From adfc6c4bc496e82bdba72a39aaccf4619e82c421 Mon Sep 17 00:00:00 2001
From: h7x4 <h7x4abk3g@protonmail.com>
Date: Mon, 17 May 2021 18:39:28 +0200
Subject: [PATCH] Several fixes

---
 exam_template/python/FSA.py                   |  19 +-
 exam_template/python/Graph.py                 |  21 +-
 exam_template/python/Hasse.py                 |  20 +-
 exam_template/python/Powerset.py              |  13 ++
 exam_template/python/Relations.py             | 193 ++++++++++++++----
 exam_template/python/Truthtable.py            |  35 +---
 exam_template/python/common.py                |   7 +-
 exam_template/python/run.py                   |  31 ++-
 .../python/tex_templates/Powerset.tex         |   0
 exam_template/python/tex_templates/Python.tex |   8 +
 .../Relations/EquivalenceProof.tex            |  22 ++
 .../tex_templates/{ => Relations}/Hasse.tex   |   0
 .../tex_templates/Relations/PosetProof.tex    |  22 ++
 .../graphics/directedGraph.tex                |  33 +++
 .../graphics/equivalenceDiagram.tex           |  20 ++
 exam_template_graphics/graphics/hasse.tex     |  18 +-
 .../graphics/hasseDiagramByDivisibility.tex   |  49 +++++
 .../graphics/proveEquivalence.tex             |  42 ++++
 .../graphics/provePoset.tex                   |  27 +++
 .../graphics/src/directedGraph.txt            |  19 ++
 exam_template_graphics/graphics/src/hasse.txt |   2 +-
 .../src/hasseDiagramByDivisibility.txt        |   4 +
 .../graphics/src/powerset.txt                 |   3 +
 .../graphics/src/python.txt                   |   2 +
 .../graphics/src/truthtable.txt               |   2 +-
 .../graphics/src/undirectedGraph.txt          |   4 +-
 .../graphics/truthtable.tex                   |  18 +-
 .../graphics/undirectedGraph.tex              |   1 +
 exam_template_graphics/main.tex               |  57 ++++--
 exam_template_graphics/main.toc               |  26 ++-
 30 files changed, 563 insertions(+), 155 deletions(-)
 create mode 100644 exam_template/python/tex_templates/Powerset.tex
 create mode 100644 exam_template/python/tex_templates/Python.tex
 create mode 100644 exam_template/python/tex_templates/Relations/EquivalenceProof.tex
 rename exam_template/python/tex_templates/{ => Relations}/Hasse.tex (100%)
 create mode 100644 exam_template/python/tex_templates/Relations/PosetProof.tex
 create mode 100644 exam_template_graphics/graphics/directedGraph.tex
 create mode 100644 exam_template_graphics/graphics/equivalenceDiagram.tex
 create mode 100644 exam_template_graphics/graphics/hasseDiagramByDivisibility.tex
 create mode 100644 exam_template_graphics/graphics/proveEquivalence.tex
 create mode 100644 exam_template_graphics/graphics/provePoset.tex
 create mode 100644 exam_template_graphics/graphics/src/directedGraph.txt
 create mode 100644 exam_template_graphics/graphics/src/hasseDiagramByDivisibility.txt
 create mode 100644 exam_template_graphics/graphics/src/powerset.txt
 create mode 100644 exam_template_graphics/graphics/src/python.txt

diff --git a/exam_template/python/FSA.py b/exam_template/python/FSA.py
index be9d299..66967e8 100644
--- a/exam_template/python/FSA.py
+++ b/exam_template/python/FSA.py
@@ -2,6 +2,8 @@ from sys import argv
 from pathlib import Path
 import re
 
+from common import replaceContent
+
 placementChart = {
   'a': 'above',
   'b': 'below',
@@ -62,16 +64,17 @@ def generate_latex(inputLines):
   
   return '\n'.join(output)
 
-def processFileContent(raw, template):
+def processFileContent(raw):
   content = generate_latex(raw)
-  return template.replace('%CONTENT', content)
+  return replaceContent(content, 'FSA')
 
 if __name__ == '__main__':
-  filename = argv[1]
+  pass
+  # filename = argv[1]
 
-  with open(filename) as file:
-    content = generate_latex(file.read())
+  # with open(filename) as file:
+  #   content = generate_latex(file.read())
 
-  with open(str(Path(__file__).parent.absolute()) + '/tex_templates/FSA.tex') as template:
-    with open(argv[2], 'w') as destination_file:
-      destination_file.write(template.read().replace('%CONTENT', content))
\ No newline at end of file
+  # with open(str(Path(__file__).parent.absolute()) + '/tex_templates/FSA.tex') as template:
+  #   with open(argv[2], 'w') as destination_file:
+  #     destination_file.write(template.read().replace('%CONTENT', content))
\ No newline at end of file
diff --git a/exam_template/python/Graph.py b/exam_template/python/Graph.py
index 43afd7b..f965c64 100644
--- a/exam_template/python/Graph.py
+++ b/exam_template/python/Graph.py
@@ -2,7 +2,7 @@ from sys import argv
 from pathlib import Path
 from math import sin, cos, pi
 
-from common import printc
+from common import printc, replaceContent
 
 class Matrix:
   """ Adjacency matrix which supports 0 and 1 """
@@ -186,7 +186,7 @@ def generateNodeCoords(n):
 
   return nodeCoords
 
-def processFileContent(raw, template):
+def processFileContent(raw):
   lines = raw.split('\n')
   lines.pop(1)
   outputType = lines.pop(0)
@@ -198,15 +198,20 @@ def processFileContent(raw, template):
 
   if outputType == 'toGraph':
     content = graph.toLaTeX()
-    return template.replace('%NODES', content[0]).replace('%EDGES', content[1])
+    return replaceContent(
+      content,
+      'Graph',
+      replaceF = lambda temp, cont: temp.replace('%NODES', cont[0]).replace('%EDGES', cont[1])
+    )
   else:
     content = graph.toMatrix().toLaTeX()
-    return template.replace('%CONTENT', content)
+    return replaceContent(content, 'Matrix')
 
