25 files changed, 2288 insertions, 0 deletions

diff --git a/src/Lecture4/live/live.zip b/src/Lecture4/live/live.zip
new file mode 100644
index 0000000..81e11a8
--- /dev/null
+++ b/src/Lecture4/live/live.zip
diff --git a/src/Lecture4/live/live1.py b/src/Lecture4/live/live1.py
new file mode 100644
index 0000000..da505f2
--- /dev/null
+++ b/src/Lecture4/live/live1.py
@@ -0,0 +1,17 @@
+print(2+2)
+
+x = input("Input something: ")
+print("Your input was:", x, "of type", type(x))
+
+x_number = int(x)
+print("Converted to a number:", x_number, "of type", type(x_number))
+
+if x_number > 10:
+        print("Your number was large!")
+        print("It was larger than 10")
+        z = x_number-10
+        print("This is a smaller number:", z)
+else:
+        print("Your number was small")
+        
+print("Bye")
diff --git a/src/Lecture4/live/live2.py b/src/Lecture4/live/live2.py
new file mode 100644
index 0000000..041bda3
--- /dev/null
+++ b/src/Lecture4/live/live2.py
@@ -0,0 +1,7 @@
+x = int(input("Input something: "))
+
+while x > 10:
+        print("Large number!", x)
+        x = x - 1
+        
+print("Bye")
diff --git a/src/Lecture4/live/live3.py b/src/Lecture4/live/live3.py
new file mode 100644
index 0000000..14aa89b
--- /dev/null
+++ b/src/Lecture4/live/live3.py
@@ -0,0 +1,9 @@
+x = int(input("Input something: "))
+
+A = [1,2,3]
+
+for i in range(2,9):
+        z = 10**i
+        print("A power of 10:", z)
+        
+print("Bye")
diff --git a/src/Lecture4/live/live4.py b/src/Lecture4/live/live4.py
new file mode 100644
index 0000000..b011675
--- /dev/null
+++ b/src/Lecture4/live/live4.py
@@ -0,0 +1,39 @@
+
+def fun(a, b):
+        print("This is function fun")
+        print("I am executing!")
+        print("Your parameter a:", a)
+        z = a + b
+        if z > 10:
+                print("Your sum is large!", z)
+        while z > 5:
+                print("Decreasing sum:", z-1)
+                z = z - 1
+
+#fun(2, 11)
+#print("..")
+#fun(0, 7)
+
+def g(x, y):
+        #print("This is function g")
+        return (x**2 +1)*y
+        
+print(g(10,2)-100)
+
+
+def fibo(n):
+        if n == 0:
+                return 0
+        if n == 1:
+                return 1
+        return fibo(n-1) + fibo(n-2)
+
+
+
+print(fibo(5))
+F = [fibo(x) for x in range(6)]
+print(F)
+
+
+
+
diff --git a/src/Lecture4/live/live_interactive.py b/src/Lecture4/live/live_interactive.py
new file mode 100644
index 0000000..671cbad
--- /dev/null
+++ b/src/Lecture4/live/live_interactive.py
@@ -0,0 +1,172 @@
+2+2
+3*5
+3/5
+3 // 5
+2.5 + (456 - 0.3)
+2 ** 10
+13 // 5
+13 % 5
+sqrt(3)
+import math
+sqrt(3)
+math.sqrt(3)
+help()
+math
+asfdads
+2+2
+help("import")
+sqrt(10)
+math.sqrt(10)
+from math import *
+sqrt(10)
+10 - _
+_
+x = 10 + sqrt(3)
+x
+abc_3 = 45+3*(2-1.4)
+abc_3
+x / (abc_3+2)
+x
+x = 3*abc_3
+x
+abc_3 = 0
+abc_3
+x
+1 = 1
+1 == 1
+1 == 3
+x
+type(x)
+abc_3
+type(abc_3)
+type(3/2)
+type(3/1)
+3/1
+type(1 == 1)
+y = False
+z = (2 == 2)
+y
+z
+type(z)
+type(y)
+y and z
+True and True
+y or z
+not True
+3 >= 4
+3 >= 3
+3 > 3
+3 != 4
+hello
+"hello"
+type("hello")
+st = "Hello, World!"
