a

.gitea/workflows/build-script.yaml

@@ -7,16 +7,13 @@ on:
   pull_request:
     branches: [ "**" ]
 
-env:
-  TYPST_SOURCE_DIR: src
-  BUILD_DIR: build
-
 jobs:
   build-typst:
     runs-on: ubuntu-latest
 
     # Run the whole job inside a Docker container that has Typst installed
     steps:
+      - uses: typst-community/setup-typst@v4
       - name: Checkout repository
         uses: actions/checkout@v4
         with:
@@ -27,38 +24,25 @@ jobs:
       - name: Debug Ls
         run: ls -la "$PWD" && echo "$PWD && echo ${{ github.workspace }}"
 
-      - name: Build Typst builder image
-        uses: docker/build-push-action@v2
-        with:
-          tags: typst-builder-image:latest
-          push: false
+      - name: Make build directory
+        run: mkdir -p build
 
-      - name: Compile all .typ files
-        uses: addnab/docker-run-action@v3
-        env:
-          TYPST_SOURCE_DIR: ${{ env.TYPST_SOURCE_DIR }}
-          BUILD_DIR: ${{ env.BUILD_DIR }}
-        with:
-          image: typst-builder-image:latest
-          options: --volumes-from=${{ env.JOB_CONTAINER_NAME }}
-          cwd: ${{ github.workspace }}
-          run: "cd ${{ github.workspace }} && TYPST_SOURCE_DIR=${{ env.TYPST_SOURCE_DIR }} BUILD_DIR=${{ env.BUILD_DIR }} bash -c ./compile-all.bash"
+      - name: Compile Analysis1
+        continue-on-error: true
+        run: typst compile --root src src/cheatsheets/Analysis1.typ build/Analysis1.pdf
 
-      - name: Upload PDFs
-        if: always()
-        uses: actions/upload-artifact@v3
-        with:
-          name: typst-pdfs
-          path: ${{ env.BUILD_DIR }}/*.pdf
-          if-no-files-found: warn
+      - name: Compile Schaltungstheorie
+        continue-on-error: true
+        run: typst compile --root src src/cheatsheets/Schaltungstheorie.typ build/Schaltungstheorie.pdf
+
+      - name: Compile LinAlg
+        continue-on-error: true
+        run: typst compile --root src src/cheatsheets/LinearAlgebra.typ build/LinearAlgebra.pdf
 
       - name: Create Gitea Release
-        uses: softprops/action-gh-release@v1
+        continue-on-error: true
+        uses: akkuman/gitea-release-action@v1
         with:
-          tag_name: ${{ steps.tag.outputs.tag }}
-          name: Typst PDFs ${{ steps.tag.outputs.tag }}
-          body: |
-            Automated release of Typst-generated PDFs.
-
-            Commit: ${{ github.sha }}
-          files: ${{ env.BUILD_DIR }}/*.pdf
+          name: "Formelsammlungen PDFs"
+          tag_name: "latest"
+          files: build/*.pdf

.gitignore

@@ -1 +1,7 @@
-venv
+.venv
+out
+node_modules
+__pycache__/
+
+package-lock.json
+package.json

.vscode/tasks.json

@@ -1,17 +0,0 @@
-{
-    "tasks": [
-        {
-            "label": "Compile All",
-            "type": "shell",
-            "command": "TYPST_SOURCE_DIR=src BUILD_DIR=output ./compile-all.bash",
-            "group": {
-                "kind": "build",
-                "isDefault": true
-            },
-            "problemMatcher": [],
-            "options": {
-                "cwd": "${workspaceFolder}"
-            }
-        }
-    ]
-}

compile-all.bash

@@ -1,31 +0,0 @@
-#!/usr/bin/env bash
-
-set -euo pipefail
-SRC_DIR="${TYPST_SOURCE_DIR}"
-OUT_DIR="${BUILD_DIR}"
-
-if [[ ! -d "$SRC_DIR" ]]; then
-    echo "Source directory '$SRC_DIR' does not exist."
-    exit 1
-fi
-
-mkdir -p "$OUT_DIR"
-
-
-# Find all .typ files under $SRC_DIR (excluding hidden dirs)
-mapfile -d '' files < <(printf '%s\0' "$SRC_DIR"/*.typ 2>/dev/null)
-
-if [[ ${#files[@]} -eq 0 ]]; then
-    echo "No .typ files found in '$SRC_DIR'."
-    exit 0
-fi
-
-for f in "${files[@]}"; do
-    # Trim leading ./ if present
-    rel="${f#./}"
-    # Destination path: build/<same-subdirs>/<filename>.pdf
-    dest_pdf="${OUT_DIR}/$(basename "${rel%.typ}").pdf"
-
-    echo "Compiling: $f  ->  $dest_pdf"
-    typst compile "$f" "$dest_pdf"
-done

