10457040668696) + (16, 59.74771093408638) (17, 66.70680783627301) + (18, 73.97642153853138) (19, 81.5517138078997) + }; + \end{axis} +\end{tikzpicture}
diff --git a/examples/images/finite-topological-plot.tikz /dev/null @@ -1,28 +0,0 @@ -% A plot of the number of topological spaces of n points in logarithmic scale -% Copyright Pablo (C) 2023 -\begin{tikzpicture} - \begin{axis}[ - xlabel={$n$}, - ylabel={$\log(\text{\# topological spaces of $n$ points})$}, - xmin=0, xmax=20, - ymin=0, ymax=85, - legend pos=north west, - ymajorgrids=true, - grid style=dashed, - title={Finite Topological Spaces}, - ] - - \addplot[ycomb, mark=*, color=blue] - coordinates { - (1, 0.0) (2, 0.0) (3, 1.3862943611198906) - (4, 3.367295829986474) (5, 5.872117789475416) - (6, 8.845345196421732) (7, 12.25260788832186) - (8, 16.070505071998763) (9, 20.2813120724568) - (10, 24.870523629947815) (11, 29.825692867915237) - (12, 35.135878446962565) (13, 40.79136515152374) - (14, 46.783499368150814) (15, 53.10457040668696) - (16, 59.74771093408638) (17, 66.70680783627301) - (18, 73.97642153853138) (19, 81.5517138078997) - }; - \end{axis} -\end{tikzpicture}
diff --git /dev/null b/examples/images/galois-lattice-antisomorphism.tex @@ -0,0 +1,39 @@ +% This picture represents the lattice antisomorphism between the lattice of the +% subgroups of the Galois group of a Galois extension and the lattice of +% intermediary subfields of such extension. +% Copyright Pablo (C) 2023 +\begin{tikzpicture}[ampersand replacement=\&] + % The elements of both lattices + \matrix(m)[matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em] + { + \& K \& \& 1 \& \\ + \& L_1 \cdot L_2 \& \& H_1 \cap H_2 \& \\ + L_1 \& \& H_1 \& \& \\ + \& \& L_2 \& \& H_2 \\ + \& L_1 \cap L_2 \& \& \langle H_1, H_2 \rangle \& \\ + \& k \& \& \operatorname{Gal}(K/k) \& \\ + }; + + % The relations of both lattices + \draw (m-1-2) -- (m-2-2) + -- (m-3-1) + -- (m-5-2) + -- (m-6-2) + (m-2-2) -- (m-4-3) + -- (m-5-2); + \draw (m-1-4) -- (m-2-4) + -- (m-3-3) + -- (m-5-4) + -- (m-6-4) + (m-2-4) -- (m-4-5) + -- (m-5-4); + + % The antisomorphism + \draw[dotted] (m-1-2) -- (m-1-4) + (m-2-2) -- (m-2-4) + (m-3-1) -- (m-3-3) + (m-4-3) -- (m-4-5) + (m-5-2) -- (m-5-4) + (m-6-2) -- (m-6-4); +\end{tikzpicture} +
diff --git a/examples/images/galois-lattice-antisomorphism.tikz /dev/null @@ -1,39 +0,0 @@ -% This picture represents the lattice antisomorphism between the lattice of the -% subgroups of the Galois group of a Galois extension and the lattice of -% intermediary subfields of such extension. -% Copyright Pablo (C) 2023 -\begin{tikzpicture}[ampersand replacement=\&] - % The elements of both lattices - \matrix(m)[matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em] - { - \& K \& \& 1 \& \\ - \& L_1 \cdot L_2 \& \& H_1 \cap H_2 \& \\ - L_1 \& \& H_1 \& \& \\ - \& \& L_2 \& \& H_2 \\ - \& L_1 \cap L_2 \& \& \langle H_1, H_2 \rangle \& \\ - \& k \& \& \operatorname{Gal}(K/k) \& \\ - }; - - % The relations of both lattices - \draw (m-1-2) -- (m-2-2) - -- (m-3-1) - -- (m-5-2) - -- (m-6-2) - (m-2-2) -- (m-4-3) - -- (m-5-2); - \draw (m-1-4) -- (m-2-4) - -- (m-3-3) - -- (m-5-4) - -- (m-6-4) - (m-2-4) -- (m-4-5) - -- (m-5-4); - - % The antisomorphism - \draw[dotted] (m-1-2) -- (m-1-4) - (m-2-2) -- (m-2-4) - (m-3-1) -- (m-3-3) - (m-4-3) -- (m-4-5) - (m-5-2) -- (m-5-4) - (m-6-2) -- (m-6-4); -\end{tikzpicture} -
diff --git /dev/null b/examples/images/geodesic.tex @@ -0,0 +1,54 @@ +% This picture represents the fact that geodesics locally minimize distances +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.5] + % The cirference + \draw (0, 0) circle (3); + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -3); + \draw ellipse (3 and 1); + \end{scope} + + % Greenwhich + \begin{scope} + \clip (-3, -3) rectangle (0, 3); + \draw ellipse (1 and 3); + \end{scope} + + % The curve + \begin{scope} + \clip (-3, 0) rectangle (0, -3); + \draw[very thick] ellipse (1 and 3); + \end{scope} + \begin{scope} + \clip (3, -3) rectangle (0, 3); + \draw[very thick, dotted] ellipse (1 and 3); + \end{scope} + + % The ends + \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt); + + \draw (-0.87, -1.5) circle (0.3); + \draw (-1.17, -1.5) -- (-4, 1); + + % Zoom in ares + \begin{scope}[shift={(-6, 1)}] + \draw (0, 0) circle (2); + + % The geodesic + \draw[very thick] (0, -2) -- (0, 2); + \filldraw (0, -2) circle (2pt) (0, 2) circle (2pt); + + % Another curve + \draw[dotted] ( 0, 2) to[out=180, in=90] + (-0.6, 1.4) to[out=270, in=150] + ( 0.5, 0.7) to[out=-30, in=0] + ( 0.3, 0.1) to[out=180, in=180] + ( 0.5, 0.6) to[out=0, in=120] + ( 1.3, 0.7) to[out=-60, in=60] + ( 0.4, -0.5) to[out=240, in=90] + ( 0, -2); + \end{scope} +\end{tikzpicture} +
diff --git a/examples/images/geodesic.tikz /dev/null @@ -1,54 +0,0 @@ -% This picture represents the fact that geodesics locally minimize distances -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.5] - % The cirference - \draw (0, 0) circle (3); - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % Greenwhich - \begin{scope} - \clip (-3, -3) rectangle (0, 3); - \draw ellipse (1 and 3); - \end{scope} - - % The curve - \begin{scope} - \clip (-3, 0) rectangle (0, -3); - \draw[very thick] ellipse (1 and 3); - \end{scope} - \begin{scope} - \clip (3, -3) rectangle (0, 3); - \draw[very thick, dotted] ellipse (1 and 3); - \end{scope} - - % The ends - \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt); - - \draw (-0.87, -1.5) circle (0.3); - \draw (-1.17, -1.5) -- (-4, 1); - - % Zoom in ares - \begin{scope}[shift={(-6, 1)}] - \draw (0, 0) circle (2); - - % The geodesic - \draw[very thick] (0, -2) -- (0, 2); - \filldraw (0, -2) circle (2pt) (0, 2) circle (2pt); - - % Another curve - \draw[dotted] ( 0, 2) to[out=180, in=90] - (-0.6, 1.4) to[out=270, in=150] - ( 0.5, 0.7) to[out=-30, in=0] - ( 0.3, 0.1) to[out=180, in=180] - ( 0.5, 0.6) to[out=0, in=120] - ( 1.3, 0.7) to[out=-60, in=60] - ( 0.4, -0.5) to[out=240, in=90] - ( 0, -2); - \end{scope} -\end{tikzpicture} -