+st
+type(st)
+len(st)
+"hello" + ", world"
+"abc" + "abc"
+2 * "abc"
+10 * "abc"
+"hello" * "abc"
+True + False
+[1,2,3,1,-1.5]
+[1,True,"hello"]
+L = [1,True,"hello"]
+type(L)
+{1,2,3,1,-1.5}
+{12, 25, 10, -1}
+len(L)
+len({1,1,1})
+{1,1,1}
+1 in L
+-42 in L
+1.5 in {2,3.1,1.5}
+S = {-2, 0, 10, 25}
+max(S)
+min(S)
+sum(S)
+sum([10,2,45])
+L
+min(L)
+L2 = [1,2, 1, -2, 0, 2]
+set(L2)
+list({1,2,1,3,-2})
+S
+list(S)
+[x**2 for x in [-1,4,1,0] if x < 3]
+{x**2 for x in [-1,4,1,0] if x < 3}
+{x+2 for x in [-1,4,1,0] if x < 3}
+{x+2 for x in {-1,4,1,0} if x < 3}
+[x+2 for x in {-1,4,1,0} if x < 3]
+[x+2 for x in {-1,4,1,0} if True]
+[x+2 for x in {-1,4,1,0}]
+[x+2 for x in {-1,4,1,0} if x+10-3.24 < x^2]
+[i*j for i in [0,1,2,3] for j in {-1,1}]
+range(0,4)
+type(range(0,4))
+[i*j for i in range(0,4) for j in {-1,1}]
+list(range(0,4))
+list(range(3,4))
+list(range(3,10))
+list(range(10))
+list(range(1,10,2))
+list(range(10,1,-1))
+L
+L[0]
+L[1]
+L[2]
+L[10]
+L[-1]
+L[len(L)-1]
+L[len(L)-3]
+L[-3]
+L2
+L[1:4]
+L2[1:4]
+L2[1:4:2]
+R=range(10)
+R
+R=list(range(10))
+R
+R[2:8:2]
+R[9:3:-1]
+R
+type(R)
+R[3]
+R[3] = 3.14
+R
+R.append(10)
+R
+R.insert(3,3.0)
+R
+R[3]
+del R[4]
+R
+L
+R
+L + R
+L
+R
+L * 3
+3 * L
+S
+type(S)
+S.add(3)
+S
+S.add(10)
+S
+S.remove(25)
+S
+T = {3, -2, 27, 99}
+{3, -2} < T
+{3, -2} < S
+S >= {3, -2}
+S >= S
+S > S
+S | T
+S & T
+S - T
+2+3
+import readline
+readline.write_history_file('live_interactive.py')
diff --git a/src/Lecture4/slides/6-PythonIntroduction.aux b/src/Lecture4/slides/6-PythonIntroduction.aux
new file mode 100644
index 0000000..49f1525
--- /dev/null
+++ b/src/Lecture4/slides/6-PythonIntroduction.aux
@@ -0,0 +1,76 @@
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+\providecommand\hyper@newdestlabel[2]{}
+\providecommand{\transparent@use}[1]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
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diff --git a/src/Lecture4/slides/6-PythonIntroduction.log b/src/Lecture4/slides/6-PythonIntroduction.log
new file mode 100644
index 0000000..7f499c9
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+++ b/src/Lecture4/slides/6-PythonIntroduction.log
@@ -0,0 +1,1283 @@
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+ \write18 enabled.