 
 
 if __name__ == '__main__':
-  matrix = Matrix([[False, False, True], [True, False, True], [True, False, False]])
-  print(matrix)
-  print(matrix.toGraph())
-  print(matrix.toGraph().isUndirected())
\ No newline at end of file
+  pass
+  # matrix = Matrix([[False, False, True], [True, False, True], [True, False, False]])
+  # print(matrix)
+  # print(matrix.toGraph())
+  # print(matrix.toGraph().isUndirected())
\ No newline at end of file
diff --git a/exam_template/python/Hasse.py b/exam_template/python/Hasse.py
index d98bdfe..a8dd5cb 100644
--- a/exam_template/python/Hasse.py
+++ b/exam_template/python/Hasse.py
@@ -1,7 +1,7 @@
 from sys import argv
 from pathlib import Path
 
-from common import printc
+from common import printc, replaceContent
 
 # Increase if the diagram becomes too clobbered
 HEIGHT_SEPARATOR = 1
@@ -64,23 +64,11 @@ def latex_hasse(hasse):
 
   return '\n'.join(output)
 
-def processFileContent(raw, template):
+def processFileContent(raw):
   rels = getRels(raw)
   content = latex_hasse(hasse_diagram(rels))
-  return template.replace("%CONTENT", content)
+  return replaceContent(content, 'Hasse')
 
 
 if __name__ == '__main__':
-  filename = argv[1]
-
-  with open(filename) as file:
-    rels = getRels(file.read())
-
-  # rels = getRels()
-  # rels = divisibility_graph(30)
-
-  content = latex_hasse(hasse_diagram(rels))
-  
-  with open(str(Path(__file__).parent.absolute()) + '/tex_templates/Hasse.tex') as template:
-    with open(argv[2], 'w') as destination_file:
-      destination_file.write(template.read().replace('%CONTENT', content))
+  pass
diff --git a/exam_template/python/Powerset.py b/exam_template/python/Powerset.py
index baecb06..486a7ff 100644
--- a/exam_template/python/Powerset.py
+++ b/exam_template/python/Powerset.py
@@ -1,5 +1,7 @@
 from itertools import combinations
 
+from common import replaceContent
+
 class Set:
   def __init__(self, elements):
     self.elements = set(elements)
@@ -27,6 +29,10 @@ class Set:
 
   def __le__(self, value):
     return self < value
+  
+  @classmethod
+  def fromString(cls, string):
+    return cls(string.split(' '))
 
   def cardinality(self):
     return len(self)
@@ -44,6 +50,13 @@ class Set:
       column.append(str(e) + ' \\\\')
     return '\\{\n' + '\n'.join(column) + '\n\\}'
 
+
+def processFileContent(raw):
+  s = Set.fromString(raw)
+  content = s.powerset().to_vertical_latex()
+
+  return replaceContent(content, 'Powerset')
+
 #TODO: make process input func
 
 if __name__ == "__main__":
diff --git a/exam_template/python/Relations.py b/exam_template/python/Relations.py
index 9272cfe..84e944e 100644
--- a/exam_template/python/Relations.py
+++ b/exam_template/python/Relations.py
@@ -1,11 +1,10 @@
 from sys import argv
 from pathlib import Path
 
-from common import printc, printerr
-from Graph import Graph
+from common import printc, printerr, replaceContent
+import Graph
 
 # Increase if hasse diagram becomes too clobbered
-HEIGHT_SEPARATOR = 1
 
 def pairToString(pair):
   if str(pair[0]).isdigit() or str(pair[1]).isdigit():
@@ -19,6 +18,18 @@ def stringToPair(string):
   else:
     return tuple(list(string))
 
+def textLatex(string):
+  return '\\text{' + string + '}'
+
+def mathModeListLatex(elements):
+  if len(elements) > 7 or len(elements) and max(len(str(e)) for e in elements) > 10:
+    return '\\begin{gather*}\n' \
+         + ' \\\\\n'.join(elements) + '\n' \
+         + '\\end{gather*}'
+  else:
+    return f'\\[ {", ".join(elements)} \\]'
+
+
 
 class Relation:
   def __init__(self, pairs): # pair = (str,str)
@@ -29,7 +40,7 @@ class Relation:
 
   @classmethod
   def fromString(cls, string):
-    relations = (stringToPair(x) for x in relations.split(' '))
+    relations = (stringToPair(x) for x in string.split(' '))
     return cls(relations)
 
   @classmethod
@@ -43,7 +54,7 @@ class Relation:
     return cls(pairs)
 
 
-  def isReflexive(self):
+  def isReflexive(self, verbose=False):
     elements = set(list(sum(self.pairs, ())))
     result = all((x,x) in self.pairs for x in elements)
 
@@ -51,31 +62,47 @@ class Relation:
       printc('Not reflexive, missing following pairs:', color='green')
       missingPairs = [(x,x) for x in elements if (x,x) not in self.pairs]
       print(f'\\[ {", ".join(pairToString(p) for p in missingPairs)} \\]')
+      if verbose:
+        return (False, missingPairs)
+
+    if verbose:
+      return (True, [(x,x) for x in elements if (x,x) in self.pairs])
     
     return result
 
-  def isSymmetric(self):
+  def isSymmetric(self, verbose=False):
     result = all((y,x) in self.pairs for x,y in self.pairs)
 
     if not result:
       printc('Not symmetric, missing following pairs:', color='green')
       missingPairs = [(x,y) for x,y in self.pairs if (y,x) not in self.pairs]
       print(f'\\[ {", ".join(pairToString(p) for p in missingPairs)} \\]')
-  
+      if verbose:
+        return (False, missingPairs)
+      
+    if verbose:
+      return (True, [((x,y), (y,x)) for x,y in self.pairs if (y,x) in self.pairs and x < y])
+
     return result
 
