Commit ffc80e37 authored by Harry Fuchs's avatar Harry Fuchs

introduce gitlab-ci

parent fdb1bfa0
Pipeline #2149 passed with stage
in 1 minute and 10 seconds
image: registry.dune-project.org/docker/ci/debian:10
jobtesting:
script:
- "./do-ci-stuff.sh"
artifacts:
paths:
- "diffgeoII/output"
expire_in: 1 week
cp edit-this-file.tex tmp.tex
python3 preprocessor.py
pandoc -f org -t latex tmp.tex -s -o gdim.tex --metadata-file meta.yaml --template="latex.template"
inotifywait -e close_write,moved_to,create -m . |
while read -r directory events filename; do
if [ "$filename" = "edit-this-file.tex" ]; then
cp edit-this-file.tex tmp.tex
python3 preprocessor.py
pandoc -f org -t latex tmp.tex -s -o gdim.tex --metadata-file meta.yaml --template="latex.template"
clear && clear
echo "start pdflatex"
clear && clear
echo "start pdflatex"
pdflatex -interaction=nonstopmode gdim.tex
#pdflatex gdim.tex
if [ "$1" == "fail-on-error" ]; then
latexoption=""
mkdir output
cp gdim.tex ./output/dgeo-alekseev.tex
echo "STOP"
#TODO make pdflatex work
exit 0
else
latexoption="-interaction=nonstopmode"
fi
#TODO rename
mv gdim.pdf dgeo-alekseev.pdf
echo "wait for next change..."
fi
done
pdflatex $latexoption gdim.tex
if [ $$? = 0 ] ; then \
pdflatex $$NAME ; \
pdflatex $$NAME ; \
else \
\echo "Compilation failed" ; \
exit 20
fi
#pdflatex gdim.tex
#TODO rename
mv gdim.pdf dgeo-alekseev.pdf
mkdir output
cp dgeo-alekseev.pdf ./output/
......@@ -521,7 +521,8 @@ $$
\\ \eins_{(\lambda v, w)} - \lambda\eins_{(v,w)}
\\ \eins_{(v, \lambda w)} - \lambda\eins_{(v,w)}
\end{subarray}
\mathrel{\middle|}
\mathrel{%TODO\middle
|}
\begin{subarray}{l}
v_1, v_2, v\in V,
\\w_1, w_2, w\in W,
......@@ -529,7 +530,8 @@ $$
\end{subarray}
\right\}\right\rangle
}_{:=\langle\ldots\rangle}
\\&=& \left\{ f + \langle\ldots\rangle \mathrel{\middle|} f \in \mathcal F_{\mathbb R} (V\times W)\right\}
\\&=& \left\{ f + \langle\ldots\rangle \mathrel{%TODO \middle
|} f \in \mathcal F_{\mathbb R} (V\times W)\right\}
$$
$$
......@@ -574,7 +576,8 @@ Entsprechend ist
$$
V\otimes W
§ &=&\{f+\langle\ldots \rangle \mathrel | f \in \mathcal F(V\times W) \}
§ \\&=& \left\{ \sum_{i=1}^n \lambda_i\cdot\eins{(v,w)_i} + \langle\ldots\rangle\mathrel{\middle |} (v,w)_i\in V\times W, \lambda_i\in\mathbb R, i\in \mathbb \{1,\ldots,n\}, n\in \mathbb N \right\}
§ \\&=& \left\{ \sum_{i=1}^n \lambda_i\cdot\eins{(v,w)_i} + \langle\ldots\rangle\mathrel{%TODO\middle
|} (v,w)_i\in V\times W, \lambda_i\in\mathbb R, i\in \mathbb \{1,\ldots,n\}, n\in \mathbb N \right\}
§ \\&=& \operatorname{span}\{ \eins_{(v,w)} + \langle\ldots\rangle\mathrel | (v,w)\in V\times W \}
% \\&=& \operatorname{span}\{ [\eins_{(v,w)}] \mathrel | v\in V, w\in W \}
§ \\
......@@ -1027,7 +1030,7 @@ $$
\alpha_{12}e_1\wedge e_2 + \alpha_{13}e_1\wedge e_j + \alpha_{14} e_1\wedge e_4 + \ldots = 0
$$
$\rightarrow \alpha_{13} e_1e_3\wedgee_2\wedgee_4 = 0 = -\alpha_{13}(e_1\wedge e_2 \wedge e_3 \wedge e_4)$
$\rightarrow \alpha_{13} e_1e_3\wedge e_2\wedge e_4 = 0 = -\alpha_{13}(e_1\wedge e_2 \wedge e_3 \wedge e_4)$
$$
e_1\wedge \ldots \wedge e_n \neq 0 \Leftrightarrow e_1\otimes \ldots \otimes e_n \notin I(V)
......@@ -1133,9 +1136,10 @@ $$
$\longrightarrow$ $m$ definiert eine Abbildung
%TODO check \lbrack
$$
\overline{m} \colon \bigwedge^kV &\to& \mathbb R
\\ [v_1\wedge\ldots\wedge v_n] \mapsto m(v_1\otimes \ldots \otimes v_n)
\\ \lbrack v_1\wedge\ldots\wedge v_n \rbrack \mapsto m(v_1\otimes \ldots \otimes v_n)
$$
** Proposition
......@@ -1261,10 +1265,10 @@ E\to M$ ($\pi$ heißt Bündelprojektion) mit folgenden Eigenschaften:
$$
E|_U := \pi^{-1}(U) \overset{\overset{\psi}{\underset{\text{diffeomorph}}\cong}}\longrightarrow U \times \mathbb R^k
$$
sodass $\forall q\in U$, $\forall v_1$, $v_2 \in E_q = \pi^{-1}(q)$, $\forall \lambda \in \mathbb R$ gilt: ($\pi_^{\mathbb R^k} \colon U\times \mathbb R^k \to \mathbb R^k$ Projektion)
sodass $\forall q\in U$, $\forall v_1$, $v_2 \in E_q = \pi^{-1}(q)$, $\forall \lambda \in \mathbb R$ gilt: ($\pi_{??}^{??}{\mathbb R^k} \colon U\times \mathbb R^k \to \mathbb R^k$ Projektion)%TODO ??