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diff --git a/src/Lecture4/slides/6-PythonIntroduction.out b/src/Lecture4/slides/6-PythonIntroduction.out
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+\documentclass[11pt]{beamer}
+\usetheme{Madrid}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+
+\usepackage{tikz}
+\usetikzlibrary{calc}
+\usepackage{svg}
+
+\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto}
+\title[Python Intro and a bit of Sage]%
+{A Practical Introduction to Python (and a bit of Sage)}
+\logo{\includegraphics[scale=0.1]{img/unilu.jpg}} 
+%\institute{University of Luxembourg} 
+
+\date{2021-04-02} 
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}{Second part - schedule}
+  \begin{tabular}{l|c|c|l}
+    \textbf{Date} & \textbf{Topics} & \textbf{Homework} & \textbf{Deadline}  \\
+    \hline
+    April 2   & Python ``review'', a bit of Sage & (see March 26) & April 18 \\
+    \hline
+    April 23  & Sage: Algebra and Crypto & Homework 3 & May 9                \\
+    \hline
+    May 7     & Sage: Analysis and Statistics  & Homework 4 & May 30         \\
+    \hline
+    May 21    & Fast code, other software  &
+  \end{tabular}
+\end{frame}
+
+
+\begin{frame}{What is programming?}
+  \begin{columns}
+    \column{0.35\textwidth}
+      \includegraphics[scale=0.12]{img/laptop.png}
+    \column{0.1\textwidth}
+      \begin{center}\includegraphics[scale=0.12]{img/equal.png}\end{center}
+    \column{0.35\textwidth}
+      \includegraphics[scale=0.9]{img/calc.jpg}
+  \end{columns}
+  \begin{itemize}
+    \item Software (apps): commands written in a \emph{programming language}
+    \item Programming language: mix of English and symbols
+    \item The code is \emph{compiled} to machine language (C, C++) or\\
+          \emph{interpreted} by some software in the middle (Python)
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Python}
+  \begin{columns}
+    \column{0.7\textwidth}
+      \url{https://www.python.org}
+
+      \vspace{0.3cm}
+      \begin{itemize}
+        \item Interpreted: slower than C, usable interactively
+        \item Simple syntax, easy to learn
+        \item Very popular
+        \item Sage is based on Python
+      \end{itemize}
+    \column{0.25\textwidth}
+      \includegraphics[scale=0.16]{img/python.png}
+  \end{columns}
+\end{frame}
+
+\begin{frame}{The interpreter - Python as a calculator}
+  \begin{center}
+    \includegraphics[scale=0.3]{img/term.png}
+  \end{center}
+\end{frame}
+
+\begin{frame}{The interpreter - Python as a calculator}
+  \url{https://www.python.org/shell}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Each line executed as you enter it, result is printed
+    \item Usual math operations work: try them!
+      \begin{center}
+        \texttt{a+b, a-b, a*b, a/b}\\
+        \texttt{a**b (power), a//b (integer division), a\%b (remainder)}
+      \end{center}
+    \item More math functions:
+      \begin{center} \begin{tabular}{l}
+        \texttt{import math} \\
+        \texttt{math.sqrt(3)}
+      \end{tabular} \end{center}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Help!}
+  \begin{itemize}
+    \item Type \texttt{help()} for interactive help
+    \item Try \texttt{help("math")} and \texttt{help("import")}
+    \item What does
+      \begin{center} \texttt{from math import *} \end{center}
+    do?