-  def isAntiSymmetric(self):
+  def isAntiSymmetric(self, verbose=False):
     result = not any((y,x) in self.pairs and y != x for x,y in self.pairs)
 
     if not result:
       printc('Not antisymmetric, following pairs are symmetric:', color='green')
       symmetricPairs = [((x,y), (y,x)) for x,y in self.pairs if (y,x) in self.pairs and y > x]
-      print(f'\\[ {", ".join(f"{pairToString(p)} and {pairToString(q)}" for p,q in symmetricPairs)} \\]')
+      print(f'\\[ {", ".join(f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}""" for p,q in symmetricPairs)} \\]')
+      if verbose:
+        return (False, symmetricPairs)
+
+    if verbose:
+      return (True, [])
 
     return result
 
-  def isTransitive(self):
+  def isTransitive(self, verbose=False):
     result = True
+    transitivePairs = []
     nonTransitivePairs = []
 
     for x,y in self.pairs:
@@ -83,33 +110,110 @@ class Relation:
         if not (y != z or ((x,w) in self.pairs)):
           nonTransitivePairs.append(((x,y), (z,w)))
           result = False
+        elif (y == z and x != y != w and ((x,w) in self.pairs)):
+          transitivePairs.append(((x,y), (z,w)))
     
     if not result:
       printc('Not transitive, following pairs are missing its transitive counterpart:', color='green')
-      print(f'\\[ {", ".join(f"{pairToString(p)} and {pairToString(q)} without {pairToString((p[0], q[1]))}" for p,q in nonTransitivePairs)} \\]')
+      print(f'\\[ {", ".join(f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}{textLatex(" without ")}{pairToString((p[0], q[1]))}""" for p,q in nonTransitivePairs)} \\]')
+      if verbose:
+        return (False, nonTransitivePairs)
+    
+    if verbose:
+      return (True, transitivePairs)
 
     return result
 
-  def isEquivalenceRelation(self):
+  def isEquivalenceRelation(self, verbose=False):
+
+    if verbose:
+      isReflexive,  reflexivePairs  = self.isReflexive(verbose=True)
+      isSymmetric,  symmetricPairs  = self.isSymmetric(verbose=True)
+      isTransitive, transitivePairs = self.isTransitive(verbose=True)
+
+      if not isReflexive:
+        return 'The relation is not an equivalence relation, because it is not reflexive.'
+        + ' The following elements should be related:\n\n'
+        + f'\\[ {", ".join(pairToString(p) for p in reflexivePairs)} \\]'
+      if not isSymmetric:
+        return 'The relation is not an equivalence relation, because it is not symmetric.'
+        + ' It is missing the following symmetric pairs of relations\n\n'
+        + f'\\[ {", ".join(f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}""" for p,q in symmetricPairs)} \\]'
+      if not isTransitive:
+        return 'The relation is not an equivalence relation, because it is not transitive.'
+        + ' The following pairs of relations are missing its transitive counterpart\n\n'
+        + f'\\[ {", ".join(f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}{textLatex(" without ")}{pairToString((p[0], q[1]))}""" for p,q in transitivePairs)} \\]'
+      
+
+      rxStr = mathModeListLatex([pairToString(p) for p in reflexivePairs])
+      smStr = mathModeListLatex([f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}""" for p,q in symmetricPairs])
+      trStr = mathModeListLatex([f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}{textLatex(" with ")}{pairToString((p[0], q[1]))}""" for p,q in transitivePairs])
+      
+      return replaceContent(
+        (rxStr, smStr, trStr),
+        'Relations/EquivalenceProof',
+        lambda temp, cont: temp.replace('%REFLEXIVE', cont[0]).replace('%SYMMETRIC', cont[1]).replace('%TRANSITIVE', cont[2])
+        )
+
     return self.isReflexive() and self.isSymmetric() and self.isTransitive()
 
-  def isPartialOrder(self):
-    return self.isReflexive() and self.isAntiSymmetric() and self.isTransitive()
-  
-  def getHassePairs(self):
-    if not self.isPartialOrder():
+  def isPartialOrder(self, verbose=False):
+
+    result = self.isReflexive() and self.isAntiSymmetric() and self.isTransitive()
+
+    if result:
+      hasse= self.getHassePairs(checkIfPartialOrder=False)
+      min_el = set(a for a,b in hasse if a not in list(zip(*hasse))[1])
+      printc(f"Minimal elements: $\{{ {', '.join(str(e) for e in min_el)} \}}$ \\\\")
+
+      max_el = set(v for k,v in hasse if v not in (x for x,_ in hasse))
+      printc(f"Maximal elements: $\{{ {', '.join(str(e) for e in max_el)} \}}$" )
+
+    if verbose:
+      isReflexive,     reflexivePairs     = self.isReflexive(verbose=True)
+      isAntiSymmetric, antiSymmetricPairs = self.isAntiSymmetric(verbose=True)
+      isTransitive,    transitivePairs    = self.isTransitive(verbose=True)
+
+      if not isReflexive:
+        return 'The relation is not a partial order, because it is not reflexive.'
+        + ' The following elements should be related:\n\n'
+        + f'\\[ {", ".join(pairToString(p) for p in reflexivePairs)} \\]'
+      if not isAntiSymmetric:
+        return 'The relation is not a partial order, because it is not antisymmetric.'
+        + ' The following relations are symmetric\n\n'
+        + f'\\[ {", ".join(f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}""" for p,q in antiSymmetricPairs)} \\]'
+      if not isTransitive:
+        return 'The relation is not a partial order, because it is not transitive.'
+        + ' The following pairs of relations are missing its transitive counterpart\n\n'
+        + f'\\[ {", ".join(f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}{textLatex(" without ")}{pairToString((p[0], q[1]))}""" for p,q in transitivePairs)} \\]'
+      
+      rxStr = mathModeListLatex([pairToString(p) for p in reflexivePairs])
+      trStr = mathModeListLatex([f"""{pairToString(p)}{textLatex(" and ")}{pairToString(q)}{textLatex(" with ")}{pairToString((p[0], q[1]))}""" for p,q in transitivePairs])
+      
+      return replaceContent(
+        (rxStr, trStr),
+        'Relations/PosetProof',
+        lambda temp, cont: temp.replace('%REFLEXIVE', cont[0]).replace('%TRANSITIVE', cont[1])
+        )
+
+    return result
+
+  def getHassePairs(self, checkIfPartialOrder=True):
+    if checkIfPartialOrder and not self.isPartialOrder():
       printerr('This is not a partial order')
       return
+    
+    nonReflexivePairs = set((x,y) for x,y in self.pairs if x != y)
+
     hassePairs = set()
-    for x1, y1 in self.pairs:
-      for x2, y2 in self.pairs:
+    for x1, y1 in nonReflexivePairs:
+      for x2, y2 in nonReflexivePairs:
         if y1 == x2:
           hassePairs.add((x1, y2))
-    return self.pairs - hassePairs
+    return nonReflexivePairs - hassePairs
   
   def latexifyHasseDiagram(self):
     hasse = self.getHassePairs()
-    min_el = set(a for a,b in hasse if a not in list(zip(*hasse))[1])
     keys = set(item for tup in hasse for item in tup)
     y_pos = dict.fromkeys(keys, 0)
 