reihen_plot.py

@@ -1,17 +0,0 @@
-from matplotlib import pyplot as plt
-
-f = lambda x_prev: 1/4 * (x - 3)
-x = 0
-
-reihe = [x]
-
-for i in range(100):
-    x = f(x)
-    reihe.append(x)
-
-plt.plot(reihe, marker='o', linestyle='-')
-plt.title("Reihen Plot")
-plt.xlabel("n")
-plt.ylabel("x_n")
-plt.grid()
-plt.savefig("reihen_plot.png", dpi=500)

src/Analysis1.typ

@@ -1,259 +0,0 @@
-#import "@preview/biceps:0.0.1": *
-#import "@preview/cetz:0.4.2"
-
-#import "lib/styles.typ": *
-#import "lib/common.typ": *
-
-#show: stdTemplate
-
-#place(
-  top+left,
-  stdBlock([
-    == #hlHeading([Trig Identitäten])
-    $sin(x+y) = cos(x)sin(y) + sin(x)cos(y)$ \
-    $cos(x+y) = cos(x)cos(y) - sin(x)sin(y)$ \
-
-    $cos(2x) = cos^2(x) - sin^2(x)$ \
-    $sin(2x) = 2sin(x)cos(x)$
-
-    #grid(
-      gutter: 5mm,
-      columns: (auto, auto),
-      [$cos^2(x) = (1 + cos(2x))/2$],
-      [$sin^2(x) = (1 - cos(2x))/2$]
-    )
-
-    $cos^2(x) + sin^2(x) = 1$
-    
-    #grid(
-      gutter: 5mm,
-      columns: (auto, auto),
-      [$cos(-x) = cos(x)$],
-      [$sin(-x) = -sin(x)$],
-    )
-
-    Subsitution mit Hilfsvariable
-
-    #grid(
-      gutter: 5mm,
-      row-gutter: 3mm,
-      columns: (auto, auto),
-      [$tan(x)=sin(x)/cos(x)$],
-      [$cot(x)=cos(x)/sin(x)$],
-      [$tan(x)=-cot(x + pi/2)$],
-      [$cot(x)=-tan(x + pi/2)$],
-      [$cos(x - pi/2) = sin(x)$],
-      [$sin(x + pi/2) = cos(x)$],
-    )
-    $sin(x)cos(y) = 1/2sin(x - y) + 1/2sin(x + y)$
-
-    Für $x in [-1, 1]$ \
-    $arcsin(x) = -arccos(x) - pi/2 in [-pi/2, pi/2]$ \
-    $arccos(x) = -arcsin(x) + pi/2 in [0, pi]$
-  ])
-)
-#place(
-  top + left,
-  dx: 6.5cm,
-  sinTable
-)
-
-#place(
-  top+left,
-  dx: 0cm,
-  dy: 8cm,
-  stdBlock([
-    #grid(
-      columns:(auto, auto), 
-      gutter: 1mm,
-      [
-        == #hlHeading([Folgen])
-        $ lim_(x->infinity) a_n $
-        - *Beschränkt*: $exists k in RR$ so dass $abs(a_n) <= k$
-          - $epsilon$-Interval: $x in (a - epsilon, a + epsilon) <=> abs(x - a) < epsilon$
-          - *Beweiß:* Induktion
-          - Hat min. eine konvergent Teilfolge
-
-        - *Monoton: steigen/fallend* $a_(n+1) gt.eq.lt a_n$
-          - *Beweisen:* Induktion mit \ $a_(n+1) gt.eq.lt a_n$ oder $a_(n+1) / a_(n) gt.lt 1 $  oder Umformung
-
-        - *Konvergent*:
-          - Es gibt $forall epsilon > 0$ eine Index $n_epsilon in NN$ sodass \ $abs(a_n - a) < epsilon space forall n > n_epsilon$
-          - Divergent $-> infinity$, wenn $forall k in RR : exists space  a_n > k$
-          - Divergent $-> -infinity$, wenn $forall k in RR : exists space  a_n < k$
-          - Genzwert is eindeutig
-
-        - *Konvergenz $a_n -> a$ $<=>$ beschränkt UND monoton*
-          - $<=>$ Alle Teilefolgen konvergent zu $a$