diff --git /dev/null b/examples/images/grothendieck-riemann-roch.tex @@ -0,0 +1,99 @@ +% Original artwork by Alexander Grothendieck: the commutative diagram from the +% Grothendieck-Riemann-Roch theorem, surrounded by fire and two devils carrying +% forks. +% Generated with svg2tikz <https://github.com/xyz2tex/svg2tikz> from +% https://en.wikipedia.org/wiki/File:Grothendieck-Riemann-Roch.jpg +% Copyleft Pablo (C) 2021 +\begin{tikzpicture}[y=0.80pt, x=0.80pt, yscale=-1, xscale=1, inner sep=0pt, outer sep=0pt] + \path[fill=black,line width=0.080pt] (705.6108,0.0011) .. controls (705.2593,-0.0223) and (704.9780,0.3330) .. (704.9780,0.8580) .. controls (704.8780,1.5580) and (704.9776,5.0583) .. (705.0776,8.6583) .. controls (705.2776,15.8583) and (706.8781,19.8579) .. (710.5781,22.2579) .. controls (712.5781,23.5579) and (713.0778,24.7586) .. (713.2778,29.9586) .. controls (713.3461,43.0978) and (713.1607,57.2962) .. 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diff --git /dev/null b/examples/images/hyperbolic-plane-disc.tex @@ -0,0 +1,17 @@ +% This picture represents the Poincaré disc model of the hyperbolic plane +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The disk + \draw (0, 0) circle (1); + + % A strait line in the hyperbolic plane + \begin{scope} + \clip (0, 0) circle (1); + \draw (1, 1) circle (1); + \end{scope} + + % The intersection of the strait line with infinity + \fill (0, 1) circle (1pt); + \fill (1, 0) circle (1pt); +\end{tikzpicture} +
diff --git a/examples/images/hyperbolic-plane-disc.tikz /dev/null @@ -1,17 +0,0 @@ -% This picture represents the Poincaré disc model of the hyperbolic plane -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The disk - \draw (0, 0) circle (1); - - % A strait line in the hyperbolic plane - \begin{scope} - \clip (0, 0) circle (1); - \draw (1, 1) circle (1); - \end{scope} - - % The intersection of the strait line with infinity - \fill (0, 1) circle (1pt); - \fill (1, 0) circle (1pt); -\end{tikzpicture} -
diff --git /dev/null b/examples/images/k4.tex @@ -0,0 +1,20 @@ +% This picture represents the complete graph of four vertices +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.75] + % The vertices + \coordinate (a) at (0,0); + \coordinate (b) at (4,0); + \coordinate (c) at (2,1); + \coordinate (d) at (2,3); + \foreach \node in {a,b,c,d} + \filldraw (\node) circle (2pt); + + % The edges + \draw (a) -- (b) + -- (c) + -- (a) + -- (d) + -- (b) + -- (c) + -- (d); +\end{tikzpicture}
diff --git a/examples/images/k4.tikz /dev/null @@ -1,20 +0,0 @@ -% This picture represents the complete graph of four vertices -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.75] - % The vertices - \coordinate (a) at (0,0); - \coordinate (b) at (4,0); - \coordinate (c) at (2,1); - \coordinate (d) at (2,3); - \foreach \node in {a,b,c,d} - \filldraw (\node) circle (2pt); - - % The edges - \draw (a) -- (b) - -- (c) - -- (a) - -- (d) - -- (b) - -- (c) - -- (d); -\end{tikzpicture}
diff --git /dev/null b/examples/images/mobius.tex @@ -0,0 +1,46 @@ +% This picture represents the Mobius strip +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[y=.4pt, x=.4pt] +\draw (0.3750,94.8557) .. controls (0.3750,118.2940) and (18.2610,128.9391) + .. (18.2610,128.9391) + .. controls (18.2610,128.9391) and (100.4215,189.9374) + .. (108.0803,192.4671) + .. controls (115.7391,194.9968) and (133.1027,196.1368) + .. (155.5078,192.5264) + .. controls (177.9130,188.9160) and (216.1559,174.9892) + .. (227.9735,172.1608) + .. controls (239.7910,169.3324) and (263.2421,163.9249) + .. (266.0229,163.1687) + .. controls (268.8038,162.4126) and (281.6012,158.5692) + .. (285.4151,147.2840) + .. controls (289.2289,135.9988) and (305.4271,66.9205) + .. (305.4271,64.6198) + .. controls (305.4271,62.3190) and (308.4490,49.2497) + .. (297.1977,37.7280) + .. controls (285.9463,26.2063) and (253.1688,11.1757) + .. (238.1181,7.5004) + .. controls (223.0674,3.8252) and (181.1675,-4.4643) + .. (139.7209,4.1781) + .. controls (98.2743,12.8205) and (45.1991,41.1365) + .. (25.2434,53.9603) + .. controls (5.2876,66.7840) and (0.3753,83.9002) + .. (0.3750,94.8557) + -- cycle; + +\draw (25.2346,53.9597) .. controls (25.2346,53.9597) and (51.5362,38.8097) + .. (69.5976,38.8097) + .. controls (114.8245,38.8097) and (165.6800,41.2423) + .. (233.5759,89.8457) + .. controls (291.8650,131.5720) and (285.4160,147.2882) + .. (285.4160,147.2882); + +\draw (18.2610,128.9391) .. controls (37.1485,143.1315) and (52.2382,142.9063) + .. (56.2468,142.9063) + .. controls (124.3626,142.9063) and (193.5770,87.8758) + .. (225.7207,87.8758) + .. controls (229.1642,87.8758) and (233.6249,89.8426) + .. (233.6249,89.8426); + +\draw (69.5541,38.8315) .. controls (69.5541,38.8315) and (30.1077,87.1975) + .. (56.3111,142.7452); +\end{tikzpicture}
diff --git a/examples/images/mobius.tikz /dev/null @@ -1,46 +0,0 @@ -% This picture represents the Mobius strip -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[y=.4pt, x=.4pt] -\draw (0.3750,94.8557) .. controls (0.3750,118.2940) and (18.2610,128.9391) - .. (18.2610,128.9391) - .. controls (18.2610,128.9391) and (100.4215,189.9374) - .. (108.0803,192.4671) - .. controls (115.7391,194.9968) and (133.1027,196.1368) - .. (155.5078,192.5264) - .. controls (177.9130,188.9160) and (216.1559,174.9892) - .. (227.9735,172.1608) - .. controls (239.7910,169.3324) and (263.2421,163.9249) - .. (266.0229,163.1687) - .. controls (268.8038,162.4126) and (281.6012,158.5692) - .. (285.4151,147.2840) - .. controls (289.2289,135.9988) and (305.4271,66.9205) - .. (305.4271,64.6198) - .. controls (305.4271,62.3190) and (308.4490,49.2497) - .. (297.1977,37.7280) - .. controls (285.9463,26.2063) and (253.1688,11.1757) - .. (238.1181,7.5004) - .. controls (223.0674,3.8252) and (181.1675,-4.4643) - .. (139.7209,4.1781) - .. controls (98.2743,12.8205) and (45.1991,41.1365) - .. (25.2434,53.9603) - .. controls (5.2876,66.7840) and (0.3753,83.9002) - .. (0.3750,94.8557) - -- cycle; - -\draw (25.2346,53.9597) .. controls (25.2346,53.9597) and (51.5362,38.8097) - .. (69.5976,38.8097) - .. controls (114.8245,38.8097) and (165.6800,41.2423) - .. (233.5759,89.8457) - .. controls (291.8650,131.5720) and (285.4160,147.2882) - .. (285.4160,147.2882); - -\draw (18.2610,128.9391) .. controls (37.1485,143.1315) and (52.2382,142.9063) - .. (56.2468,142.9063) - .. controls (124.3626,142.9063) and (193.5770,87.8758) - .. (225.7207,87.8758) - .. controls (229.1642,87.8758) and (233.6249,89.8426) - .. (233.6249,89.8426); - -\draw (69.5541,38.8315) .. controls (69.5541,38.8315) and (30.1077,87.1975) - .. (56.3111,142.7452); -\end{tikzpicture}