@@ -127,19 +231,13 @@ class Relation:
   
     for y in inv_ypos.keys():
       for i, n in enumerate(inv_ypos[y]):
-        output.append(f'\\node ({n}) at ({i - len(inv_ypos[y])/2}, {y * HEIGHT_SEPARATOR}) {{${n}$}};')
+        output.append(f'\\node ({n}) at ({i - len(inv_ypos[y])/2}, {y * 0.5 * (len(hasse) ** 0.4)}) {{${n}$}};')
   
     output.append('')
 
     for x,y in hasse:
       output.append(f'\\draw ({x}) -- ({y});')
 
-
-    printc(f"Minimal elements: $\{{ {', '.join(str(e) for e in min_el)} \}}$ \\\\")
-
-    max_el = set(v for k,v in hasse if v not in (x for x,_ in hasse))
-    printc(f"Maximal elements: $\{{ {', '.join(str(e) for e in max_el)} \}}$" )
-
     return '\n'.join(output)
 
   def latexifyGraph(self):
@@ -150,33 +248,46 @@ class Relation:
       graphType = 'directed'
       pairs = self.pairs
     
-    pass
+    nodes = set()
+    for x,y in pairs:
+      nodes.add(x)
+      nodes.add(y)
     
+    edges = "\n".join(pairToString(p) for p in pairs)
+    
+    processingString = f'toGraph\n\n{graphType}\n\n{ " ".join(nodes) }\n\n{edges}'
+    return Graph.processFileContent(processingString)
 
-def processFileContent(raw, template):
+
+def processFileContent(raw):
   outputType, inp =  raw.split('\n\n')
 
-  if inp.startsWith('divisibilityPosetTo'):
+  if inp.startswith('divisibilityPosetTo'):
     n = int(inp.split(' ')[1])
     relation = Relation.fromDivisibilityPosetTo(n)
   else: 
     relation = Relation.fromString(inp)
 
   if outputType == 'proveEquivalence':
-    content = relation.isEquivalenceRelation()
+    content = relation.isEquivalenceRelation(verbose=True)
+    return content
+
   elif outputType == 'provePoset':
-    content = relation.isPartialOrder()
+    content = relation.isPartialOrder(verbose=True)
+    return content
+
   elif outputType == 'hasseDiagram':
     content = relation.latexifyHasseDiagram()
+    return replaceContent(content, 'Relations/Hasse')
+
   elif outputType == 'graph':
     content = relation.latexifyGraph()
-
-  content = Relation.fromString(raw).latexifyHasseDiagram()
-  return template.replace("%CONTENT", content)
+    return content 
 
 if __name__ == '__main__':
-  inp = 'AA BB CC DD AB AC AD BC BD CD'
-  relations = [stringToPair(p) for p in inp.split(' ')]
-  # print(Relation(relations).isEquivalenceRelation())
-  print(Relation(relations).isPartialOrder())
-  print(Relation.fromDivisibilityPosetTo(30).isPartialOrder())
+  pass
+  # inp = 'AA BB CC DD AB AC AD BC BD CD'
+  # relations = [stringToPair(p) for p in inp.split(' ')]
+  # # print(Relation(relations).isEquivalenceRelation())
+  # print(Relation(relations).isPartialOrder())
+  # print(Relation.fromDivisibilityPosetTo(30).isPartialOrder())
diff --git a/exam_template/python/Truthtable.py b/exam_template/python/Truthtable.py
index f5e101e..3426e63 100644
--- a/exam_template/python/Truthtable.py
+++ b/exam_template/python/Truthtable.py
@@ -1,7 +1,7 @@
 from sys import argv
 from pathlib import Path
 
-from common import printerr
+from common import printerr, replaceContent
 
 try:
   from tabulate import tabulate
@@ -20,18 +20,21 @@ class OverloadedBool:
     self.val = val
   
   def __bool__(self):
-    return self.val
+    val = self.val
+    while(type(val) is OverloadedBool):
+      val = val.val
+    return val
 
   def __str__(self):
     return str(self.val)
 
   def __add__(self, bool2):
     """ Implies """
-    return (not self.val or bool2)
+    return OverloadedBool(not self.val or bool2)
 
   def __sub__(self, bool2):
     """ Iff """
-    return (not self.val or bool2) and (not bool2 or self.val)
+    return OverloadedBool((not self.val or bool2) and (not bool2 or self.val))
 
 def flattenImpliesIff(exps):
   return [exp.replace('implies', '+').replace('iff', '-').replace('E', '') for exp in exps]
@@ -51,7 +54,7 @@ def generateTruthTable(exps):
     def calculateGridLine():
       line = []
       for exp in exps:
-        exec(f'line.append(({exp}).__bool__())')
+        exec(f'line.append(({exp}))')
       return line
     
     truthtable.append(calculateGridLine())
@@ -95,30 +98,14 @@ def printTruthtable(exps, truthtable):
   except:
     pass
 
-
-def processFileContent(raw, template):
+def processFileContent(raw):
   exps = parseExpressionList(raw)
   truthtable = generateTruthTable(exps)
 
   printTruthtable(exps, generateTruthTable(exps))
 
   content = latexify(exps, truthtable)
-  return template.replace('%CONTENT', content)
-
-
+  return replaceContent(content, 'Truthtable')
 
 if __name__ == '__main__':
-  filename = argv[1]
-
-  with open(filename) as file:
-    exps = parseExpressionList(file.read())
-    truthtable = generateTruthTable(exps)
-
-    from tabulate import tabulate
-    printTruthtable(exps, generateTruthTable(exps))
-
-    content = latexify(exps, truthtable)
-
-  with open(str(Path(__file__).parent.absolute()) + '/tex_templates/Truthtable.tex') as template:
-    with open(argv[2], 'w') as destination_file:
-      destination_file.write(template.read().replace('%CONTENT', content))
\ No newline at end of file
+  pass
\ No newline at end of file
diff --git a/exam_template/python/common.py b/exam_template/python/common.py
index 974d7ef..77774a9 100644
--- a/exam_template/python/common.py
+++ b/exam_template/python/common.py
@@ -1,3 +1,4 @@
+from pathlib import Path
 
 clear = '\033[0m'
 colors = {
@@ -13,4 +14,8 @@ def printc(text, color='blue'):
   print(f'{colors[color]}{text}{clear}')
 