-          - Wenn Häufungspunk $eq.not$ $=>$ divergent
-          - Sandwitch-Theorem
-
-        - *Cauchyfolge*
-          Ein folge die diese Eigenschaft hat: \
-          $forall epsilon > 0 space exists N_epsilon in NN space forall m,n > N_epsilon : abs(a_n - a_m) < epsilon$ \
-          Cauchyfolge $<=>$ Konvergenz
-      ], 
-      grid.vline(stroke: 0.1mm + black, position: start),
-      pad([
-        === Grenzwert Finden:
-        - "Bottom up" von Bekannten Ausdrücken
-        - Fixpunk Gleösenichung l $a = f(a)$  für $f(a_n)$
-        - Bernoulli-Ungleichung für $(a_n)^n$ \
-          $(1 + a)^n >= 1 + n a$ für $a >= -1$
-        - #MathAlignLeft($1 + u <= 1/(1-u), u < 1$)
-          
-        Für Konvergent Folgen:
-        #grid(
-          columns: (auto, auto),
-          align: bottom,
-          gutter: 2mm,
-          [$ lim_(n->infinity) (a_n + b_n) = a + b $],
-          grid.cell(
-            rowspan:  2,
-            [$ lim_(n->infinity) (a_n / b_n) = a / b $],
-          ),
-          MathAlignLeft($ lim_(n->infinity) (a_n dot b_n) = a dot b $),
-          MathAlignLeft($ lim_(n->infinity) sqrt(a_n) = sqrt(a) $),
-          MathAlignLeft($ lim_(n->infinity) abs(a_n) = abs(a) $),
-          MathAlignLeft($ lim_(n->infinity) c dot a_n = c dot lim_(n->infinity) a_n $),
-        )
-
-        == Spezifische Folgen
-        #grid(
-          columns: (auto, auto, auto),
-          column-gutter: 4mm,
-          row-gutter: 2mm,
-          align: bottom,
-          MathAlignLeft($ lim_(n->infinity) 1/n = 0 $),
-          MathAlignLeft($ lim_(n->infinity) q^n = 0 $),
-          MathAlignLeft($ lim_(n->infinity) q^n = 0 $),
-          grid.cell(colspan: 2, MathAlignLeft($ lim_(n->infinity) sqrt(n) = + infinity $)), [],
-          grid.cell(colspan: 2, MathAlignLeft($ lim_(n->infinity) k = k, k in RR $)), [],
-          grid.cell(colspan: 2, MathAlignLeft($ exp(x) =  e^x = lim_(n->infinity) (1 + x/n)^n $))
-        )
-
-        == Teilfolgen
-        - Indizies müssen immer streng monoton \
-          wachsend sein. (z.B. is $a_1, a_1, a_2, a_2$ KEIN\
-          Teilfolge von $a_n$)
-        - Beschränkte $a_n$ $=>$ *min eine* \
-          konvergent Teilfolge
-        - Konvergent $a_n$ $=>$ *genau ein* Häufungspunkt
-        
-
-      ], left: 1mm)
-    )
-  ])
-)
-
-#place(
-  top+left,
-  dx: 13cm,
-  dy: 0cm,
-  stdBlock([
-    == #hlHeading([Reihen])
-
-    Wenn $sum_(n=1)^infinity a_n$ konverigiert $=>$ $a_n$ Nullfolge \
-    Wenn $a_n$ keine Nullfolge $=>$ $sum_(n=1)^infinity$ divergent
-
-    === Absolute Konvergenz
-    Bedeuted $sum_(n=1)^infinity abs(a_n) = a ==> sum_(n=1)^infinity a_n$ konvergent 
-    
-    $sum_(n=1)^infinity abs(a_n)$ beschränkt + (monoto steigended) $= sum_(n=1)^infinity abs(a_n)$
-
-    === Partialsummen