diff --git /dev/null b/examples/images/natural-number-line.tex @@ -0,0 +1,11 @@ +% This picture represents the natural number line +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The line + \draw[-latex] (0,0) -- (6, 0) node[right]{$\mathbb{N}$}; + + % The the numbers + \foreach \x in {0,1,2,3,4,5} + \draw[shift={(\x,0)}] (0,3pt) -- (0,-3pt) node[below]{$\x$}; +\end{tikzpicture} +
diff --git a/examples/images/natural-number-line.tikz /dev/null @@ -1,11 +0,0 @@ -% This picture represents the natural number line -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The line - \draw[-latex] (0,0) -- (6, 0) node[right]{$\mathbb{N}$}; - - % The the numbers - \foreach \x in {0,1,2,3,4,5} - \draw[shift={(\x,0)}] (0,3pt) -- (0,-3pt) node[below]{$\x$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/ordinal-number-line.tex @@ -0,0 +1,24 @@ +% This picture represents the ordinal number line +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The line + \draw[-latex] (0,0) -- (6.5,0) node[right]{$\mathbf{ON}$}; + + % The numbers + \foreach \x in {0, 1, 2} + \draw[shift={(\x,0)}] (0pt,3pt) -- (0pt,-3pt) node[below]{$\x$}; + + \foreach \offset in {0, 3} + \foreach \x in {2.5,2.75,2.875,2.9375,2.96875,2.984375} + \draw[shift={(\offset+\x,0)}] (0pt,3pt) -- (0pt,-3pt); + + \foreach \offset in {1, 2} + \draw[shift={(3+\offset,0)}] (0pt,3pt) -- (0pt,-3pt) + node[below]{$\omega + \offset$}; + + \draw[shift={(3,0)}] (0pt,3pt) -- (0pt,-3pt) node[below]{$\omega$}; + + \draw[shift={(6,0)}] (0, 3pt) -- (0,-3pt) + node[below]{$\omega + \omega$}; +\end{tikzpicture} +
diff --git a/examples/images/ordinal-number-line.tikz /dev/null @@ -1,24 +0,0 @@ -% This picture represents the ordinal number line -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The line - \draw[-latex] (0,0) -- (6.5,0) node[right]{$\mathbf{ON}$}; - - % The numbers - \foreach \x in {0, 1, 2} - \draw[shift={(\x,0)}] (0pt,3pt) -- (0pt,-3pt) node[below]{$\x$}; - - \foreach \offset in {0, 3} - \foreach \x in {2.5,2.75,2.875,2.9375,2.96875,2.984375} - \draw[shift={(\offset+\x,0)}] (0pt,3pt) -- (0pt,-3pt); - - \foreach \offset in {1, 2} - \draw[shift={(3+\offset,0)}] (0pt,3pt) -- (0pt,-3pt) - node[below]{$\omega + \offset$}; - - \draw[shift={(3,0)}] (0pt,3pt) -- (0pt,-3pt) node[below]{$\omega$}; - - \draw[shift={(6,0)}] (0, 3pt) -- (0,-3pt) - node[below]{$\omega + \omega$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/quaternion-rotation.tex @@ -0,0 +1,46 @@ +% This drawing represents the correspondance between conjugation by pure +% unitary quaternions and rotations in the 3-dimensional euclidian space: the +% coordinates of a unitary quaternion p number with zero real cofficient induce +% a line through the origin in the 3-dimensional enclidian space, and +% conjugation by cos t + p sin t acts as rotation by 2 t around this axis. +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The rotation axis + \begin{scope}[rotate=-60] + % The axis + \draw[->] (0, 0) -- (0, 2.5) node[right]{$p$}; + + % The rotation + \draw[->] (0.43, 2) node[right]{$2 \theta$} arc (30:360:0.5 and 0.25); + + % The origin and the intersection of ratation axis with the unit sphere + \filldraw (0, 0) circle (1pt) (0, 1) circle (1pt); + \end{scope} + + % The circunference + \draw (0, 0) circle (1.5); + + % The equator + \begin{scope} + \clip (-1.5, 0) rectangle (1.5, -1.5); + \draw ellipse (1.5 and 0.5); + \end{scope} + + % The equator (on the other side of the sphere) + \begin{scope} + \clip (-1.5, 0) rectangle (1.5, 1.5); + \draw[dotted] ellipse (1.5 and 0.5); + \end{scope} + + % Greenwhich + \begin{scope} + \clip (-1.5, -1.5) rectangle (0, 1.5); + \draw ellipse (0.5 and 1.5); + \end{scope} + + % Greenwhich (on the other side of the sphere) + \begin{scope} + \clip (1.5, -1.5) rectangle (0, 1.5); + \draw[dotted] ellipse (0.5 and 1.5); + \end{scope} +\end{tikzpicture}
diff --git a/examples/images/quaternion-rotation.tikz /dev/null @@ -1,46 +0,0 @@ -% This drawing represents the correspondance between conjugation by pure -% unitary quaternions and rotations in the 3-dimensional euclidian space: the -% coordinates of a unitary quaternion p number with zero real cofficient induce -% a line through the origin in the 3-dimensional enclidian space, and -% conjugation by cos t + p sin t acts as rotation by 2 t around this axis. -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The rotation axis - \begin{scope}[rotate=-60] - % The axis - \draw[->] (0, 0) -- (0, 2.5) node[right]{$p$}; - - % The rotation - \draw[->] (0.43, 2) node[right]{$2 \theta$} arc (30:360:0.5 and 0.25); - - % The origin and the intersection of ratation axis with the unit sphere - \filldraw (0, 0) circle (1pt) (0, 1) circle (1pt); - \end{scope} - - % The circunference - \draw (0, 0) circle (1.5); - - % The equator - \begin{scope} - \clip (-1.5, 0) rectangle (1.5, -1.5); - \draw ellipse (1.5 and 0.5); - \end{scope} - - % The equator (on the other side of the sphere) - \begin{scope} - \clip (-1.5, 0) rectangle (1.5, 1.5); - \draw[dotted] ellipse (1.5 and 0.5); - \end{scope} - - % Greenwhich - \begin{scope} - \clip (-1.5, -1.5) rectangle (0, 1.5); - \draw ellipse (0.5 and 1.5); - \end{scope} - - % Greenwhich (on the other side of the sphere) - \begin{scope} - \clip (1.5, -1.5) rectangle (0, 1.5); - \draw[dotted] ellipse (0.5 and 1.5); - \end{scope} -\end{tikzpicture}
diff --git /dev/null b/examples/images/real-number-line.tex @@ -0,0 +1,14 @@ +% This picture represents the real number line +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The line + \draw[latex-latex] (-3,0) -- (3,0) node[right]{$\mathbb{R}$}; + + % The numbers + \foreach \x in {-2,-1,0,1,2} + \draw[shift={(\x,0)}] (0pt,0pt) -- (0pt,-3pt) node[below]{$\x$}; + + % A real number x between 0 and 1 + \draw[shift={(0.6,0)}] (0pt,6pt) -- (0pt,-6pt) node[below]{$x$}; +\end{tikzpicture} +