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Variables}
+  \texttt{variable\_name = value \qquad \# This is an assignment}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Save results, use them later
+    \item \texttt{variable\_name}: combination of letters, numbers, underscores
+    \item \texttt{=} always means \emph{assignment}, never \emph{equality}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Types}
+  \texttt{type(variable\_name) \qquad \# Get the type of a variable}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    %\item Tells the computer how to read a variable
+    \item In other languages you must specify the type of a variable
+    \item Python figures out automatically (\emph{dynamic typing})
+    \item Each type allows different operations
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Other types: Boolean and String}
+  \texttt{my\_bool = True}
+
+  \texttt{s1 = "hello!" \qquad \# Same as 'hello!'}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item \texttt{bool}: \texttt{True} or \texttt{False}
+      \begin{itemize}
+        \item Operations on \texttt{bool}:
+              \texttt{and}, \texttt{or}, \texttt{not}
+        \item Operations with boolean result: \texttt{==}, \texttt{!=},
+              \texttt{>}, \texttt{<}, \texttt{>=}, \texttt{<=}
+      \end{itemize}
+    \item \texttt{str}: a string of characters
+      \begin{itemize}
+        \item Useful operations:
+
+          \begin{tabular}{ll}
+            \texttt{len({\bf str})} & \texttt{\# Length, integer value}   \\
+            \texttt{{\bf str} + {\bf str}} & \texttt{\# Concatenation} \\
+            \texttt{{\bf int} * {\bf str}} & \texttt{\# Repetition}
+          \end{tabular}
+      \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Lists and sets}
+  %\texttt{(2.5, True, "hello") \qquad \# Tuple}
+
+  \texttt{[2.5, True, "hello"] \qquad \# List}
+
+  \texttt{\{2.5, True, "hello"\} \qquad \# Set}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    %\item Different collections of objects
+    %\item Tuple: immutable
+    \item Lists: keep order and duplicates
+    \item Sets: disregard order and duplicates, allow set operations
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Lists and sets}
+  Things in common (\emph{\texttt{A} is a list or a set}):
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item \texttt{len(A)}: number of elements (\texttt{\bf int})
+    \item \texttt{x in A}: check if \texttt{x} is in \texttt{A}
+          (\texttt{\bf bool})
+    \item If \texttt{A} contains numbers: \texttt{max(A)}, \texttt{min(A)},
+          \texttt{sum(A)}
+  \end{itemize}
+
+  \vspace{0.3cm}
+  Pass from one type to the other: \texttt{set(A)} and \texttt{list(A)}
+\end{frame}
+
+\begin{frame}{List (and set) comprehension}
+  \texttt{[x**2 {\bf for} x {\bf in} [-1,4,1,0] {\bf if} x < 3]
+          \quad\# Result: [1,1,0]}
+
+  \texttt{\{x**2 {\bf for} x {\bf in} [-1,4,1,0] {\bf if} x < 3\}
+          \quad\# Result: \{0,1\}}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Mathematical way to define lists and sets
+    \item Complete syntax:
+
+          \vspace{0.2cm}
+          \texttt{[f(x,y,\dots) {\bf for} x {\bf in} L {\bf for} y {\bf in} M
+                   \dots \quad {\bf if} cond(x,y,\dots)]}
+
+          \vspace{0.2cm}
+          \begin{itemize}
+            \item Use as many variables \texttt{x, y, \dots} as you want