-    Sind die Partialsummen von $sum_(k=1)^infinity abs(a)$ beschränkt\
-    $==>$ _Absolute Konvergent_
-
-    === Cauchy-Kriterium
-    konvergent wenn $forall epsilon$ existiert ein $n_epsilon in NN$ \
-    sodass $abs(s_n - s_m) = abs(sum_(k=m+1)^(n)) < epsilon space$ \
-    $forall n_epsilon < m < n $
-
-    === Leibnitzkriterium
-    Wenn monton fallend, $a_n >= 0$, Null folge dann
-
-    $sum_(n=1)^infinity (-1)^n dot a_n$ konvergent
-
-    === Majorandenkriterium
-    Seien $a_n, b_n$ mit $abs(a_n) <= b_n space (forall n > N, N in NN)$
-    1. $sum_(n=0)^infinity b_n$ konvergent $==> sum_(n=0)^infinity abs(a_n)$ konvergent \
-      Suche $b_n$ für Konvergenz
-    2. $sum_(n=0)^infinity abs(a_n)$ divergent $==> sum_(n=0)^infinity b_n$ divergent \
-      Suche $abs(a_n)$ für Divergenz
-
-    Nützlich:
-    - Dreiecksungleichung
-    - $forall space n in NN$ \
-      $exists space k,q in RR$ \
-      für $q > 1$: $n^k <= q^n$ ab einem bestimmten.
-
-    === Quotientenkriterium und Wurzelkriterium
-    1. $rho = lim_(n -> infinity) abs((a_(n+1))/(a_n)) $
-    2. $rho = lim_(n -> infinity) root(n, abs(a_(n+1))) $ \
-      (Stärker, am besten für $(...)^n$)
-
-    divergent: $rho > 1$, keine Aussage $rho = 1$, konvergent $rho < 1$
-    === Spezifische Reihen
-      Geometrische Reihe: $sum_(n=0)^infinity q^n$
-      - konvergent $abs(q) < 1$, divergent  $abs(q) >= 1$
-      - Grenzwert: (Muss $n=0$) $=1/(1-q)$
-      Harmonische Reihe: $sum_(n=0)^infinity 1/n = +infinity$
-
-      1. $e^x = sum_(n=0)^infinity (x^n)/(n!)$
-      2. $ln(x) = sum_(n=0)^infinity (-1)^n x^(n+1)$
-  ])
-)
-
-#place(
-  top+left,
-  dx: 0cm,
-  dy: 20cm,
-  stdBlock([
-    == Kriterien Übersich für Reihen $sum_(n=0)^infinity a_n$
-    #line()
-
-    #grid(
-      columns: (auto, auto),
-      gutter: 3mm,
-      [
-        *Notwendinge Kriterien*\
-        ($not$ Bedingung $=>$ div.)
-        - Cauchy-Kriterium
-        - #MathAlignLeft($ lim_(n->infinity)a_n = 0 $)
-        - Konvergenz der Partialsummen
-        - Beschränktheit der Partialsummen
-      ],
-      [
-        *Hinreichende Kriterien* \
-        (Bedingung $=>$ konv.)
-        - Absolute Konvergenz
-        - Leibnitz-Kroterium
-        - Beschränktheit der Partialsummen
-        - Quotienten-/Wurzel-kriterium
-        - Majorandenkriterium
-      ]
-    )
-  ])
-)
-
-#pagebreak()
-#place(
-  left+top,
-  dx: 0cm,
-  dy: 0cm,
-  stdBlock([
-    == #hlHeading([Funktionen])
-    === Stetigkeit
-    Stetig an der stelle $x_0$ wenn: $ lim_(x->x_0+) f(x) = lim_(x->x_0-) f(x) =f(x_0) $
-    $f(x)$ muss nicht definiert sein an $x_0$
-    === Differenzierbar
-    An der stelle $x_0$ wenn
-    #MathAlignLeft($ 
-      lim_(h -> 0) (f(x_0 + h)-f(x_0))/h =\
-      lim_(h -> 0) (f(x_0 - h)-f(x_0))/h = f'(x)
-    $)
-    definiert ist
-
-  ])
-)