diff --git a/examples/images/real-number-line.tikz /dev/null @@ -1,14 +0,0 @@ -% This picture represents the real number line -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The line - \draw[latex-latex] (-3,0) -- (3,0) node[right]{$\mathbb{R}$}; - - % The numbers - \foreach \x in {-2,-1,0,1,2} - \draw[shift={(\x,0)}] (0pt,0pt) -- (0pt,-3pt) node[below]{$\x$}; - - % A real number x between 0 and 1 - \draw[shift={(0.6,0)}] (0pt,6pt) -- (0pt,-6pt) node[below]{$x$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/real-ordinal-surreal-venn.tex @@ -0,0 +1,18 @@ +% This picture represents the relationshipt between the real, ordinal and +% surreal numbers +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The reals + \draw (0,0) circle (1) + (-1.5,0) node{$\mathbb{R}$}; + + % The ordinals + \draw (-1,0) circle (1) + (0.5,0) node{$\mathbf{ON}$}; + + % The surreals (+ natural numbers) + \draw (-2.5, 1.5) rectangle (1.5,-1.5) + (-0.5,0) node{$\mathbb{N}$} + (1.5,-1.5) node[right]{$\mathbf{No}$}; +\end{tikzpicture} +
diff --git a/examples/images/real-ordinal-surreal-venn.tikz /dev/null @@ -1,18 +0,0 @@ -% This picture represents the relationshipt between the real, ordinal and -% surreal numbers -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The reals - \draw (0,0) circle (1) - (-1.5,0) node{$\mathbb{R}$}; - - % The ordinals - \draw (-1,0) circle (1) - (0.5,0) node{$\mathbf{ON}$}; - - % The surreals (+ natural numbers) - \draw (-2.5, 1.5) rectangle (1.5,-1.5) - (-0.5,0) node{$\mathbb{N}$} - (1.5,-1.5) node[right]{$\mathbf{No}$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/riemannian-metric.tex @@ -0,0 +1,43 @@ +% This picture is a comparison between the euclian distance and the Riemannian +% distance in a three-dimensional sphere +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The cirference + \draw (0, 0) circle (3); + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -3); + \draw ellipse (3 and 1); + \end{scope} + + % The equator (on the other side of the sphere) + \begin{scope} + \clip (-3, 0) rectangle (3, 3); + \draw[dotted] ellipse (3 and 1); + \end{scope} + + % The dots + \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt); + + \draw[thick, dotted] (0, 3) -- (-1, 0); + + % Greenwhich + \begin{scope} + \clip (-3, -3) rectangle (0, 3); + \draw ellipse (1 and 3); + \end{scope} + + % Greenwhich (on the other side of the sphere) + \begin{scope} + \clip (3, -3) rectangle (0, 3); + \draw[dotted] ellipse (1 and 3); + \end{scope} + + % Greenwhich (on the other side of the sphere) + \begin{scope} + \clip (-3, 0) rectangle (0, 3); + \draw[very thick] ellipse (1 and 3); + \end{scope} +\end{tikzpicture} +
diff --git a/examples/images/riemannian-metric.tikz /dev/null @@ -1,43 +0,0 @@ -% This picture is a comparison between the euclian distance and the Riemannian -% distance in a three-dimensional sphere -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The cirference - \draw (0, 0) circle (3); - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % The equator (on the other side of the sphere) - \begin{scope} - \clip (-3, 0) rectangle (3, 3); - \draw[dotted] ellipse (3 and 1); - \end{scope} - - % The dots - \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt); - - \draw[thick, dotted] (0, 3) -- (-1, 0); - - % Greenwhich - \begin{scope} - \clip (-3, -3) rectangle (0, 3); - \draw ellipse (1 and 3); - \end{scope} - - % Greenwhich (on the other side of the sphere) - \begin{scope} - \clip (3, -3) rectangle (0, 3); - \draw[dotted] ellipse (1 and 3); - \end{scope} - - % Greenwhich (on the other side of the sphere) - \begin{scope} - \clip (-3, 0) rectangle (0, 3); - \draw[very thick] ellipse (1 and 3); - \end{scope} -\end{tikzpicture} -
diff --git /dev/null b/examples/images/rigid-motion-reflections.tex @@ -0,0 +1,29 @@ +% This picture represents the fact that reflections are rigid motions +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The first square + \begin{scope}[shift={(1.5, -1)}] + \draw (0, 0) -- ++( 2, 0) + -- ++( 0, 2) + -- ++(-2, 0) + -- cycle; + + \draw[thick] (0, 2) -- (1, 0); + \draw[thick] (1, 2) -- (2, 0); + \draw (0, 0) -- (2, 2); + \end{scope} + + \draw (1, 0) node{$\leadsto$}; + + % The seccond square + \begin{scope}[shift={(-1.5, -1)}] + \draw (0, 0) -- ++( 2, 0) + -- ++( 0, 2) + -- ++(-2, 0) + -- cycle; + + \draw[thick] (0, 0) -- (1, 2); + \draw[thick] (1, 0) -- (2, 2); + \draw (0, 2) -- (2, 0); + \end{scope} +\end{tikzpicture}
diff --git a/examples/images/rigid-motion-reflections.tikz /dev/null @@ -1,29 +0,0 @@ -% This picture represents the fact that reflections are rigid motions -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The first square - \begin{scope}[shift={(1.5, -1)}] - \draw (0, 0) -- ++( 2, 0) - -- ++( 0, 2) - -- ++(-2, 0) - -- cycle; - - \draw[thick] (0, 2) -- (1, 0); - \draw[thick] (1, 2) -- (2, 0); - \draw (0, 0) -- (2, 2); - \end{scope} - - \draw (1, 0) node{$\leadsto$}; - - % The seccond square - \begin{scope}[shift={(-1.5, -1)}] - \draw (0, 0) -- ++( 2, 0) - -- ++( 0, 2) - -- ++(-2, 0) - -- cycle; - - \draw[thick] (0, 0) -- (1, 2); - \draw[thick] (1, 0) -- (2, 2); - \draw (0, 2) -- (2, 0); - \end{scope} -\end{tikzpicture}
diff --git /dev/null b/examples/images/rigid-motion-rotation.tex @@ -0,0 +1,17 @@ +% This picture represents the fact that rotations are rigid motions +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=1.25] + % The axis + \draw (-1, 0) -- (1, 0) (0, -1) -- (0, 1); + + % The right square + \draw (-.5, .5) -- ++(1, 0) -- ++(0, -1) -- ++(-1, 0) -- cycle; + + % The rotated square + \begin{scope}[rotate=-45] + \draw (-.5, .5) -- ++(1, 0) -- ++(0, -1) -- ++(-1, 0) -- cycle; + \end{scope} + + % The rotation + \draw[->] (90:.75) ++(.25, .25) arc (90:0:.75); +\end{tikzpicture}
