- Commit
- 4857371dbf5b38522b422ef5fa813329768b18cd
- Parent
- 767423e07eeb26015ee810fd2b085f0532203db6
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Fixed some of the TikZ drawings
latex-setup
My personal LaTeX setup 🦁️⚙️
Diffstat
26 files changed, 88 insertions, 1415 deletions
diff --git a/images/26-nodes-diagram.tikz b/images/26-nodes-diagram.tikz @@ -1,4 +1,5 @@ % 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}
diff --git a/images/complex-surreal-venn.tikz b/images/complex-surreal-venn.tikz @@ -1,15 +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{\(\RR\)} - (0,0) circle (1.5); + \draw (0.75, 0) node{$\mathbb{R}$} + ( 0, 0) circle (1.5); % The complex numbers - \draw (-1.5,0) node[left]{\(\CC\)} - (1.5,0) circle (1.5); + \draw (-1.5, 0) node[left]{$\mathbb{C}$} + ( 1.5, 0) circle (1.5); % The surreal numbers - \draw (3,0) node[right]{\No}; + \draw (3,0) node[right]{$\mathbf{No}$}; \end{tikzpicture}
diff --git a/images/coxerter-group-reflections.tikz b/images/coxerter-group-reflections.tikz @@ -1,6 +1,7 @@ % 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]{$a$};
diff --git a/images/dihedral-representation-is-irreducible.tikz b/images/dihedral-representation-is-irreducible.tikz @@ -1,5 +1,6 @@ % 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]{$x$};
diff --git a/images/dihedral-representation.tikz b/images/dihedral-representation.tikz @@ -1,4 +1,5 @@ % 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]{$x$};
diff --git a/images/euclidian-plane.tikz b/images/euclidian-plane.tikz @@ -1,4 +1,5 @@ % This picture represents the cartesian plain +% Copyright Pablo (C) 2021 \begin{tikzpicture} \draw (0, 0) node[left]{$\mathbb{R}^2$} -- (2, 0) --
diff --git a/images/galois-lattice-antisomorphism.tikz b/images/galois-lattice-antisomorphism.tikz @@ -1,18 +1,18 @@ % 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. -% -% NOTE: This diagram requires the xalgebra package (for \Gal and \mfrac) +% Copyright Pablo (C) 2021 \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 \& \& \{e\} \& \\ - \& 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 \& \& \Gal(\mfrac{K}{k}) \& \\ - }; + { + \& K \& \& \{e\} \& \\ + \& 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}(\mathlarger{\sfrac{K}{k}}) \& \\ + }; % The relations of both lattices \draw (m-1-2) -- (m-2-2)
diff --git a/images/geodesic.tikz b/images/geodesic.tikz @@ -1,4 +1,5 @@ % 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);
diff --git a/images/hyperbolic-plane-disc.tikz b/images/hyperbolic-plane-disc.tikz @@ -1,4 +1,5 @@ % This picture represents the Poincaré disc model of the hyperbolic plane +% Copyright Pablo (C) 2021 \begin{tikzpicture} % The disk \draw (0, 0) circle (1);
diff --git a/images/k4.tikz b/images/k4.tikz @@ -1,4 +1,5 @@ % 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);
diff --git a/images/natural-number-line.tikz b/images/natural-number-line.tikz @@ -1,4 +1,5 @@ % This picture represents the natural number line +% Copyright Pablo (C) 2021 \begin{tikzpicture} % The line \draw[-latex] (0,0) -- (6, 0) node[right]{$\mathbb{N}$};
diff --git a/images/ordinal-number-line.tikz b/images/ordinal-number-line.tikz @@ -1,4 +1,5 @@ % This picture represents the ordinal number line +% Copyright Pablo (C) 2021 \begin{tikzpicture} % The line \draw[-latex] (0,0) -- (6.5,0) node[right]{$\mathbf{Ord}$};
diff --git a/images/projective-system-universal-property.tikz b/images/projective-system-universal-property.tikz @@ -3,6 +3,7 @@ % functor between I^op and the category of obejcts of the projective system % given my the projective system itself (for each index i it yields X_i and for % each inequality i <= j it yeilds \varphi_{i, j} +% Copyright Pablo (C) 2021 \begin{tikzpicture}[ampersand replacement=\&] % The objects \matrix(m)[matrix of math nodes,row sep=3em,column sep=3em,minimum width=2em]