 def printerr(text):  
-  print(f'\033[31;5m[ERROR] {text}{clear}')
\ No newline at end of file
+  print(f'\033[31;5m[ERROR] {text}{clear}')
+
+def replaceContent(content, template, replaceF = lambda temp, cont: temp.replace("%CONTENT", cont)):
+  with open(str(Path(__file__).parent.absolute()) + f'/tex_templates/{template}.tex') as template:
+    return replaceF(template.read(), content)
\ No newline at end of file
diff --git a/exam_template/python/run.py b/exam_template/python/run.py
index 77ac917..3f5ef7d 100644
--- a/exam_template/python/run.py
+++ b/exam_template/python/run.py
@@ -15,22 +15,21 @@ def fetchContentType(content):
 
 def processContent(content):
   contentType, content =  fetchContentType(content)
-  with open(str(Path(__file__).parent.absolute()) + f'/tex_templates/{contentType}.tex') as template:
-    if contentType == 'Hasse':
-      result = Hasse.processFileContent(content, template.read())
-    elif contentType == 'FSA':
-      result = FSA.processFileContent(content, template.read())
-    elif contentType == 'Graph':
-      result = Graph.processFileContent('toGraph\n\n' + content, template.read())
-    elif contentType == 'Matrix':
-      result = Graph.processFileContent('toMatrix\n\n' + content, template.read())
-    elif contentType == 'Relations':
-      result = Relations.processFileContent(content, template.read())
-    elif contentType == 'Truthtable':
-      result = Truthtable.processFileContent(content, template.read())
-    else:
-      printerr('DIDN\'T RECOGNIZE FILE TYPE')
-      exit(1)
+
+  if contentType == 'FSA':
+    result = FSA.processFileContent(content)
+  elif contentType == 'Graph':
+    result = Graph.processFileContent('toGraph\n\n' + content)
+  elif contentType == 'Matrix':
+    result = Graph.processFileContent('toMatrix\n\n' + content)
+  elif contentType == 'Relations':
+    result = Relations.processFileContent(content)
+  elif contentType == 'Truthtable':
+    result = Truthtable.processFileContent(content)
+  else:
+    printerr('DIDN\'T RECOGNIZE FILE TYPE')
+    exit(1)
+
   return result
     
 if __name__ == '__main__':
diff --git a/exam_template/python/tex_templates/Powerset.tex b/exam_template/python/tex_templates/Powerset.tex
new file mode 100644
index 0000000..e69de29
diff --git a/exam_template/python/tex_templates/Python.tex b/exam_template/python/tex_templates/Python.tex
new file mode 100644
index 0000000..37f07af
--- /dev/null
+++ b/exam_template/python/tex_templates/Python.tex
@@ -0,0 +1,8 @@
+
+\codeFile{%CODEFILE}{python}
+
+Output:
+
+\begin{verbatim}
+%OUTPUT
+\end{verbatim}
\ No newline at end of file
diff --git a/exam_template/python/tex_templates/Relations/EquivalenceProof.tex b/exam_template/python/tex_templates/Relations/EquivalenceProof.tex
new file mode 100644
index 0000000..46a7ad7
--- /dev/null
+++ b/exam_template/python/tex_templates/Relations/EquivalenceProof.tex
@@ -0,0 +1,22 @@
+
+In order for this relation to be an equivalence equation, it has to be reflexive, symmetric and transitive.
+
+\textbf{Reflexive:}
+
+All elements are related to themself
+
+%REFLEXIVE
+
+\textbf{Symmetric:}
+
+All relations has its symmetric counterpart
+
+%SYMMETRIC
+
+\textbf{Transitive:}
+
+All pair of relations where $xRy$ and $yRz$ has its transitive counterpart
+
+%TRANSITIVE
+
+Hence the relation is an equivalence relation
\ No newline at end of file
diff --git a/exam_template/python/tex_templates/Hasse.tex b/exam_template/python/tex_templates/Relations/Hasse.tex
similarity index 100%
rename from exam_template/python/tex_templates/Hasse.tex
rename to exam_template/python/tex_templates/Relations/Hasse.tex
diff --git a/exam_template/python/tex_templates/Relations/PosetProof.tex b/exam_template/python/tex_templates/Relations/PosetProof.tex
new file mode 100644
index 0000000..f168ced
--- /dev/null
+++ b/exam_template/python/tex_templates/Relations/PosetProof.tex
@@ -0,0 +1,22 @@
+
+In order for this relation to be a partial order, it has to be reflexive, antisymmetric and transitive.
+
+\textbf{Reflexive:}
+
+All elements are related to themself
+
+%REFLEXIVE
+
+\textbf{Antisymmetric:}
+
+No relation have a symmetric counterpart \\
+
+(Listing the ones that don't have a symmetric counterpart would just be listing the whole set) \\
+
+\textbf{Transitive:}
+
+All pair of relations where $xRy$ and $yRz$ has its transitive counterpart
+
+%TRANSITIVE
+
+Hence the relation is a partial order
diff --git a/exam_template_graphics/graphics/directedGraph.tex b/exam_template_graphics/graphics/directedGraph.tex
new file mode 100644
index 0000000..42db8fe
--- /dev/null
+++ b/exam_template_graphics/graphics/directedGraph.tex
@@ -0,0 +1,33 @@
+\newcommand{\arrow}[2]{\path [-{Latex[scale=1]}] (#1) edge (#2);}
+
+\begin{tikzpicture}
+
+  \begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
+    \node (A) at (0,4.0) {$A$};
+\node (B) at (-2.82843,2.82843) {$B$};
+\node (C) at (-4.0,0.0) {$C$};
+\node (D) at (-2.82843,-2.82843) {$D$};
+\node (E) at (-0.0,-4.0) {$E$};
+\node (F) at (2.82843,-2.82843) {$F$};
+\node (G) at (4.0,-0.0) {$G$};
+\node (H) at (2.82843,2.82843) {$H$};
+  \end{scope}
+
+  \begin{scope}[every draw/.style={}]
+    \draw [-{Latex[scale=1]}] (A) to (B);
+\draw [-{Latex[scale=1]}] (A) to (C);
+\draw [-{Latex[scale=1]}] (C) to (D);
+\draw [-{Latex[scale=1]}] (D) to (E);
+\draw [-{Latex[scale=1]}, bend left=8] (H) to (A);
+\draw [-{Latex[scale=1]}] (F) to (D);
+\draw [-{Latex[scale=1]}] (C) to (B);
+\draw [-{Latex[scale=1]}] (F) to (G);
+\draw [-{Latex[scale=1]}] (D) to (E);
+\draw [-{Latex[scale=1]}] (D) to (G);
+\draw [-{Latex[scale=1]}, bend left=8] (A) to (H);
+\draw [-{Latex[scale=1]}] (F) to (B);
+\draw [-{Latex[scale=1]}, bend left=8] (H) to (C);
+\draw [-{Latex[scale=1]}, bend left=8] (C) to (H);
+  \end{scope}
+
+\end{tikzpicture}
diff --git a/exam_template_graphics/graphics/equivalenceDiagram.tex b/exam_template_graphics/graphics/equivalenceDiagram.tex
new file mode 100644
index 0000000..dd80172
--- /dev/null
+++ b/exam_template_graphics/graphics/equivalenceDiagram.tex
@@ -0,0 +1,20 @@
+\newcommand{\arrow}[2]{\path [-{Latex[scale=1]}] (#1) edge (#2);}
+
+\begin{tikzpicture}
+
+  \begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
+    \node (B) at (0,2.5) {$B$};
+\node (D) at (-2.37764,0.77254) {$D$};
+\node (C) at (-1.46946,-2.02254) {$C$};
+\node (A) at (1.46946,-2.02254) {$A$};
+\node (E) at (2.37764,0.77254) {$E$};
+  \end{scope}
+
+  \begin{scope}[every draw/.style={}]
+    \draw (A) -- (C);
+\draw (A) -- (E);
+\draw (B) -- (D);
+\draw (C) -- (E);
+  \end{scope}
+
+\end{tikzpicture}
diff --git a/exam_template_graphics/graphics/hasse.tex b/exam_template_graphics/graphics/hasse.tex
index add93b2..48f4c70 100644
--- a/exam_template_graphics/graphics/hasse.tex
+++ b/exam_template_graphics/graphics/hasse.tex
@@ -1,16 +1,16 @@
 \begin{tikzpicture}
   \tikzset{every node/.style={shape=circle,draw,inner sep=2pt}}
 