diff --git a/examples/images/rigid-motion-rotation.tikz /dev/null @@ -1,17 +0,0 @@ -% This picture represents the fact that rotations are rigid motions -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=1.25] - % The axis - \draw (-1, 0) -- (1, 0) (0, -1) -- (0, 1); - - % The right square - \draw (-.5, .5) -- ++(1, 0) -- ++(0, -1) -- ++(-1, 0) -- cycle; - - % The rotated square - \begin{scope}[rotate=-45] - \draw (-.5, .5) -- ++(1, 0) -- ++(0, -1) -- ++(-1, 0) -- cycle; - \end{scope} - - % The rotation - \draw[->] (90:.75) ++(.25, .25) arc (90:0:.75); -\end{tikzpicture}
diff --git /dev/null b/examples/images/smooth-function.tex @@ -0,0 +1,34 @@ +% This picture represents the definition of a smooth map between manifolds +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The manifolds + \begin{scope}[shift={(-2, 0)}] + \draw (-1.5, -0.5) to[relative, out=20, in=160] + +( 2, 0) to[relative, out=20, in=160] + +( 1, 1) to[relative, out=-20, in=-160] + +( -2, 0) to[relative, out=-20, in=-160] + cycle; + \draw (0.5, -0.5) node[right]{$M$}; + \end{scope} + \begin{scope}[shift={(2, 0)}] + \draw (-1.5, -0.5) to[relative, out=20, in=160] + +( 2, 0) to[relative, out=20, in=160] + +( 1, 1) to[relative, out=-20, in=-160] + +( -2, 0) to[relative, out=-20, in=-160] + cycle; + \draw (0.5, -0.5) node[right]{$N$}; + \end{scope} + + % The functions + \draw[->] (-1, 0.9) to[out=30, in=150] node[above]{$f$} (1, 0.9); + \draw[->] (-1, -1.7) to[out=30, in=150] + node[above]{$\psi \circ f \circ \varphi^{-1}$} (1, -1.7); + \draw[->] (-2, -0.7) -- node[left]{$\varphi$} +(0, -1); + \draw[->] ( 2, -0.7) -- node[left]{$\psi$} +(0, -1); + + % The open sets in euclidian space + \draw[dashed] (-2, -3) node{$\varphi(U)$} ellipse (1 and 0.5); + \draw[dashed] ( 2, -3) node{$\psi(V)$} ellipse (1 and 0.5); + \draw (-3.5, -4) node[left]{$\mathbb{R}^m$} rectangle +(3, 2); + \draw ( 0.5, -4) node[left]{$\mathbb{R}^n$} rectangle +(3, 2); +\end{tikzpicture}
diff --git a/examples/images/smooth-function.tikz /dev/null @@ -1,34 +0,0 @@ -% This picture represents the definition of a smooth map between manifolds -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The manifolds - \begin{scope}[shift={(-2, 0)}] - \draw (-1.5, -0.5) to[relative, out=20, in=160] - +( 2, 0) to[relative, out=20, in=160] - +( 1, 1) to[relative, out=-20, in=-160] - +( -2, 0) to[relative, out=-20, in=-160] - cycle; - \draw (0.5, -0.5) node[right]{$M$}; - \end{scope} - \begin{scope}[shift={(2, 0)}] - \draw (-1.5, -0.5) to[relative, out=20, in=160] - +( 2, 0) to[relative, out=20, in=160] - +( 1, 1) to[relative, out=-20, in=-160] - +( -2, 0) to[relative, out=-20, in=-160] - cycle; - \draw (0.5, -0.5) node[right]{$N$}; - \end{scope} - - % The functions - \draw[->] (-1, 0.9) to[out=30, in=150] node[above]{$f$} (1, 0.9); - \draw[->] (-1, -1.7) to[out=30, in=150] - node[above]{$\psi \circ f \circ \varphi^{-1}$} (1, -1.7); - \draw[->] (-2, -0.7) -- node[left]{$\varphi$} +(0, -1); - \draw[->] ( 2, -0.7) -- node[left]{$\psi$} +(0, -1); - - % The open sets in euclidian space - \draw[dashed] (-2, -3) node{$\varphi(U)$} ellipse (1 and 0.5); - \draw[dashed] ( 2, -3) node{$\psi(V)$} ellipse (1 and 0.5); - \draw (-3.5, -4) node[left]{$\mathbb{R}^m$} rectangle +(3, 2); - \draw ( 0.5, -4) node[left]{$\mathbb{R}^n$} rectangle +(3, 2); -\end{tikzpicture}
diff --git /dev/null b/examples/images/smooth-manifold.tex @@ -0,0 +1,52 @@ +% This picture represents the definition of a smooth manifold +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The manifold + \begin{scope}[shift={(-0.5, 0)}] + % The frontire + \draw (-4, 2) to[relative, out=20, in=160] + ( 2, 0) to[relative, out=20, in=160] + ( 4, 3) to[relative, out=-20, in=-160] + cycle; + \draw (-4, 2) node[below]{$M$}; + + % The open sets of the manifold and their intersection + \begin{scope}[shift={(1, 2.2)}] + \draw (-0.5, 0) ellipse (0.7 and 0.5); + \draw (-1.2, 0) node[right]{$U$}; + \draw (0.5, 0) ellipse (0.7 and 0.5); + \draw (1.2, 0) node[left]{$V$}; + \clip (-0.5, 0) ellipse (0.7 and 0.5); + \draw[pattern=north west lines] (0.5, 0) ellipse (0.7 and 0.5); + \end{scope} + \end{scope} + + % The cards + \draw[->] (-0.7, 1.7) to[relative, out=-20, in=-160] + node[left]{$\varphi_U$} (-2, -0.7); + \draw[->] (1.7, 1.7) to[relative, out=20, in=160] + node[right]{$\varphi_V$} (2, -0.7); + + % The corresponding open sets in euclidian space + \begin{scope}[shift={(0, -1.5)}] + % The open sets + \draw (-2, 0) ellipse (1 and 0.6) (2, 0) ellipse (1 and 0.6); + \draw (-3, 0.5) node[above]{$\varphi_U(U)$}; + \draw (3, 0.5) node[above]{$\varphi_V(V)$}; + + % The intersections + \begin{scope} + \clip (-2, 0) ellipse (1 and 0.6); + \draw[pattern=north west lines] (-0.5, 0) ellipse (1 and 0.6); + \end{scope} + \begin{scope} + \clip (2, 0) ellipse (1 and 0.6); + \draw[pattern=north west lines] (0.5, 0) ellipse (1 and 0.6); + \end{scope} + + % The diffeomorphism + \draw[->] (-0.9, 0) -- + node[above]{$\varphi_V \circ \varphi_U^{-1}$} (0.9, 0); + \end{scope} +\end{tikzpicture} +
diff --git a/examples/images/smooth-manifold.tikz /dev/null @@ -1,52 +0,0 @@ -% This picture represents the definition of a smooth manifold -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The manifold - \begin{scope}[shift={(-0.5, 0)}] - % The frontire - \draw (-4, 2) to[relative, out=20, in=160] - ( 2, 0) to[relative, out=20, in=160] - ( 4, 3) to[relative, out=-20, in=-160] - cycle; - \draw (-4, 2) node[below]{$M$}; - - % The open sets of the manifold and their intersection - \begin{scope}[shift={(1, 2.2)}] - \draw (-0.5, 0) ellipse (0.7 and 0.5); - \draw (-1.2, 0) node[right]{$U$}; - \draw (0.5, 0) ellipse (0.7 and 0.5); - \draw (1.2, 0) node[left]{$V$}; - \clip (-0.5, 0) ellipse (0.7 and 0.5); - \draw[pattern=north west lines] (0.5, 0) ellipse (0.7 and 0.5); - \end{scope} - \end{scope} - - % The cards - \draw[->] (-0.7, 1.7) to[relative, out=-20, in=-160] - node[left]{$\varphi_U$} (-2, -0.7); - \draw[->] (1.7, 1.7) to[relative, out=20, in=160] - node[right]{$\varphi_V$} (2, -0.7); - - % The corresponding open sets in euclidian space - \begin{scope}[shift={(0, -1.5)}] - % The open sets - \draw (-2, 0) ellipse (1 and 0.6) (2, 0) ellipse (1 and 0.6); - \draw (-3, 0.5) node[above]{$\varphi_U(U)$}; - \draw (3, 0.5) node[above]{$\varphi_V(V)$}; - - % The intersections - \begin{scope} - \clip (-2, 0) ellipse (1 and 0.6); - \draw[pattern=north west lines] (-0.5, 0) ellipse (1 and 0.6); - \end{scope} - \begin{scope} - \clip (2, 0) ellipse (1 and 0.6); - \draw[pattern=north west lines] (0.5, 0) ellipse (1 and 0.6); - \end{scope} - - % The diffeomorphism - \draw[->] (-0.9, 0) -- - node[above]{$\varphi_V \circ \varphi_U^{-1}$} (0.9, 0); - \end{scope} -\end{tikzpicture} -