$$
\pi_{\mathbb R^k} \circ \psi(v_1 + \lambda v_2) = \pi_^{\mathbb R^k} \circ \psi(v_1) + \lambda\cdot\pi_{\mathbb R^k} \circ \psi(v_2)
\pi_{\mathbb R^k} \circ \psi(v_1 + \lambda v_2) = \pi_{??}^{??}{\mathbb R^k} \circ \psi(v_1) + \lambda\cdot\pi_{\mathbb R^k} \circ \psi(v_2)
$$
(die Vektorraumoperation auf $E_q$ entsprechen den auf $\mathbb R^k$ durch $\psi$)
......@@ -1320,12 +1324,25 @@ Beweis: (Für $T_{r,s}$ andere analog)
\pi^{-1} (p) = T_{r,s} (T_pM)
$$
ist ein Vektorraum
- Eigenschaft 2) Sei $(U,x)$ eine Karte um $p\in M$. Auf $U$ existiert kanonische Vektorfelder $\frac{\partial}{\partial x_1}, \ldots, \frac{\partial}{\partial x_n} \in \Gamma (TU)$ s.d für alle $q\in M: \left\frac{\partial}{\partial x_1}\right|_q,\ldots, \left\frac{\partial}{\partial x_n}\right|_q \in T_qM$ eine Basis mit Dualbasis $(\intd x^1)(q), \ldots, (\intd x^n)(q) \in T_q^* M$
- Eigenschaft 2) Sei $(U,x)$ eine Karte um $p\in M$. Auf $U$ existiert kanonische Vektorfelder $\frac{\partial}{\partial x_1}, \ldots, \frac{\partial}{\partial x_n} \in \Gamma (TU)$ s.d für alle
$q\in M: \left.\frac{\partial}{\partial x_1}\right|_q,\ldots,\left.\frac{\partial}{\partial x_n}\right|_q \in T_qM$
eine Basis mit Dualbasis $(\intd x^1)(q), \ldots, (\intd x^n)(q) \in T_q^* M$
Entsprechend gilt $\forall q\in M$:
$$
\left\{ \left.\frac{\partial}{\partial x^{i_1}}\right|_{q} \otimes \ldots \otimes \left.\frac{\partial}{\partial x^{i_r}}\right|_{q} \otimes \intd x^{j_1}(q) \otimes \ldots \otimes \intd x^{j_s} (q) \mathrel{\middle|} i_1, \ldots, i_r, j_1, \ldots, j_s \in \{ 1, \ldots, n \} \right\}
\left\{
\left.
\frac{\partial}{\partial x^{i_1}}
\right|_{q}
\otimes \ldots \otimes
\left.