src/cheatsheets/Analysis1.typ

@@ -1,4 +1,5 @@
-#import "lib/common_rewrite.typ" : *
+#import "../lib/common_rewrite.typ" : *
+#import "@preview/mannot:0.3.1"
 
 #set page(
   paper: "a4", 
@@ -9,12 +10,15 @@
     right: 5mm
   ),
   flipped:true,
-  numbering: "— 1 —",
-  number-align: center
+  footer: context [
+    #grid(
+      align: center,
+      columns: (1fr, 1fr, 1fr),
+      [#align(left, datetime.today().display("[day].[month].[year]"))], 
+      [#align(center, counter(page).display("- 1 -"))], 
+      [#align(right, image("../images/cc0.png", height: 5mm,))]
     )
-
-#set text(
-  size: 8pt,
+  ],
 )
 
 #place(top+center, scope: "parent", float: true, heading(
@@ -72,32 +76,6 @@
     )
   ]
 
-  #bgBlock(fill: colorAllgemein)[
-    #subHeading(fill: colorAllgemein)[Trigonometrie]
-  ]
-
-    #bgBlock(fill: colorAllgemein)[
-    #table(
-      inset: 1.5mm,
-      stroke: (thickness: 0.2mm),
-      columns: 4,
-      table.header(
-        [x], [deg], [cos(x)], [sin(x)]
-      ),
-      [$0$], [$0°$], [$1$], [$0$],
-      [$pi/6$], [$30°$], [$sqrt(3)/2$], [$1/2$],
-      [$pi/4$], [$45°$], [$sqrt(2)/2$], [$sqrt(2)/2$],
-      [$pi/3$], [$60°$], [$1/2$], [$sqrt(3)/2$],
-      [$pi/2$], [$90°$], [$0$], [$1$],
-      [$2/3pi$], [$120°$], [$-1/2$], [$sqrt(3)/2$],
-      [$3/4pi$], [$135°$], [$-sqrt(2)/2$], [$sqrt(2)/2$],
-      [$5/6pi$], [$150°$], [$-sqrt(3)/2$], [$1/2$],
-      [$pi$], [$180°$], [$-1$], [$0$],
-      [$3/2pi$], [$270°$], [$0$], [$-1$],
-      [$2pi$], [$360°$], [$1$], [$0$]
-    )
-  ]
-
   #bgBlock(fill: colorAllgemein)[
     #subHeading(fill: colorAllgemein)[Complexe Zahlen]
     $z = r dot e^(phi i) = r (cos(phi) + i sin(phi))$
@@ -110,9 +88,13 @@
       [$ cos(x) = (e^(i x) + e^(-i x))/(2) $]
     )
     #subHeading(fill: colorAllgemein)[Trigonmetrie]
+    *Additionstheorem* \
     $sin(x+y) = cos(x)sin(y) + sin(x)cos(y)$ \
     $cos(x+y) = cos(x)cos(y) - sin(x)sin(y)$ \
+    $tan(x) + tan(y) = (tan(a) + tan(b))/(1 - tan(a) tan(b))$ \
+    $arctan(x) + arctan(y) = arctan((x+y)/(1 - x y))$ \
 
+    *Doppelwinkel Formel* \
     $cos(2x) = cos^2(x) - sin^2(x)$ \
     $sin(2x) = 2sin(x)cos(x)$
 
@@ -467,9 +449,34 @@
     )
   ])
 
-  #colbreak()
+
+  #bgBlock(fill: colorIntegral, [
+    #subHeading(fill: colorIntegral, [Integral])
+
+    Summen: $integral f(x) + g(x) d x = integral f(x) d x + integral g(x)$
+
+    Vorfaktoren: $integral lambda f(x) d x = lambda f(x) d x$
+
+    *Partial Integration*
+    
+    $integral u(x) dot v'(x) d x = u(x)v(x) - integral u'(x) dot v(x)$
+
+    *Subsitution*
+
+    $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) dot g'(x) d x$
+    
+    1. Ersetzung: $ d x := d t dot 1/(g'(x))$ und $t := g(x)$
+    2. Grenzen: $t_0 = g(x_0)$, $t_1 = g(x_1)$
+    3. $x$-kürzen sich weg
+  ])
+
 ]
 
+#bgBlock(fill: colorAllgemein, [
+  #subHeading(fill: colorAllgemein, [Sin-Table])
+  #sinTable
+])
+
 #pagebreak()
 
 == Folgen in $CC$
@@ -517,3 +524,23 @@ Konvergenz Radius $R = [0, infinity)$$$
 )$
 