diff --git /dev/null b/examples/images/sphere-quotient.tex @@ -0,0 +1,30 @@ +% This picture represents the isomorphism between the n-dimensional sphere and +% the quotient of the (n + 1)-dimensional simple orthogonal group by the +% n-dimensional simple orthogonal group +% Copyright Pablo (C) 2023 +\begin{tikzpicture}[scale=0.5] + % The sphere + \begin{scope} + \clip (-3, -3) rectangle (3, 2.625); + \draw (0, 0) circle (3); + \end{scope} + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -3); + \draw ellipse (3 and 1); + \end{scope} + + % Greenwhich + \begin{scope} + \clip (-3, -3) rectangle (0, 2.625); + \draw ellipse (1 and 3); + \end{scope} + + \draw (-3, 2.625) -- ( 1.5, 2.625) + -- ( 3, 3.375) node[right]{$T_p \mathbb{S}^n$} + -- (-1.5, 3.375) + -- cycle; + \filldraw[black] (0, 3) circle (2pt) node[right]{$p$}; + \draw (0, 3.375) node[above]{$\operatorname{SO}_n$}; +\end{tikzpicture}
diff --git a/examples/images/sphere-quotient.tikz /dev/null @@ -1,30 +0,0 @@ -% This picture represents the isomorphism between the n-dimensional sphere and -% the quotient of the (n + 1)-dimensional simple orthogonal group by the -% n-dimensional simple orthogonal group -% Copyright Pablo (C) 2023 -\begin{tikzpicture}[scale=0.5] - % The sphere - \begin{scope} - \clip (-3, -3) rectangle (3, 2.625); - \draw (0, 0) circle (3); - \end{scope} - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % Greenwhich - \begin{scope} - \clip (-3, -3) rectangle (0, 2.625); - \draw ellipse (1 and 3); - \end{scope} - - \draw (-3, 2.625) -- ( 1.5, 2.625) - -- ( 3, 3.375) node[right]{$T_p \mathbb{S}^n$} - -- (-1.5, 3.375) - -- cycle; - \filldraw[black] (0, 3) circle (2pt) node[right]{$p$}; - \draw (0, 3.375) node[above]{$\operatorname{SO}_n$}; -\end{tikzpicture}
diff --git /dev/null b/examples/images/sphere.tex @@ -0,0 +1,31 @@ +% This picture represents a three-dimentional sphere +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.4] + % The cirference + \draw (0, 0) circle (3); + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -3); + \draw ellipse (3 and 1); + \end{scope} + + % The equator (on the other side of the sphere) + \begin{scope} + \clip (-3, 0) rectangle (3, 3); + \draw[dotted] ellipse (3 and 1); + \end{scope} + + % Greenwhich + \begin{scope} + \clip (-3, -3) rectangle (0, 3); + \draw ellipse (1 and 3); + \end{scope} + + % Greenwhich (on the other side of the sphere) + \begin{scope} + \clip (3, -3) rectangle (0, 3); + \draw[dotted] ellipse (1 and 3); + \end{scope} +\end{tikzpicture} +
diff --git a/examples/images/sphere.tikz /dev/null @@ -1,31 +0,0 @@ -% This picture represents a three-dimentional sphere -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.4] - % The cirference - \draw (0, 0) circle (3); - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % The equator (on the other side of the sphere) - \begin{scope} - \clip (-3, 0) rectangle (3, 3); - \draw[dotted] ellipse (3 and 1); - \end{scope} - - % Greenwhich - \begin{scope} - \clip (-3, -3) rectangle (0, 3); - \draw ellipse (1 and 3); - \end{scope} - - % Greenwhich (on the other side of the sphere) - \begin{scope} - \clip (3, -3) rectangle (0, 3); - \draw[dotted] ellipse (1 and 3); - \end{scope} -\end{tikzpicture} -
diff --git /dev/null b/examples/images/square-to-circle-projection.tex @@ -0,0 +1,15 @@ +\begin{tikzpicture} + \draw circle (3); + \filldraw circle (1pt); + \draw ({3 * cos(45)}, {3 * sin(45)}) + -- ({-3 * cos(45)}, {3 * sin(45)}) + -- ({-3 * cos(45)}, {-3 * sin(45)}) + -- ({3 * cos(45)}, {-3 * sin(45)}) + -- cycle; + + \coordinate (a) at ({3 * sqrt(6)/6}, {3 * sin(45)}); + \coordinate (b) at ({3 * cos(45 + 15)}, {3 * sin(45 + 15)}); + + \draw[thick, dotted] (0, 0) -- (b); + \filldraw (a) circle (1pt) (b) circle (1pt); +\end{tikzpicture}+ \ No newline at end of file
diff --git a/examples/images/square-to-circle-projection.tikz /dev/null @@ -1,15 +0,0 @@ -\begin{tikzpicture} - \draw circle (3); - \filldraw circle (1pt); - \draw ({3 * cos(45)}, {3 * sin(45)}) - -- ({-3 * cos(45)}, {3 * sin(45)}) - -- ({-3 * cos(45)}, {-3 * sin(45)}) - -- ({3 * cos(45)}, {-3 * sin(45)}) - -- cycle; - - \coordinate (a) at ({3 * sqrt(6)/6}, {3 * sin(45)}); - \coordinate (b) at ({3 * cos(45 + 15)}, {3 * sin(45 + 15)}); - - \draw[thick, dotted] (0, 0) -- (b); - \filldraw (a) circle (1pt) (b) circle (1pt); -\end{tikzpicture}- \ No newline at end of file
diff --git /dev/null b/examples/images/standard-sets-venn.tex @@ -0,0 +1,24 @@ +% This diagram represents the relationship between standard number sets +% Copyright Pablo (C) 2021 +\begin{tikzpicture} + % The complex numbers + \draw (-3,-2.5) rectangle (3,2.5) + (3,-2.5) node[right]{$\mathbb{C}$}; + + % The real numbers + \draw (0,0) circle (2) + (2, 0) node[left]{$\mathbb{R}$}; + + % The rational numbers + \draw (-0.5,0) circle (1.5) + (1,0) node[left]{$\mathbb{Q}$}; + + % The integers + \draw (-1,0) circle (1) + (0,0) node[left]{$\mathbb{Z}$}; + + % The natural numbers + \draw (-1.5,0) circle (0.5) + (-1.5,0) node{$\mathbb{N}$}; +\end{tikzpicture} +
diff --git a/examples/images/standard-sets-venn.tikz /dev/null @@ -1,24 +0,0 @@ -% This diagram represents the relationship between standard number sets -% Copyright Pablo (C) 2021 -\begin{tikzpicture} - % The complex numbers - \draw (-3,-2.5) rectangle (3,2.5) - (3,-2.5) node[right]{$\mathbb{C}$}; - - % The real numbers - \draw (0,0) circle (2) - (2, 0) node[left]{$\mathbb{R}$}; - - % The rational numbers - \draw (-0.5,0) circle (1.5) - (1,0) node[left]{$\mathbb{Q}$}; - - % The integers - \draw (-1,0) circle (1) - (0,0) node[left]{$\mathbb{Z}$}; - - % The natural numbers - \draw (-1.5,0) circle (0.5) - (-1.5,0) node{$\mathbb{N}$}; -\end{tikzpicture} -