+            \item \texttt{L, M, \dots} are lists or sets or other collections
+            \item \texttt{f(x,y,\dots)} is any expression depending on the
+                  variables
+            \item \texttt{cond(x,y,\dots)} has Boolean value
+          \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Lists: access elements and sublists}
+  \begin{tabular}{ll}
+    \texttt{A[i]} &
+    \texttt{\# i-th element of A ($i\in \{0,\dots,\texttt{len(A)}-1\}$)} \\
+    \texttt{A[i] = value} & \texttt{\# Change i-th element of A} \\
+    \texttt{A[i:j:k]} & \texttt{\# Sublist from A[i] to A[j] with step k} \\
+    \texttt{A[i:j]} & \texttt{\# Same as A[i:j:1]} \\
+    \texttt{A[i:]} & \texttt{\# Same as A[i:len(A):1]} \\
+    \texttt{A[:j]} & \texttt{\# Same as A[0:j:1]}
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{List operations}
+  \begin{tabular}{ll}
+    \texttt{A.append(x)} & \texttt{\# Append x to A ({\bf change A})} \\
+    \texttt{A.insert(i,x)} &
+    \texttt{\# Insert x in position i ({\bf change A})} \\
+    \texttt{del A[i]} & \texttt{\# Remove i-th element of A ({\bf change A})}\\
+  \end{tabular}
+
+  \vspace{1cm}
+  \begin{tabular}{ll}
+    \texttt{A+B} & \texttt{\# Concatenation of A and B ({\bf list})} \\
+    \texttt{A*n} & \texttt{\# Repetition of A ({\bf list})} \\
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{Set operations}
+  \begin{tabular}{ll}
+    \texttt{A.add(x)} & \texttt{\# Add x to A ({\bf change A})} \\
+    \texttt{A.remove(x)} & \texttt{\# Remove x from A ({\bf change A})}\\
+  \end{tabular}
+
+  \vspace{0.5cm}
+  \begin{tabular}{ll}
+    \texttt{A < B} (or \texttt{A <= B}) &
+    \texttt{\# A contained in (or equal to) B ({\bf bool})} \\
+    \texttt{A > B} (or \texttt{A >= B}) &
+    \texttt{\# A containes (or is equal to) B ({\bf bool})} \\
+  \end{tabular}
+
+  \vspace{0.5cm}
+  \begin{tabular}{ll}
+    \texttt{A | B} & \texttt{\# Union ({\bf set})} \\
+    \texttt{A \& B} & \texttt{\# Intersection ({\bf set})}\\
+    \texttt{A - B} & \texttt{\# Set difference ({\bf set})} \\
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{Writing more complex programs}
+  \begin{center}\includegraphics[scale=0.25]{img/geany.png}\end{center}
+\end{frame}
+
+\begin{frame}{Non-interactive Python}
+  \begin{itemize}
+    \item You can write a file (for example with \url{https://www.geany.org})
+    \item Output results with \texttt{print("string", or, other, values)}
+    \item Get input (\texttt{str}) with \texttt{x = input("Prompt: ")},
+          convert with \texttt{int(x)} or \texttt{float(x)}\dots
+    \item Blocks of code: use \emph{indentation} (see next slides)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]{\texttt{if} statement}
+  \begin{columns}
+    \column{0.45\textwidth}
+      \texttt{{\bf if} \emph{condition}:}
+
+      \texttt{\qquad instruction1}
+      
+      \texttt{\qquad instruction2}
+
+      \texttt{\qquad \dots}
+
+      \texttt{{\bf else}: \# This is optional}
+
+      \texttt{\qquad other inst}
+    \column{0.55\textwidth}
+      \begin{tikzpicture}
+        \tikzstyle{s} = [rectangle, rounded corners, text centered,
+                                                       draw=black, fill=red!30]
+        \tikzstyle{p} = [rectangle, text centered, draw=black, fill=orange!30]
+        \tikzstyle{d} = [rectangle, text centered, draw=black, fill=green!30]
+
+        \node(start)  [s]                     {Start};
+        \node(cond)   [d, below of=start]     {\texttt{\emph{condition}}?};