 $ R = limsup_(n -> infinity) $
+  #bgBlock(fill: colorIntegral, [
+    #subHeading(fill: colorIntegral, [Integral])
+
+    Summen: $integral f(x) + g(x) d x = integral f(x) d x + integral g(x)$
+
+    Vorfaktoren: $integral lambda f(x) d x = lambda f(x) d x$
+
+    *Partial Integration*
+    
+    $integral u(x) dot v'(x) d x = u(x)v(x) - integral u'(x) dot v(x)$
+
+    *Subsitution*
+
+    $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) dot g'(x) d x$
+    
+    1. Ersetzung: $ d x := d t dot 1/(g'(x))$ und $t := g(x)$
+    2. Grenzen: $t_0 = g(x_0)$, $t_1 = g(x_1)$
+    3. $x$-kürzen sich weg
+  ])
+

src/cheatsheets/LinearAlgebra.typ

@@ -1,7 +1,7 @@
 #import "@preview/biceps:0.0.1" : *
 #import "@preview/mannot:0.3.1"
-#import "lib/styles.typ" : *
-#import "lib/common_rewrite.typ" : *
+#import "../lib/styles.typ" : *
+#import "../lib/common_rewrite.typ" : *
 
 #set page(
   paper: "a4", 

src/cheatsheets/Schaltungstheorie.typ

@@ -0,0 +1,208 @@
+#import "../lib/common_rewrite.typ" : *
+#import "@preview/mannot:0.3.1"
+#import "@preview/zap:0.5.0"
+
+#show math.equation.where(block: true): it => math.inline(it)
+
+#set page(
+  paper: "a4", 
+  margin: (
+    bottom: 10mm,
+    top: 5mm,
+    left: 5mm,
+    right: 5mm
+  ),
+  flipped:true,
+  footer: context [
+    #grid(
+      align: center,
+      columns: (1fr, 1fr, 1fr),
+      [#align(left, datetime.today().display("[day].[month].[year]"))], 
+      [#align(center, counter(page).display("- 1 -"))], 
+      [#align(right, image("../images/cc0.png", height: 5mm,))]
+    )
+  ],
+)
+
+#let colorAllgemein = color.hsl(105.13deg, 92.13%, 75.1%)
+#let colorEineTore = color.hsl(202.05deg, 92.13%, 75.1%)
+#let colorZweiTore = color.hsl(235.9deg, 92.13%, 75.1%)
+#let colorAnalyseVerfahren = color.hsl(280deg, 92.13%, 75.1%)
+#let colorComplexAC = color.hsl(356.92deg, 92.13%, 75.1%)
+#let colorMathe = color.hsl(34.87deg, 92.13%, 75.1%)
+
+#place(top+center, scope: "parent", float: true, heading(
+  [Schaltungstheorie]
+))
+
+
+#columns(4, gutter: 2mm)[
+  #bgBlock(fill: colorEineTore)[
+    #subHeading(fill: colorEineTore)[Quelle Wandlung]
+
+    #zap.circuit({
+      import zap: *
+      set-style(scale: (x: 0.75, y:0.75), fill: none)
+      resistor("R1", (-2, 0), (0, 0))
+      vsource("V1", (-2, 0), (-2, -2))
+      wire((-2, -2), (0, -2))
+      node("n1", (0, 0), label: "1")
+      node("n2", (0, -2), label: "2")
+    })
+  ]
+
+  #bgBlock(fill: colorAnalyseVerfahren)[
+    #subHeading(fill: colorAnalyseVerfahren)[Graphen und Matrizen]
+
+    $bold(i_b)$ (oder $bold(i)$): Zweigstrom-Vektor \
+    $bold(u_b)$ (oder $bold(u)$): Zweigspannungs-Vektor \
+    $bold(i_m)$ : Maschenstrom-Vektor \
+      #text(rgb(20%, 20%, 20%))[(Strom in einer viruellen Masche)] \
+    $bold(u_k)$ : Kontenspannungs-Vektor \
+      #text(rgb(20%, 20%, 20%))[(Spannung zwischen Referenzknoten und Knoten k)] \
+
+    #line(length: 100%, stroke: (thickness: 0.2mm))
+
+    Knotenzidenzmatrix $bold(A)$
+
+    $bold(A) : bold(i_k) -> text("Knotenstrombianz") = 0$ \
+    $bold(A^T) : bold(u_b)-> bold(u_k)$
+    $ 
+      bold(A) = quad mannot.mark(mat(
+        a_11, a_12, ..., a_(1m);
+        a_21, a_22, ..., a_(2m);
+        dots.v, dots.v, dots.down, dots.v;
+        a_(n 1), a_(n 2), ..., a_(n m)
+      ), tag: #<1>)
+
+      #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Knoten]], dx: 5mm)
+      #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm)
+
+      a in {-1, 0, 1}
+    $
+    
+    #line(length: 100%, stroke: (thickness: 0.2mm))
+    
+    Mascheninsidenz Matrix $bold(B)$\
+
+
+    $bold(B) : bold(u_b) -> text("Zweigspannungsbilanz") = 0$ \
+    $bold(B^T) : bold(i_m) -> i_b$
+
+    $ 
+      bold(B) = quad mannot.mark(mat(
+        b_11, b_12, ..., b_(1m);