-\node (a) at (-0.5, 0) {$a$};
-\node (b) at (-1.0, 1) {$b$};
-\node (e) at (0.0, 1) {$e$};
-\node (c) at (-1.0, 2) {$c$};
-\node (d) at (0.0, 2) {$d$};
+\node (a) at (-0.5, 0.0) {$a$};
+\node (e) at (-1.0, 0.9518269693579393) {$e$};
+\node (b) at (0.0, 0.9518269693579393) {$b$};
+\node (d) at (-1.0, 1.9036539387158786) {$d$};
+\node (c) at (0.0, 1.9036539387158786) {$c$};
 
-\draw (e) -- (d);
-\draw (a) -- (e);
-\draw (b) -- (c);
-\draw (a) -- (b);
 \draw (e) -- (c);
+\draw (e) -- (d);
+\draw (b) -- (c);
+\draw (a) -- (e);
+\draw (a) -- (b);
 
 \end{tikzpicture}
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/hasseDiagramByDivisibility.tex b/exam_template_graphics/graphics/hasseDiagramByDivisibility.tex
new file mode 100644
index 0000000..5703803
--- /dev/null
+++ b/exam_template_graphics/graphics/hasseDiagramByDivisibility.tex
@@ -0,0 +1,49 @@
+\begin{tikzpicture}
+  \tikzset{every node/.style={shape=circle,draw,inner sep=2pt}}
+
+\node (1) at (-0.5, 0.0) {$1$};
+\node (2) at (-4.0, 1.7826024579660036) {$2$};
+\node (3) at (-3.0, 1.7826024579660036) {$3$};
+\node (5) at (-2.0, 1.7826024579660036) {$5$};
+\node (7) at (-1.0, 1.7826024579660036) {$7$};
+\node (11) at (0.0, 1.7826024579660036) {$11$};
+\node (13) at (1.0, 1.7826024579660036) {$13$};
+\node (17) at (2.0, 1.7826024579660036) {$17$};
+\node (19) at (3.0, 1.7826024579660036) {$19$};
+\node (4) at (-3.0, 3.565204915932007) {$4$};
+\node (6) at (-2.0, 3.565204915932007) {$6$};
+\node (9) at (-1.0, 3.565204915932007) {$9$};
+\node (10) at (0.0, 3.565204915932007) {$10$};
+\node (14) at (1.0, 3.565204915932007) {$14$};
+\node (15) at (2.0, 3.565204915932007) {$15$};
+\node (8) at (-1.5, 5.347807373898011) {$8$};
+\node (12) at (-0.5, 5.347807373898011) {$12$};
+\node (18) at (0.5, 5.347807373898011) {$18$};
+\node (16) at (-0.5, 7.130409831864014) {$16$};
+
+\draw (6) -- (12);
+\draw (6) -- (18);
+\draw (4) -- (12);
+\draw (5) -- (10);
+\draw (1) -- (3);
+\draw (2) -- (14);
+\draw (3) -- (9);
+\draw (4) -- (8);
+\draw (3) -- (6);
+\draw (3) -- (15);
+\draw (5) -- (15);
+\draw (2) -- (4);
+\draw (1) -- (2);
+\draw (1) -- (5);
+\draw (1) -- (11);
+\draw (2) -- (10);
+\draw (1) -- (17);
+\draw (8) -- (16);
+\draw (1) -- (7);
+\draw (1) -- (13);
+\draw (2) -- (6);
+\draw (9) -- (18);
+\draw (1) -- (19);
+\draw (7) -- (14);
+
+\end{tikzpicture}
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/proveEquivalence.tex b/exam_template_graphics/graphics/proveEquivalence.tex
new file mode 100644
index 0000000..14e76bb
--- /dev/null
+++ b/exam_template_graphics/graphics/proveEquivalence.tex
@@ -0,0 +1,42 @@
+
+In order for this relation to be an equivalence equation, it has to be reflexive, symmetric and transitive.
+
+\textbf{Reflexive:}
+
+All elements are related to themself
+
+\[ AA, DD, CC, EE, BB \]
+
+\textbf{Symmetric:}
+
+All relations has its symmetric counterpart
+
+\begin{gather*}
+AE\text{ and }EA \\
+AC\text{ and }CA \\
+BD\text{ and }DB \\
+CE\text{ and }EC
+\end{gather*}
+
+\textbf{Transitive:}
+
+All pair of relations where $xRy$ and $yRz$ has its transitive counterpart
+
+\begin{gather*}
+DB\text{ and }BD\text{ with }DD \\
+AE\text{ and }EA\text{ with }AA \\
+AE\text{ and }EC\text{ with }AC \\
+AC\text{ and }CE\text{ with }AE \\
+AC\text{ and }CA\text{ with }AA \\
+BD\text{ and }DB\text{ with }BB \\
+CE\text{ and }EA\text{ with }CA \\
+CE\text{ and }EC\text{ with }CC \\
+EA\text{ and }AE\text{ with }EE \\
+EA\text{ and }AC\text{ with }EC \\
+EC\text{ and }CE\text{ with }EE \\
+EC\text{ and }CA\text{ with }EA \\
+CA\text{ and }AE\text{ with }CE \\
+CA\text{ and }AC\text{ with }CC
+\end{gather*}
+
+Hence the relation is an equivalence relation
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/provePoset.tex b/exam_template_graphics/graphics/provePoset.tex
new file mode 100644
index 0000000..aaa773f
--- /dev/null
+++ b/exam_template_graphics/graphics/provePoset.tex
@@ -0,0 +1,27 @@
+
+In order for this relation to be a partial order, it has to be reflexive, antisymmetric and transitive.
+
+\textbf{Reflexive:}
+
+All elements are related to themself
+
+\[ AA, BB, CC, DD \]
+
+\textbf{Antisymmetric:}
+
+No relation have a symmetric counterpart \\
+
+(Listing the ones that don't have a symmetric counterpart would just be listing the whole set) \\
+
+\textbf{Transitive:}
+
+All pair of relations where $xRy$ and $yRz$ has its transitive counterpart
+
+\begin{gather*}
+AB\text{ and }BD\text{ with }AD \\
+AB\text{ and }BC\text{ with }AC \\
+BC\text{ and }CD\text{ with }BD \\
+AC\text{ and }CD\text{ with }AD
+\end{gather*}
+
+Hence the relation is a partial order
diff --git a/exam_template_graphics/graphics/src/directedGraph.txt b/exam_template_graphics/graphics/src/directedGraph.txt
new file mode 100644
index 0000000..92fe9a5
--- /dev/null
+++ b/exam_template_graphics/graphics/src/directedGraph.txt
@@ -0,0 +1,19 @@
+# Graph
+directed
+
+A B C D E F G H
+
+AB
+AC
+CD
+DE
+HA
+FD
+CB
+FG
+DE
+DG
+AH
+FB
+HC
+CH
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/src/hasse.txt b/exam_template_graphics/graphics/src/hasse.txt
index 07d095d..d1cd5a3 100644
--- a/exam_template_graphics/graphics/src/hasse.txt
+++ b/exam_template_graphics/graphics/src/hasse.txt
@@ -1,4 +1,4 @@
 # Relations
 hasseDiagram
 