+        \node(inst1)  [p, right of=cond, xshift=2.7cm] {\texttt{instruction1}};
+        \node(inst2)  [p, below of=inst1]     {\texttt{instruction2}};
+        \node(dots)   [p, below of=inst2]     {\texttt{\dots}};
+        \node(other)  [p, below of=cond, yshift=-0.5cm]  {\texttt{other inst}};
+        \node(end)    [s, below of=other, yshift=-0.5cm] {End};
+
+        \draw[->] (start) -- (cond);
+        \draw[->] (cond) -- node[anchor=south] {\texttt{True}} (inst1);
+        \draw[->] (inst1) -- (inst2);
+        \draw[->] (inst2) -- (dots);
+        \draw[->] (cond) -- node[anchor=east] {\texttt{False}} (other);
+        \draw[->] (dots) |- (end);
+        \draw[->] (other) -- (end);
+      \end{tikzpicture}
+  \end{columns}
+\end{frame}
+
+
+\begin{frame}[fragile]{\texttt{while} loop}
+  \begin{columns}
+    \column{0.45\textwidth}
+      \texttt{{\bf while} \emph{condition}:}
+
+      \texttt{\qquad instruction1}
+      
+      \texttt{\qquad instruction2}
+
+      \texttt{\qquad \dots}
+    \column{0.55\textwidth}
+      \begin{tikzpicture}
+        \tikzstyle{s} = [rectangle, rounded corners, text centered,
+                                                       draw=black, fill=red!30]
+        \tikzstyle{p} = [rectangle, text centered, draw=black, fill=orange!30]
+        \tikzstyle{d} = [rectangle, text centered, draw=black, fill=green!30]
+
+        \node(start)  [s]                     {Start};
+        \node(cond)   [d, below of=start]     {\texttt{\emph{condition}}?};
+        \node(inst1)  [p, right of=cond, xshift=2.7cm] {\texttt{instruction1}};
+        \node(inst2)  [p, below of=inst1]     {\texttt{instruction2}};
+        \node(dots)   [p, below of=inst2]     {\texttt{\dots}};
+        \node(end)    [s, below of=other, yshift=-0.5cm] {End};
+
+        \draw[->] (start) -- (cond);
+        \draw[->] (cond) -- node[anchor=south] {\texttt{True}} (inst1);
+        \draw[->] (inst1) -- (inst2);
+        \draw[->] (inst2) -- (dots);
+        \draw[->] (cond) -- node[anchor=east] {\texttt{False}} (end);
+        \draw[->] (dots) -| ($(cond.south)+(0.4,0)$);
+      \end{tikzpicture}
+  \end{columns}
+\end{frame}
+
+\begin{frame}{\texttt{for} loop}
+  \texttt{{\bf for} i {\bf in} A:}
+
+  \texttt{\qquad instruction1}
+  
+  \texttt{\qquad instruction2}
+
+  \texttt{\qquad \dots}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Repeats instructions as \texttt{i} varies in \texttt{A}
+    \item \texttt{A} can be list, set or other collection
+    \item Example: \texttt{A} can be \texttt{range(\emph{a,b,step})}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Functions}
+  \texttt{{\bf def} f(x, y, \dots): }
+
+  \texttt{\qquad instruction1}
+  
+  \texttt{\qquad instruction2}
+
+  \texttt{\qquad \dots}
+
+  \texttt{\qquad {\bf return} some\_value}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Useful to divide programs into ``pieces''
+    \item The result of \texttt{f(x,y,\dots)} is given by \texttt{return \dots}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{An example of function (with recursion)}
+  \texttt{def fibonacci(n):}
+
+  \texttt{\qquad if n == 0:}
+
+  \texttt{\qquad \qquad return 0}
+
+  \texttt{\qquad if n == 1:}
+
+  \texttt{\qquad \qquad return 1}
+
+  \texttt{\qquad return fibonacci(n-1) + fibonacci(n-2)}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Elegant, but slow (in this case)
+    \item Can get stuck in infinite loop: when?