diff --git /dev/null b/examples/images/stereographic-projection.tex @@ -0,0 +1,35 @@ +% This picture represents the stereographic projection +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.4] + % The outline of the sphere + \draw (0, 0) circle (3); + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -3); + \draw ellipse (3 and 1); + \end{scope} + + % The equator (on the other side of the sphere) + \begin{scope} + \clip (-3, 0) rectangle (3, 3); + \draw[dotted] ellipse (3 and 1); + \end{scope} + + % The plane + \draw (-9, -4) -- (-5, 0) + -- (-3, 0) + ( 3, 0) -- ( 9, 0) + -- ( 5, -4) + -- (-9, -4); + + % A line trought the sphere and the plane + \coordinate (N) at (0, 3); + \coordinate (a) at (2, -1); + \coordinate (b) at (3, -3); + \draw[dotted] (N) -- (a); + \draw (a) -- (b); + + % The dots + \filldraw (N) circle (2pt) (a) circle (2pt) (b) circle (2pt); +\end{tikzpicture}
diff --git a/examples/images/stereographic-projection.tikz /dev/null @@ -1,35 +0,0 @@ -% This picture represents the stereographic projection -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.4] - % The outline of the sphere - \draw (0, 0) circle (3); - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -3); - \draw ellipse (3 and 1); - \end{scope} - - % The equator (on the other side of the sphere) - \begin{scope} - \clip (-3, 0) rectangle (3, 3); - \draw[dotted] ellipse (3 and 1); - \end{scope} - - % The plane - \draw (-9, -4) -- (-5, 0) - -- (-3, 0) - ( 3, 0) -- ( 9, 0) - -- ( 5, -4) - -- (-9, -4); - - % A line trought the sphere and the plane - \coordinate (N) at (0, 3); - \coordinate (a) at (2, -1); - \coordinate (b) at (3, -3); - \draw[dotted] (N) -- (a); - \draw (a) -- (b); - - % The dots - \filldraw (N) circle (2pt) (a) circle (2pt) (b) circle (2pt); -\end{tikzpicture}
diff --git /dev/null b/examples/images/tangent-space.tex @@ -0,0 +1,34 @@ +% This picture represents the tangent space at a point in a smooth manifold +% Copyright Mezzo (C) 2021 +\begin{tikzpicture}[x=0.75pt, y=0.75pt, yscale=-1] + height of 300 + + % The manifold + \draw (112.04,66.62) node[below right, font=\scriptsize]{$M$}; + \draw (100,108) .. controls (140,78) and (188,143) + .. (196,182) ; + \draw (196.2,181.8) .. controls (211.8,159.6) and (265.71,101.03) + .. (318.8,111.8) ; + \draw (318.8,111.8) .. controls (323.67,112.42) and (330.33,115.42) + .. (335,118) ; + \draw[dotted] (219.48,53.8) .. controls (230.71,56.06) and (244.01,58.07) + .. (260.04,63.39) ; + \draw (260.04,63.39) .. controls (288.81,75.27) and (332.14,114.93) + .. (335,118) ; + \draw (100,108) .. controls (113.56,84.56) and (160.04,48.06) + .. (219.48,53.8) ; + + % A point p in the manifold + \filldraw (232.9,84.2) circle (1pt) + node[below right, font=\scriptsize]{$p$}; + + % The tangent space at p + \draw (238.68,46.2) -- (294.01,93.72) + -- (224.01,122.72) + -- (168.68,75.2) + -- cycle ; + \draw (173.51,76.9) node[below right, + font=\scriptsize, + rotate=-337.86, + xslant=-0.54]{$T_{p} M$}; +\end{tikzpicture}
diff --git a/examples/images/tangent-space.tikz /dev/null @@ -1,34 +0,0 @@ -% This picture represents the tangent space at a point in a smooth manifold -% Copyright Mezzo (C) 2021 -\begin{tikzpicture}[x=0.75pt, y=0.75pt, yscale=-1] - height of 300 - - % The manifold - \draw (112.04,66.62) node[below right, font=\scriptsize]{$M$}; - \draw (100,108) .. controls (140,78) and (188,143) - .. (196,182) ; - \draw (196.2,181.8) .. controls (211.8,159.6) and (265.71,101.03) - .. (318.8,111.8) ; - \draw (318.8,111.8) .. controls (323.67,112.42) and (330.33,115.42) - .. (335,118) ; - \draw[dotted] (219.48,53.8) .. controls (230.71,56.06) and (244.01,58.07) - .. (260.04,63.39) ; - \draw (260.04,63.39) .. controls (288.81,75.27) and (332.14,114.93) - .. (335,118) ; - \draw (100,108) .. controls (113.56,84.56) and (160.04,48.06) - .. (219.48,53.8) ; - - % A point p in the manifold - \filldraw (232.9,84.2) circle (1pt) - node[below right, font=\scriptsize]{$p$}; - - % The tangent space at p - \draw (238.68,46.2) -- (294.01,93.72) - -- (224.01,122.72) - -- (168.68,75.2) - -- cycle ; - \draw (173.51,76.9) node[below right, - font=\scriptsize, - rotate=-337.86, - xslant=-0.54]{$T_{p} M$}; -\end{tikzpicture}
diff --git /dev/null b/examples/images/topology-mug-donut.tex @@ -0,0 +1,214 @@ +% This picture represents a mug continuously morphing into a donut +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[y=0.70pt, x=0.70pt, yscale=-1] + \draw[cm={{0.1, 0.0, 0.0, -0.1, (0.0, 80.0)}}, line cap=round] + (4.0234, 726.0938) + .. controls (0.8203, 650.0781) and (29.3750, 515.7031) + .. (35.7812, 430.1172) + .. controls (42.1484, 344.5312) and (56.4844, 235.4297) + .. (64.5703, 155.7812) + .. controls (72.6562, 76.1328) and (179.2188, 13.2812) + .. (259.8438, 7.8125) + .. controls (331.7188, 3.6328) and (435.1172, -1.4453) + .. (485.8594, 17.9297) + .. controls (512.7344, 28.7500) and (649.2188, 76.9531) + .. (649.5703, 178.2422) + .. controls (648.0859, 211.5625) and (647.8906, 214.7266) + .. (646.6797, 244.6094) + .. controls (645.5078, 274.4531) and (662.3438, 264.4922) + .. (678.4766, 265.1172) + .. controls (694.5703, 265.7422) and (746.0547, 283.5156) + .. 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(670.8594, 627.2656); -\end{tikzpicture} -
diff --git /dev/null b/examples/images/unit-circle-covering.tex @@ -0,0 +1,43 @@ +% This picture represents the universal convering of the unit circle +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.75] +\begin{scope}[shift={(-3.5, -2.75)}] + \begin{axis}[ + view={0}{60}, + axis lines=none, + ymin=-2, + ymax=.5, + xmin=-1, + xmax=1 + ] + \addplot3[ + very thick, + domain=-1.25*pi:6.25*pi, + samples = 200, + samples y=0 + ] + ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x}); + + \addplot3[ + very thick, + dotted, + domain=-1.5*pi:-1.25*pi, + samples = 200, + samples y=0 + ] + ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x}); + + \addplot3[ + very thick, + dotted, + domain=6.25*pi:6.5*pi, + samples = 200, + samples y=0 + ] + ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x}); + \end{axis} +\end{scope} + +\draw[thick, ->] (0, 0) -- node[right]{$\pi$} (0, -1); +\draw[thick] (0, -1.5) ellipse (0.9 and 0.25); +\end{tikzpicture}