-ab ac ad ae bc ed ec
\ No newline at end of file
+aa bb cc dd ee ab ac ad ae bc ed ec
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/src/hasseDiagramByDivisibility.txt b/exam_template_graphics/graphics/src/hasseDiagramByDivisibility.txt
new file mode 100644
index 0000000..48fc891
--- /dev/null
+++ b/exam_template_graphics/graphics/src/hasseDiagramByDivisibility.txt
@@ -0,0 +1,4 @@
+# Relations
+hasseDiagram
+
+divisibilityPosetTo 20
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/src/powerset.txt b/exam_template_graphics/graphics/src/powerset.txt
new file mode 100644
index 0000000..c9f8b01
--- /dev/null
+++ b/exam_template_graphics/graphics/src/powerset.txt
@@ -0,0 +1,3 @@
+# Powerset
+
+A B C D (E F) (A (B C))
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/src/python.txt b/exam_template_graphics/graphics/src/python.txt
new file mode 100644
index 0000000..6376748
--- /dev/null
+++ b/exam_template_graphics/graphics/src/python.txt
@@ -0,0 +1,2 @@
+# python
+
diff --git a/exam_template_graphics/graphics/src/truthtable.txt b/exam_template_graphics/graphics/src/truthtable.txt
index cb6173e..e2339f4 100644
--- a/exam_template_graphics/graphics/src/truthtable.txt
+++ b/exam_template_graphics/graphics/src/truthtable.txt
@@ -1,2 +1,2 @@
 # Truthtable
-p, q, s, p and q, p implies q, E p iff q, p iff (q and s)
\ No newline at end of file
+p, q, s, p and q, E p iff q, p iff (q and s), E not ((not p and q) or (not p and not q)) or (p and q)
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/src/undirectedGraph.txt b/exam_template_graphics/graphics/src/undirectedGraph.txt
index 143c9af..496201b 100644
--- a/exam_template_graphics/graphics/src/undirectedGraph.txt
+++ b/exam_template_graphics/graphics/src/undirectedGraph.txt
@@ -14,4 +14,6 @@ FG
 DE
 DG
 AH
-FB
\ No newline at end of file
+FB
+HC
+CH
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/truthtable.tex b/exam_template_graphics/graphics/truthtable.tex
index f8e2d5c..428e35c 100644
--- a/exam_template_graphics/graphics/truthtable.tex
+++ b/exam_template_graphics/graphics/truthtable.tex
@@ -1,14 +1,14 @@
 
   \begin{truthtable}
-    {c|c|c|c|c|e|c}
-    {$p$ & $q$ & $s$ & $p \wedge q$ & $p \Rightarrow q$ & $ p \Leftrightarrow q$ & $p \Leftrightarrow (q \wedge s)$}
+    {c|c|c|c|e|c|e}
+    {$p$ & $q$ & $s$ & $p \wedge q$ & $ p \Leftrightarrow q$ & $p \Leftrightarrow (q \wedge s)$ & $ \neg ((\neg p \wedge q) \vee (\neg p \wedge \neg q)) \vee (p \wedge q)$}
     \T & \T & \T & \T & \T & \T & \T \\
-    \T & \T & \F & \T & \T & \T & \F \\
-    \T & \F & \T & \F & \F & \F & \F \\
-    \T & \F & \F & \F & \F & \F & \F \\
-    \F & \T & \T & \F & \T & \F & \F \\
-    \F & \T & \F & \F & \T & \F & \T \\
-    \F & \F & \T & \F & \T & \T & \T \\
-    \F & \F & \F & \F & \T & \T & \T \\
+    \T & \T & \F & \T & \T & \F & \T \\
+    \T & \F & \T & \F & \F & \F & \T \\
+    \T & \F & \F & \F & \F & \F & \T \\
+    \F & \T & \T & \F & \F & \F & \F \\
+    \F & \T & \F & \F & \F & \T & \F \\
+    \F & \F & \T & \F & \T & \T & \F \\
+    \F & \F & \F & \F & \T & \T & \F \\
   \end{truthtable}
   