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Sage}
+  \begin{center}
+    \includesvg[scale=0.5]{img/sage}
+
+    \url{https://www.sagemath.org}
+  \end{center}
+
+  \vspace{0.3cm}
+  \begin{itemize}
+    \item Mathematical software, uses Python as a language
+    \item Use it interactively or with Jupyter notebook
+    \item Try it online: \url{https://sagecell.sagemath.org} or
+          \url{https://cocalc.com/app}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Differences with Python}
+  \begin{tabular}{l|l}
+    \textbf{Python} & \textbf{Sage}                                          \\
+    \texttt{{\color{gray}>>>} {\color{blue}type(5)}} &
+    \texttt{{\color{gray}sage:} {\color{blue}type(5)}}                       \\
+    \texttt{<class 'int'>} & \texttt{<class 'sage.rings.integer.Integer'>}   \\
+    \texttt{{\color{gray}>>>} {\color{blue}5/2}} &
+    \texttt{{\color{gray}sage:} {\color{blue}5/2}}                           \\
+    \texttt{2.5} & \texttt{5/2}                                              \\
+    \texttt{{\color{gray}>>>} {\color{blue}type(5/2)}} &
+    \texttt{{\color{gray}sage:} {\color{blue}type(5/2)}}                     \\
+    \texttt{<class 'float'>} &
+    \texttt{<class 'sage.rings.rational.Rational'>}                          \\
+    \texttt{{\color{gray}>>>} {\color{blue}type(2.5)}} &
+    \texttt{{\color{gray}sage:} {\color{blue}type(2.5)}}                     \\
+    \texttt{<class 'float'>} &
+    \texttt{<class 'sage.rings.real\_mpfr.RealLiteral'>}                     \\
+    \texttt{{\color{gray}>>>} {\color{blue}5**3}} &
+    \texttt{{\color{gray}sage:} {\color{blue}5\^{}3}}                        \\
+    \texttt{125} & \texttt{125}
+  \end{tabular}
+\end{frame}
+
+\begin{frame}{Sage Documentation}
+  \begin{itemize}
+    \item Tutorial (guided examples): type \texttt{tutorial()} or visit
+          \url{https://doc.sagemath.org/html/en/tutorial}
+    \item \texttt{help()}: works as in Python
+    \item Reference manual (detailed technical information):
+          \url{https://doc.sagemath.org/html/en/reference}
+  \end{itemize}
+\end{frame}
+
+
+\end{document}
+
diff --git a/src/Lecture4/slides/6-PythonIntroduction.toc b/src/Lecture4/slides/6-PythonIntroduction.toc
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/src/Lecture4/slides/6-PythonIntroduction.toc
diff --git a/src/Lecture4/slides/6-PythonIntroduction.vrb b/src/Lecture4/slides/6-PythonIntroduction.vrb
new file mode 100644
index 0000000..401cc07
--- /dev/null
+++ b/src/Lecture4/slides/6-PythonIntroduction.vrb
@@ -0,0 +1,32 @@
+\frametitle{\texttt {while} loop}
+\begin{columns}
+    \column{0.45\textwidth}
+      \texttt{{\bf while} \emph{condition}:}
+
+      \texttt{\qquad instruction1}
+
+      \texttt{\qquad instruction2}
+
+      \texttt{\qquad \dots}
+    \column{0.55\textwidth}
+      \begin{tikzpicture}
+        \tikzstyle{s} = [rectangle, rounded corners, text centered,
+                                                       draw=black, fill=red!30]
+        \tikzstyle{p} = [rectangle, text centered, draw=black, fill=orange!30]
+        \tikzstyle{d} = [rectangle, text centered, draw=black, fill=green!30]
+
+        \node(start)  [s]                     {Start};
+        \node(cond)   [d, below of=start]     {\texttt{\emph{condition}}?};
+        \node(inst1)  [p, right of=cond, xshift=2.7cm] {\texttt{instruction1}};
+        \node(inst2)  [p, below of=inst1]     {\texttt{instruction2}};
+        \node(dots)   [p, below of=inst2]     {\texttt{\dots}};
+        \node(end)    [s, below of=other, yshift=-0.5cm] {End};
+
+        \draw[->] (start) -- (cond);
+        \draw[->] (cond) -- node[anchor=south] {\texttt{True}} (inst1);
+        \draw[->] (inst1) -- (inst2);
+        \draw[->] (inst2) -- (dots);
+        \draw[->] (cond) -- node[anchor=east] {\texttt{False}} (end);