+        b_21, b_22, ..., b_(2m);
+        dots.v, dots.v, dots.down, dots.v;
+        b_(n 1), b_(n 2), ..., b_(n m)
+      ), tag: #<1>)
+
+      #mannot.annot(<1>, pos:left, text(rgb("#404296"))[#rotate(-90deg)[$<-$ Maschen]], dx: 6mm)
+      #mannot.annot(<1>, pos:bottom, text(rgb("#404296"))[Zweige $->$], dy: -0.5mm)
+
+      b in {-1, 0, 1}
+    $
+
+    #line(length: 100%, stroke: (thickness: 0.2mm))
+
+    *KCL und KVL* \
+
+    KCL in Nullraum: $ bold(A) bold(i_b) = bold(0)$ \
+    KVL in Bildraum: $ bold(A^T) bold(u_k) = bold(u_b)$
+
+    KVL in Nullraum: $bold(B) bold(u_b) = bold(0)$ \
+    KCL in Bildraum: $bold(B^T) bold(i_m) = bold(i_b)$ \
+
+    *Tellegen'sche Satz* \
+    $bold(A B^T) = bold(B^T A) = 0$ \
+    $bold(u_b^T i_b) = 0$
+  ]
+
+  #bgBlock(fill: colorAnalyseVerfahren)[
+    #subHeading(fill: colorAnalyseVerfahren)[Baumkonzept]
+  ]
+
+  #bgBlock(fill: colorAnalyseVerfahren)[
+    #subHeading(fill: colorAnalyseVerfahren)[Machenstrom-/Knotenpotenzial-Analyse]
+  ]
+
+  #bgBlock(fill: colorAnalyseVerfahren)[
+    #subHeading(fill: colorAnalyseVerfahren)[Reduzierte Knotenpotenzial-Analyse]
+  ]
+
+  
+]
+
+#pagebreak()
+#place(bottom+left, scope: "parent", float: true)[
+  #bgBlock(fill: colorZweiTore)[
+    #subHeading(fill: colorZweiTore)[Umrechnung Zweitormatrizen]
+      #show table.cell: it => pad(),
+
+      #table(
+        columns: (auto, 1fr, 1fr, 1fr, 1fr, 1fr, 1fr),
+        align: center,
+        gutter: 0.1mm,
+        [In $->$], $bold(R)$, $bold(G)$, $bold(H)$, $bold(H')$, $bold(A)$, $bold(A')$,
+        
+        $bold(R)$,
+        $mat(r_11, r_12; r_21, r_22)$,
+        $1/det(bold(G)) mat(g_22, -g_12; -g_21, g_11)$,
+        $1/h_22 mat(det(bold(H)), h_12; -h_21, 1)$,
+        $1/h'_11 mat(1, -h'_12; h'_21, det(bold(H')))$,
+        $1/a_21 mat(a_11, det(bold(A)); 1, a_22)$,
+        $1/a'_21 mat(a'_22, 1; det(bold(A')), a'_11)$,
+
+        $bold(G)$,
+        $1/det(bold(R)) mat(r_22, -r_12; -r_21, r_11)$,
+        $mat(g_11, g_12; g_21, g_22)$,
+        $1/h_11 mat(1, -h_12; h_21, det(bold(H)))$,
+        $1/h'_22 mat(det(bold(H')), h'_12; -h'_21, 1)$,
+        $1/a_12 mat(a_22, -det(bold(A)); -1, a_11)$,
+        $1/a'_12 mat(a'_11, -1; -det(bold(A')), a'_22)$,
+
+        $bold(H)$,
+        $1/r_22 mat(det(bold(R)), r_12; -r_21, 1)$,
+        $1/g_11 mat(1, -g_12; g_21, det(bold(G)))$,
+        $mat(h_11, h_12; h_21, h_22)$,
+        $1/det(bold(H')) mat(h'_22, -h'_12; -h'_21, h'_11)$,
+        $1/a_22 mat(a_12, det(bold(A)); -1, a_21)$,
+        $1/a'_11 mat(a'_12, 1; -det(bold(A')), a'_21)$,
+
+        $bold(H')$,
+        $1/r_11 mat(1, -r_12; r_21, det(bold(R)))$,
+        $1/g_22 mat(det(bold(G)), g_12; -g_21, 1)$,
+        $1/det(bold(H)) mat(h_22, -h_12; -h_21, h_11)$,
+        $mat(h'_11, h'_12; h'_21, h'_22)$,
+        $1/a_11 mat(a_21, -det(bold(A)); 1, a_12)$,
+        $1/a'_22 mat(a'_21, -1; det(bold(A')), a'_12)$,
+
+        $bold(A)$,
+        $1/r_21 mat(r_11, det(bold(R)); 1, r_22)$,
+        $1/g_21 mat(-g_22, -1; -det(bold(G)), -g_11)$,
+        $1/h_21 mat(-det(bold(H)), -h_11; -h_22, -1)$,
+        $1/h'_21 mat(1, h'_22; h'_11, det(bold(H')))$,
+        $mat(a_11, a_12; a_21, a_22)$,
+        $1/det(bold(A')) mat(a'_22, a'_12; a'_21, a'_11)$,
+
+        $bold(A')$,
+        $1/r_12 mat(r_22, det(bold(R)); 1, r_11)$,
+        $1/g_12 mat(-g_11, -1; -det(bold(G)), -g_22)$,
+        $1/h_12 mat(1, h_11; h_22, det(bold(H)))$,
+        $1/h'_12 mat(-det(bold(H')), -h'_22; -h'_11, -1)$,
+        $1/det(bold(A)) mat(a_22, a_12; a_21, a_11)$,
+        $mat(a'_11, a'_12; a'_21, a'_22)$,
+      )
+  ]
+]
+
+
+
+
+#place(bottom+left, scope: "parent", float: true)[
+  #bgBlock(fill: colorAllgemein, [
+    #subHeading(fill: colorAllgemein, [Sin-Table])
+    #sinTable
+  ])
+]
+