diff --git a/images/projective-system.tikz b/images/projective-system.tikz @@ -1,5 +1,6 @@ % This picture represents the behaviour of the morphisms of a projective system % (X_i, \phi_{i, j} +% Copyright Pablo (C) 2021 \begin{tikzpicture}[ampersand replacement=\&] % The objects \matrix(m)[matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em]
diff --git a/images/quaternion-rotation.tikz b/images/quaternion-rotation.tikz @@ -1,5 +1,6 @@ % This drawing represents the correspondance between conjugation by unitary % quaternions and rotations in the 3-dimensional euclidian space +% Copyright Pablo (C) 2021 \begin{tikzpicture} % The rotation axis \begin{scope}[rotate=-60]
diff --git a/images/real-number-line.tikz b/images/real-number-line.tikz @@ -1,4 +1,5 @@ % This picture represents the real number line +% Copyright Pablo (C) 2021 \begin{tikzpicture} % The line \draw[latex-latex] (-3,0) -- (3,0) node[right]{$\mathbb{R}$};
diff --git a/images/real-ordinal-surreal-venn.tikz b/images/real-ordinal-surreal-venn.tikz @@ -1,5 +1,6 @@ % 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)
diff --git a/images/riemannian-metric.tikz b/images/riemannian-metric.tikz @@ -1,5 +1,6 @@ % 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);
diff --git a/images/smooth-function.tikz b/images/smooth-function.tikz @@ -1,12 +1,21 @@ % This picture represents the definition of a smooth map between manifolds +% Copyright Pablo (C) 2021 \begin{tikzpicture} % The manifolds \begin{scope}[shift={(-2, 0)}] - \path pic {manifold}; + \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)}] - \path pic {manifold}; + \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} @@ -18,8 +27,8 @@ \draw[->] ( 2, -0.7) -- node[left]{$\psi$} +(0, -1); % The open sets in euclidian space - \draw[dash dot] (-2, -3) node{$\varphi(U)$} ellipse (1 and 0.5); - \draw[dash dot] ( 2, -3) node{$\psi(V)$} ellipse (1 and 0.5); + \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/images/smooth-manifold.tikz b/images/smooth-manifold.tikz @@ -1,9 +1,13 @@ % 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 - \path pic {big-manifold}; + \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
diff --git a/images/sphere-quotient.tikz b/images/sphere-quotient.tikz @@ -1,39 +1,40 @@ % 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) 2021 \begin{tikzpicture}[scale=0.5] - % 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} - - % 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} - - \draw (-3, 2.625) -- (1.5, 2.625) - -- (3, 3.375) - node[right]{$T_p S^n$} - -- (-1.5, 3.375) - -- cycle; - \filldraw[black] (0, 3) circle (2pt) node[right]{$p$}; - \draw (0, 3.375) node[above]{$\SO_n(\RR)$}; + % 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} + + % 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} + + \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]{$\operatorname{SO}_n(\mathbb{R})$}; \end{tikzpicture}
diff --git a/images/sphere.tikz b/images/sphere.tikz @@ -1,4 +1,5 @@ % This picture represents a three-dimentional sphere +% Copyright Pablo (C) 2021 \begin{tikzpicture}[scale=0.4] % The cirference \draw (0, 0) circle (3);
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diff --git a/images/standard-sets-venn.tikz b/images/standard-sets-venn.tikz @@ -1,4 +1,5 @@ % 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)
diff --git a/images/unit-circle-covering.tikz b/images/unit-circle-covering.tikz @@ -1,4 +1,5 @@ % This picture represents the universal convering of the unit circle +% Copyright Pablo (C) 2021 \begin{tikzpicture}[scale=0.75] \begin{scope}[shift={(-3.5, -1)}] \begin{axis}[view={0}{60}, axis lines=none, ymin=-2, ymax=5, xmin=-2, xmax=2]
diff --git a/images/unit-circle.tikz b/images/unit-circle.tikz @@ -1,4 +1,5 @@ % 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) {$1$};