diff --git a/examples/images/unit-circle-covering.tikz /dev/null @@ -1,43 +0,0 @@ -% This picture represents the universal convering of the unit circle -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.75] -\begin{scope}[shift={(-3.5, -2.75)}] - \begin{axis}[ - view={0}{60}, - axis lines=none, - ymin=-2, - ymax=.5, - xmin=-1, - xmax=1 - ] - \addplot3[ - very thick, - domain=-1.25*pi:6.25*pi, - samples = 200, - samples y=0 - ] - ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x}); - - \addplot3[ - very thick, - dotted, - domain=-1.5*pi:-1.25*pi, - samples = 200, - samples y=0 - ] - ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x}); - - \addplot3[ - very thick, - dotted, - domain=6.25*pi:6.5*pi, - samples = 200, - samples y=0 - ] - ({0.25 * sin(deg(-x))}, {0.17 * cos(deg(-x))}, {-x}); - \end{axis} -\end{scope} - -\draw[thick, ->] (0, 0) -- node[right]{$\pi$} (0, -1); -\draw[thick] (0, -1.5) ellipse (0.9 and 0.25); -\end{tikzpicture}
diff --git /dev/null b/examples/images/unit-circle.tex @@ -0,0 +1,10 @@ +% This picture represents the unit complex circle +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=1.2] + \node[above] (O) at (0,1) {$i$}; + \node[right] (O) at (1,0) {$1$}; + \filldraw[black] (0, 1) circle (1pt); + \filldraw[black] (1, 0) circle (1pt); + \draw (0, 0) circle (1); +\end{tikzpicture} +
diff --git a/examples/images/unit-circle.tikz /dev/null @@ -1,10 +0,0 @@ -% This picture represents the unit complex circle -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=1.2] - \node[above] (O) at (0,1) {$i$}; - \node[right] (O) at (1,0) {$1$}; - \filldraw[black] (0, 1) circle (1pt); - \filldraw[black] (1, 0) circle (1pt); - \draw (0, 0) circle (1); -\end{tikzpicture} -
diff --git /dev/null b/examples/images/upper-central-projection.tex @@ -0,0 +1,44 @@ +% A graphical depiction of the central projection between the upper +% semi-sphere and the Euclidean plane: we map each point in the upper half of +% the sphere to the projection of this point in the tangent plane at the north +% pole by drawing a line between this point and the center of the sphere and +% then taking the intersection of this line with the plane. +% Copyright Pablo (C) 2021 +\begin{tikzpicture}[scale=0.8] + % The outline of the semi-sphere + \begin{scope} + \clip (-3, 0) rectangle (3, 3); + \draw (0, 0) circle (3); + \end{scope} + + % The equator + \begin{scope} + \clip (-3, 0) rectangle (3, -1); + \draw ellipse (3 and 1); + \end{scope} + + % The equator (on the other side of the sphere) + \draw[dotted] ellipse (3 and 1); + + % The plane + \draw[dotted] (-4.5, 1.5) -- + ( 1.5, 1.5) -- + ( 4.5, 4.5) -- + (-1.5, 4.5) -- cycle; + + % The north pole + \filldraw (0, 3) circle (2pt); + + % The center of the sphere + \filldraw (0, 0) circle (2pt); + + % A line trhough the center of the sphere + \draw (0, 0) -- (1.8, 3); + + % The intersection of the line with the plane + \filldraw (1.8, 3) circle (2pt); + + % The intersection of the line and the sphere + \filldraw (1.56, 2.57) circle (2pt); +\end{tikzpicture} +
diff --git a/examples/images/upper-central-projection.tikz /dev/null @@ -1,44 +0,0 @@ -% A graphical depiction of the central projection between the upper -% semi-sphere and the Euclidean plane: we map each point in the upper half of -% the sphere to the projection of this point in the tangent plane at the north -% pole by drawing a line between this point and the center of the sphere and -% then taking the intersection of this line with the plane. -% Copyright Pablo (C) 2021 -\begin{tikzpicture}[scale=0.8] - % The outline of the semi-sphere - \begin{scope} - \clip (-3, 0) rectangle (3, 3); - \draw (0, 0) circle (3); - \end{scope} - - % The equator - \begin{scope} - \clip (-3, 0) rectangle (3, -1); - \draw ellipse (3 and 1); - \end{scope} - - % The equator (on the other side of the sphere) - \draw[dotted] ellipse (3 and 1); - - % The plane - \draw[dotted] (-4.5, 1.5) -- - ( 1.5, 1.5) -- - ( 4.5, 4.5) -- - (-1.5, 4.5) -- cycle; - - % The north pole - \filldraw (0, 3) circle (2pt); - - % The center of the sphere - \filldraw (0, 0) circle (2pt); - - % A line trhough the center of the sphere - \draw (0, 0) -- (1.8, 3); - - % The intersection of the line with the plane - \filldraw (1.8, 3) circle (2pt); - - % The intersection of the line and the sphere - \filldraw (1.56, 2.57) circle (2pt); -\end{tikzpicture} -
diff --git a/src/gallery_entry.rs b/src/gallery_entry.rs @@ -64,7 +64,7 @@ pub struct GalleryEntry { #[derive(Debug, Clone, Copy, PartialEq, Eq)] pub enum FileFormat { - TikZ, + TeX, Svg, Png, Jpeg, @@ -234,8 +234,8 @@ impl<'de> Deserialize<'de> for GalleryEntry { Unexpected::Str(&path_str), &"valid file path (couldn't guess file format)", )); - }, - Some("tikz") => FileFormat::TikZ, + } + Some("tex") => FileFormat::TeX, Some("svg") => FileFormat::Svg, Some("png") => FileFormat::Png, Some("jpeg" | "jpg") => FileFormat::Jpeg,
diff --git a/src/main.rs b/src/main.rs @@ -495,7 +495,7 @@ fn render_thumbnail(pic: GalleryEntry) -> bool { } match pic.file_format { - FileFormat::TikZ => { + FileFormat::TeX => { // TODO: Remove the dependancie on tikztosvg to optimize IO? // currently tikztosvg creates new directories in tmp for each // single file. Maybe we could optimize IO by reusing the same dir @@ -632,7 +632,7 @@ fn thumb_path(pic: &GalleryEntry) -> PathBuf { result.push(THUMBS_PATH); match pic.file_format { - FileFormat::TikZ => { + FileFormat::TeX => { result.push(pic.file_name.clone() + ".svg"); } FileFormat::Svg => { @@ -651,7 +651,7 @@ impl<'a> Display for ThumbPath<'a> { write!(f, "/{THUMBS_PATH}/{name}", name = Escaped(&self.0.file_name))?; match self.0.file_format { - FileFormat::TikZ => write!(f, ".svg")?, + FileFormat::TeX => write!(f, ".svg")?, FileFormat::Svg => {} FileFormat::Jpeg | FileFormat::Png => write!(f, ".webp")?, }