\ No newline at end of file
diff --git a/exam_template_graphics/graphics/undirectedGraph.tex b/exam_template_graphics/graphics/undirectedGraph.tex
index 87b373d..196265b 100644
--- a/exam_template_graphics/graphics/undirectedGraph.tex
+++ b/exam_template_graphics/graphics/undirectedGraph.tex
@@ -20,6 +20,7 @@
 \draw (B) -- (C);
 \draw (B) -- (F);
 \draw (C) -- (D);
+\draw (C) -- (H);
 \draw (D) -- (E);
 \draw (D) -- (F);
 \draw (D) -- (G);
diff --git a/exam_template_graphics/main.tex b/exam_template_graphics/main.tex
index 009605b..7886141 100644
--- a/exam_template_graphics/main.tex
+++ b/exam_template_graphics/main.tex
@@ -16,10 +16,21 @@
 \renewcommand{\theenumiii}{\alph{enumiii})}
 
 \usepackage{verbatim}
+\usepackage{listings}
+
+\newcommand{\listFile}[1]{
+  \lstinputlisting
+    [ frame=single,
+      basicstyle=\small,
+      breaklines
+    ]
+    {graphics/src/#1.txt}
+}
 
 \newcommand{\verbatimDiagram}[1]{
-  \section{#1}
-  \verbatiminput{graphics/src/#1.txt}
+  \subsection{#1}
+
+  \listFile{#1}
 
   \includeDiagram{graphics/#1.tex}
 
@@ -27,9 +38,9 @@
 }
 
 \newcommand{\verbatimInput}[1]{
-  \section{#1}
+  \subsection{#1}
 
-  \verbatiminput{graphics/src/#1.txt}
+  \listFile{#1}
 
   \input{graphics/#1.tex}
 
@@ -43,20 +54,42 @@
 
   \tableofcontents
 
-  \verbatimDiagram{hasse}
+  \newpage{}
 
-  \verbatimDiagram{automata}
+  \section{Propositional Logic}
 
-  \verbatimInput{truthtable}
+    \verbatimInput{truthtable}
 
-  \verbatimDiagram{undirectedGraph}
+  \section{Sets}
 
-  \verbatimDiagram{complete6}
+  \section{Relations}
 
-  \verbatimDiagram{adjacency}
+    \verbatimInput{proveEquivalence}
 
-  \verbatimInput{undirectedGraphToMatrix}
+    \verbatimInput{provePoset}
 
-  \verbatimDiagram{directedFromMatrix}
+    \verbatimDiagram{equivalenceDiagram}
+
+    \verbatimDiagram{hasse}
+
+    \verbatimDiagram{hasseDiagramByDivisibility}
+
+  \section{Graph theory}
+
+    \verbatimDiagram{undirectedGraph}
+
+    \verbatimDiagram{directedGraph}
+
+    \verbatimDiagram{complete6}
+
+    \verbatimDiagram{adjacency}
+
+    \verbatimInput{undirectedGraphToMatrix}
+
+    \verbatimDiagram{directedFromMatrix}
+
+  \section{Finite state automata}
+
+    \verbatimDiagram{automata}
 
 \end{document}
\ No newline at end of file
diff --git a/exam_template_graphics/main.toc b/exam_template_graphics/main.toc
index 16a8a90..a96543f 100644
--- a/exam_template_graphics/main.toc
+++ b/exam_template_graphics/main.toc
@@ -1,9 +1,19 @@
 \babel@toc {english}{}
-\contentsline {section}{\numberline {1}hasse}{1}{section.1}%
-\contentsline {section}{\numberline {2}automata}{2}{section.2}%
-\contentsline {section}{\numberline {3}truthtable}{3}{section.3}%
-\contentsline {section}{\numberline {4}undirectedGraph}{4}{section.4}%
-\contentsline {section}{\numberline {5}complete6}{5}{section.5}%
-\contentsline {section}{\numberline {6}adjacency}{6}{section.6}%
-\contentsline {section}{\numberline {7}undirectedGraphToMatrix}{7}{section.7}%
-\contentsline {section}{\numberline {8}directedFromMatrix}{8}{section.8}%
+\contentsline {section}{\numberline {1}Propositional Logic}{2}{section.1}%
+\contentsline {subsection}{\numberline {1.1}truthtable}{2}{subsection.1.1}%
+\contentsline {section}{\numberline {2}Sets}{3}{section.2}%
+\contentsline {section}{\numberline {3}Relations}{3}{section.3}%
+\contentsline {subsection}{\numberline {3.1}proveEquivalence}{3}{subsection.3.1}%
+\contentsline {subsection}{\numberline {3.2}provePoset}{4}{subsection.3.2}%
+\contentsline {subsection}{\numberline {3.3}equivalenceDiagram}{5}{subsection.3.3}%
+\contentsline {subsection}{\numberline {3.4}hasse}{6}{subsection.3.4}%
+\contentsline {subsection}{\numberline {3.5}hasseDiagramByDivisibility}{7}{subsection.3.5}%
+\contentsline {section}{\numberline {4}Graph theory}{8}{section.4}%
+\contentsline {subsection}{\numberline {4.1}undirectedGraph}{8}{subsection.4.1}%
+\contentsline {subsection}{\numberline {4.2}directedGraph}{9}{subsection.4.2}%
+\contentsline {subsection}{\numberline {4.3}complete6}{10}{subsection.4.3}%
+\contentsline {subsection}{\numberline {4.4}adjacency}{11}{subsection.4.4}%
+\contentsline {subsection}{\numberline {4.5}undirectedGraphToMatrix}{12}{subsection.4.5}%
+\contentsline {subsection}{\numberline {4.6}directedFromMatrix}{13}{subsection.4.6}%
+\contentsline {section}{\numberline {5}Finite state automata}{14}{section.5}%
+\contentsline {subsection}{\numberline {5.1}automata}{14}{subsection.5.1}%