+        \draw[->] (dots) -| ($(cond.south)+(0.4,0)$);
+      \end{tikzpicture}
+  \end{columns}
diff --git a/src/Lecture4/slides/img/calc.jpg b/src/Lecture4/slides/img/calc.jpg
new file mode 100644
index 0000000..09438d1
--- /dev/null
+++ b/src/Lecture4/slides/img/calc.jpg
diff --git a/src/Lecture4/slides/img/equal.png b/src/Lecture4/slides/img/equal.png
new file mode 100644
index 0000000..39948a6
--- /dev/null
+++ b/src/Lecture4/slides/img/equal.png
diff --git a/src/Lecture4/slides/img/geany.png b/src/Lecture4/slides/img/geany.png
new file mode 100644
index 0000000..7910546
--- /dev/null
+++ b/src/Lecture4/slides/img/geany.png
diff --git a/src/Lecture4/slides/img/laptop.png b/src/Lecture4/slides/img/laptop.png
new file mode 100644
index 0000000..0f9eaf5
--- /dev/null
+++ b/src/Lecture4/slides/img/laptop.png
diff --git a/src/Lecture4/slides/img/python.png b/src/Lecture4/slides/img/python.png
new file mode 100644
index 0000000..d775a99
--- /dev/null
+++ b/src/Lecture4/slides/img/python.png
diff --git a/src/Lecture4/slides/img/sage.svg b/src/Lecture4/slides/img/sage.svg
new file mode 100644
index 0000000..642e67b
--- /dev/null
+++ b/src/Lecture4/slides/img/sage.svg
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diff --git a/src/Lecture4/slides/img/term.png b/src/Lecture4/slides/img/term.png
new file mode 100644
index 0000000..fb0519a
--- /dev/null
+++ b/src/Lecture4/slides/img/term.png
diff --git a/src/Lecture4/slides/img/unilu.jpg b/src/Lecture4/slides/img/unilu.jpg
new file mode 100644
index 0000000..5265563
--- /dev/null
+++ b/src/Lecture4/slides/img/unilu.jpg
diff --git a/src/Lecture4/slides/svg-inkscape/sage_svg-tex.pdf b/src/Lecture4/slides/svg-inkscape/sage_svg-tex.pdf
new file mode 100644
index 0000000..5f75b82
--- /dev/null
+++ b/src/Lecture4/slides/svg-inkscape/sage_svg-tex.pdf
diff --git a/src/Lecture4/slides/svg-inkscape/sage_svg-tex.pdf_tex b/src/Lecture4/slides/svg-inkscape/sage_svg-tex.pdf_tex
new file mode 100644
index 0000000..348dc56
--- /dev/null
+++ b/src/Lecture4/slides/svg-inkscape/sage_svg-tex.pdf_tex
@@ -0,0 +1,58 @@
+%% Creator: Inkscape 1.0.2 (e86c870879, 2021-01-15), www.inkscape.org
+%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
+%% Accompanies image file 'sage_svg-tex.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics{<filename>.pdf}
+%% To scale the image, write
+%%   \def\svgwidth{<desired width>}
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics[width=<desired width>]{<filename>.pdf}
+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
+%% installed) using
+%%   \usepackage{import}
+%% in the preamble, and then including the image with
+%%   \import{<path to file>}{<filename>.pdf_tex}
+%% Alternatively, one can specify
+%%   \graphicspath{{<path to file>/}}
+%% 
+%% For more information, please see info/svg-inkscape on CTAN:
+%%   http://tug.ctan.org/tex-archive/info/svg-inkscape
+%%
+\begingroup%
+  \makeatletter%
+  \providecommand\color[2][]{%
+    \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\transparent[1]{%
+    \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
+    \renewcommand\transparent[1]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \newcommand*\fsize{\dimexpr\f@size pt\relax}%
+  \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
+  \ifx\svgwidth\undefined%
+    \setlength{\unitlength}{375bp}%
+    \ifx\svgscale\undefined%
+      \relax%
+    \else%
+      \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
+    \fi%
+  \else%
+    \setlength{\unitlength}{\svgwidth}%
+  \fi%
+  \global\let\svgwidth\undefined%
+  \global\let\svgscale\undefined%
+  \makeatother%
+  \begin{picture}(1,0.26172667)%
+    \lineheight{1}%
+    \setlength\tabcolsep{0pt}%
+    \put(0,0){\includegraphics[width=\unitlength,page=1]{sage_svg-tex.pdf}}%
+  \end{picture}%
+\endgroup%