Exemple de notebook avec Python

Explications

Le kernel Python est installé par défaut avec Jupyter.

Exemples

In [1]:
print("Ceci est du code Python")

Ceci est du code Python
In [3]:
import sys
print(sys.version)

3.6.9 (default, Oct  8 2020, 12:12:24) 
[GCC 8.4.0]

Fonction factorielle

Pour calculer la fonction $n! := 1 \times 2 \times \dots \times n$ ($n\in\mathbb{N}$), on peut penser à une solution récursive (qui coutera en espace mémoire à cause de la pile d'appel) et une solution impérative.

In [11]:
def fact(n: int) -> int:
    # note: ces indications de type sont optionnelles, mais appréciées
    """ Factorielle de n, n! = 1 * 2 * .. * n."""
    if n <= 1:
        return 1
    else:
        return n * fact(n-1)

Note : ces commentaires "docstring" entre """ trois guillements""" sont optionnels mais appécies, car cela donne une documentation à chaque fonction :

In [14]:
help(fact)  # depuis une console Python normale

Help on function fact in module __main__:

fact(n:int) -> int
    Factorielle de n, n! = 1 * 2 * .. * n.
In [17]:
# depuis IPython ou Jupyter
fact?

Signature: fact(n:int) -> int
Docstring: Factorielle de n, n! = 1 * 2 * .. * n.
File:      ~/publis/Info-Prepas-MP2I/Modele-de-livre-avec-Jupyter-Book.git/notebooks/<ipython-input-11-4665928d2bba>
Type:      function

Exemples :

In [7]:
for i in range(1, 23):
    print(f"fact({i:2}) = {fact(i)}")

fact( 1) = 1
fact( 2) = 2
fact( 3) = 6
fact( 4) = 24
fact( 5) = 120
fact( 6) = 720
fact( 7) = 5040
fact( 8) = 40320
fact( 9) = 362880
fact(10) = 3628800
fact(11) = 39916800
fact(12) = 479001600
fact(13) = 6227020800
fact(14) = 87178291200
fact(15) = 1307674368000
fact(16) = 20922789888000
fact(17) = 355687428096000
fact(18) = 6402373705728000
fact(19) = 121645100408832000
fact(20) = 2432902008176640000
fact(21) = 51090942171709440000
fact(22) = 1124000727777607680000

Et la solution impérative :

In [9]:
def fact_imp(n: int) -> int:
    """ Factorielle de n, n! = 1 * 2 * .. * n."""
    f: int = 1
    for i in range(2, n+1):
        f = f * i  # f *= i est aussi possible 
    return f
In [10]:
for i in range(1, 23):
    print(f"fact_imp({i:2}) = {fact_imp(i)}")

fact_imp( 1) = 1
fact_imp( 2) = 2
fact_imp( 3) = 6
fact_imp( 4) = 24
fact_imp( 5) = 120
fact_imp( 6) = 720
fact_imp( 7) = 5040
fact_imp( 8) = 40320
fact_imp( 9) = 362880
fact_imp(10) = 3628800
fact_imp(11) = 39916800
fact_imp(12) = 479001600
fact_imp(13) = 6227020800
fact_imp(14) = 87178291200
fact_imp(15) = 1307674368000
fact_imp(16) = 20922789888000
fact_imp(17) = 355687428096000
fact_imp(18) = 6402373705728000
fact_imp(19) = 121645100408832000
fact_imp(20) = 2432902008176640000
fact_imp(21) = 51090942171709440000
fact_imp(22) = 1124000727777607680000

Figures avec TikZ

Voir https://github.com/jbn/itikz

In [7]:
%load_ext itikz

The itikz extension is already loaded. To reload it, use:
  %reload_ext itikz
In [8]:
%%itikz --file-prefix tikz-figures-from-Python- --implicit-pic
\draw[help lines] grid (5, 5);
\draw[fill=black!50] (1, 1) rectangle (2, 2);
\draw[fill=black!50] (2, 1) rectangle (3, 2);
\draw[fill=black!50] (3, 1) rectangle (4, 2);
\draw[fill=black!50] (3, 2) rectangle (4, 3);
\draw[fill=black!50] (2, 3) rectangle (3, 4);
Out[8]:
In [9]:
%%itikz --file-prefix tikz-figures-from-Python-  --implicit-pic --scale=0.4
\tikzstyle{vertexcover} = [circle,fill=green,draw];
\tikzstyle{matching} = [ draw=blue!55, line width=5];
\tikzstyle{matchingN} = [ draw=green!55, line width=5];
\tikzstyle{vertex} = [circle,fill=none,draw];
\node[vertex] (v2) at (0,0) {};
\node[vertexcover] (v3) at (0,3) {};
\node[vertexcover] (v4) at (2,2) {};
\node[vertexcover] (v11) at (3,0) {};
\node[vertexcover] (v5) at (2,-2) {};
\node[vertexcover] (v6) at (1,-3) {};
\node[vertexcover] (v8) at (-1,-3) {};
\node[vertexcover] (v9) at (-2,-2) {};
\node[vertexcover] (v10) at (-3,0) {};
\node[vertexcover] (v1) at (-2,2) {};
\draw  (v1) edge (v2);
\draw  (v3) edge (v2);
\draw  (v4) edge (v2);
\draw  (v5) edge (v2);
\draw  (v6) edge (v2);
\draw  (v8) edge (v2);
\draw  (v9) edge (v2);
\draw  (v2) edge (v10);
\draw  (v2) edge (v11);
Out[9]:
In [10]:
!ls tikz-figures-from-Python-*

tikz-figures-from-Python-b7c37e91289ef17e6c34e0d00645dabd.svg
tikz-figures-from-Python-b7c37e91289ef17e6c34e0d00645dabd.tex
tikz-figures-from-Python-c33720202396643581aed22f595383d4.svg
tikz-figures-from-Python-c33720202396643581aed22f595383d4.tex

D'autres exemples ?

TODO: plus tard !

Pour en apprendre plus