\frac{\partial}{\partial x^{i_r}}
\right|_{q}
\otimes \intd x^{j_1}(q) \otimes \ldots
\otimes \intd x^{j_s} (q) \mathrel{%TODO\middle
|} i_1, \ldots, i_r, j_1, \ldots, j_s \in \{ 1, \ldots, n \} \right\}
$$
ist eine Basis von $T_{r,s} (T_q M)$. Entsprechend haben wir für jedes $q\in U$ eine Koordinatenabbildung
......@@ -1438,7 +1455,7 @@ bildet eine Basis in $\bigwedge^k T^*qM$ $\forall q\in U$
Daher sieht jede Differentialform $\omega \in \underline{O}^k(M)$ auf $U$ so aus:
$$
\omega|_U = \sum_{1\leqslanti_1 < \ldots < i_k \leqslant n} \omega_{i_1, \ldots, i_k} \intd x^{i_1} \wedge \intd x^{i_2} \wedge \ldots \wedge \intd x^{i_k}
\omega|_U = \sum_{1\leqslant i_1 < \ldots < i_k \leqslant n} \omega_{i_1, \ldots, i_k} \intd x^{i_1} \wedge \intd x^{i_2} \wedge \ldots \wedge \intd x^{i_k}
$$
für gewisse $\omega_{i_1,\ldots, i_k} \in C^\infty(U)$
......@@ -1446,7 +1463,8 @@ für gewisse $\omega_{i_1,\ldots, i_k} \in C^\infty(U)$
Algebraisch heißt es:
$$
\left\{ \frac{\partial}{\partial x^{i_1}} \otimes \ldots \otimes \frac{\partial}{\partial x^{i_r}} \otimes \intd x^{j_1} \otimes \ldots \otimes \intd x^{j_s} \mathrel{\middle |} i_1, \ldots, i_r, j_1,\ldots, j_s \in \{ 1,\ldots, n \} \right\}
\left\{ \frac{\partial}{\partial x^{i_1}} \otimes \ldots \otimes \frac{\partial}{\partial x^{i_r}} \otimes \intd x^{j_1} \otimes \ldots \otimes \intd x^{j_s} \mathrel{%TODO\middle
|} i_1, \ldots, i_r, j_1,\ldots, j_s \in \{ 1,\ldots, n \} \right\}
$$
bildet eine Basis von $\Gamma(T_{r,s}(TM)|_U)$ über $C^\infty(U)$ Entsprechend für $\left\{ \intd x^{i_1}\wedge\ldots\wedge\intd x^{i_k} \mathrel| \ldots \right\}$ für $\underline O^k(U)$
......@@ -1575,7 +1593,7 @@ Mit dieser Definition gilt:
$$
- $\intd(\intd f) = 0$, $f+\Omega^0(M)$, weil
$$
\intd(\intd f) = \intd\left( \sum_{i=1}^{n} \frac{\partial f}{\partial x^i} \right) = \sum_{j=1}^{n} \sum_{i=1}^n \left( \frac{\partial^2 f}{\partialx^i\partial x^j} \intd x^j \wedge dx^i \right) = 0
\intd(\intd f) = \intd\left( \sum_{i=1}^{n} \frac{\partial f}{\partial x^i} \right) = \sum_{j=1}^{n} \sum_{i=1}^n \left( \frac{\partial^2 f}{\partial x^i\partial x^j} \intd x^j \wedge dx^i \right) = 0
$$
- (4') für $k= 0$ ist $\intd f|_U = \sum_{i=1}^{n} \frac{\partial f}{\partial x^i} \intd x^i = \intd \underbrace{f}_{\text{Differential von } f}$
- (5') wenn $\omega_1 = \omega_2$ auf $\underbrace{ V }_{\text{offen}}\subseteq U$, dann gilt
......@@ -1617,7 +1635,7 @@ Die Eigenschaften (1) - (4) implizieren, dass in jeder Karte $(U,x)$ (1') - (4')
Beispiel:
Sei $M=\mathbb R^2$, $\omega = P\intd x + \Q \intd y$
Sei $M=\mathbb R^2$, $\omega = P\intd x + Q \intd y$
$$
\intd \omega &=& \left( \frac{\partial P}{\partial x} \intd x + \frac{\partial P}{\partial y} \intd y \right) \wedge \intd x
......
inotifywait -e close_write,moved_to,create -m . |
while read -r directory events filename; do
if [ "$filename" = "edit-this-file.tex" ]; then
./compile.sh
echo "wait for next change..."
fi
done
......@@ -94,7 +94,7 @@ $if(linestretch)$
\usepackage{setspace}
\setstretch{$linestretch$}
$endif$
\usepackage{amssymb,amsmath,unicode-math}
\usepackage{amssymb,amsmath}
\usepackage{ifxetex,ifluatex}
\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
\usepackage[$if(fontenc)$$fontenc$$else$T1$endif$]{fontenc}
......
......@@ -21,7 +21,7 @@ with open(filename, 'r') as file:
copy = re.sub("\$\$1\n", '\\\\begin{equation*}\n', copy, 1)
copy = re.sub("\$\$1\n", '\\\\end{equation*}\n', copy, 1)
print(data, copy)
#print(data, copy)
if data == copy:
break
......
source ./do-install-stuff.sh
source ./do-compile-stuff.sh
sh install-path-pandoc
cd diffgeoII
source ./compile.sh fail-on-error
uname -a
pwd
#apt-get not working
TGZ=pandoc-2.7.2-linux.tar.gz
DEST=.local
mkdir $DEST
export PATH=$PATH:$(pwd)/$DEST/bin
echo "export PATH=$PATH:$(pwd)/$DEST/bin" > install-path-pandoc
pwd
ls
echo $PATH
curl -O -L -C - "https://github.com/jgm/pandoc/releases/download/2.7.2/$TGZ"
tar xvzf $TGZ --strip-components 1 -C $DEST
ls .local
pandoc --version
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