src/lib/common_rewrite.typ

@@ -26,3 +26,20 @@
 #let MathAlignLeft(e) = {
   align(left, block(e))
 }
+
+#let sinTable = [
+  #let data = json("../sintable.json")
+  #table(
+    columns: data.at("x").len() + 1,
+    rows: data.keys().len(),
+    stroke: none,
+    table.hline(stroke: (thickness: 0.3mm)),
+    fill: (x, y) => if (calc.rem(y, 2) == 0) { color.lighten(gray, 50%) } else { white },
+      ..for (label) in data.keys() {
+      ([*#eval(label, mode: "math")*], table.hline(stroke: (thickness: 0.3mm)), )
+      for i in data.at(label) {
+        (eval(i, mode: "math"),)
+      }
+    }
+  )
+]

src/sintable.json

@@ -0,0 +1,18 @@
+
+{
+    "x": [
+        "0", "pi/6", "pi/4", "pi/3", "pi/2", "(2pi)/3", "(3pi)/4", "(5pi)/6", "pi", "(7pi)/6", "(5pi)/4", "(4pi)/3", "(3pi)/2", "(5pi)/3", "(7pi)/4", "(11pi)/6", "2pi"
+    ],
+    "alpha": [
+        "0°", "30°", "45°", "60°", "90°", "120°", "135°", "150°", "180°", "210°", "225°", "240°", "270°", "300°", "315°", "330°", "360°"
+    ],
+    "cos(x)": [
+        "1", "sqrt(3)/2", "sqrt(2)/2", "1/2", "0", "-1/2", "-sqrt(2)/2", "-sqrt(3)/2", "-1", "-sqrt(3)/2", "-sqrt(2)/2", "-1/2", "0", "1/2", "sqrt(2)/2", "sqrt(3)/2", "1"
+    ],
+    "sin(x)": [
+        "0", "1/2", "sqrt(2)/2", "sqrt(3)/2", "1", "sqrt(3)/2", "sqrt(2)/2", "1/2", "0", "-1/2", "-sqrt(2)/2", "-sqrt(3)/2", "-1", "-sqrt(3)/2", "-sqrt(2)/2", "-1/2", "0"
+    ],
+    "tan(x)": [
+        "0", "1/sqrt(3)", "1", "sqrt(3)", "x", "-sqrt(3)", "-1", "-1/sqrt(3)", "0", "1/sqrt(3)", "1", "sqrt(3)", "x", "-sqrt(3)", "-1", "-1/sqrt(3)", "0"
+    ]
+}