From 69934aabb7bc737ff8c0a3a455dc0740c28a38f2 Mon Sep 17 00:00:00 2001
From: zimmersandro <sandro.zimmermann@stud.fhgr.ch>
Date: Sun, 1 Nov 2026 17:53:36 +0100
Subject: [PATCH] =?UTF-8?q?Beispiele=20f=C3=BCr=20Kartesisches=20Produkt?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 mengen/kartesiches_produkt.py | 99 +++++++++++++++++++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 mengen/kartesiches_produkt.py

diff --git a/mengen/kartesiches_produkt.py b/mengen/kartesiches_produkt.py
new file mode 100644
index 0000000..0211f32
--- /dev/null
+++ b/mengen/kartesiches_produkt.py
@@ -0,0 +1,99 @@
+#%%
+import numpy as np
+import matplotlib.pyplot as plt
+
+def setup_axes(ax, xlim, ylim, xticks, yticks):
+    """Stellt die Achsen als klassisches x-y-Koordinatensystem mit Ursprung dar."""
+    ax.spines['left'].set_position('zero')
+    ax.spines['bottom'].set_position('zero')
+    ax.spines['right'].set_visible(False)
+    ax.spines['top'].set_visible(False)
+
+    ax.plot(1, 0, ">k", transform=ax.get_yaxis_transform(), clip_on=False)
+    ax.plot(0, 1, "^k", transform=ax.get_xaxis_transform(), clip_on=False)
+
+    ax.set_xlabel('x', loc='right', fontsize=13)
+    ax.set_ylabel('y', loc='top', rotation=0, fontsize=13)
+
+    ax.set_xlim(*xlim)
+    ax.set_ylim(*ylim)
+    ax.set_xticks(xticks)
+    ax.set_yticks(yticks)
+    ax.grid(True, linestyle='--', alpha=0.4)
+    ax.axis("image")
+
+
+# --- 1. {1, 2} × {1, 2} ---
+fig, ax = plt.subplots(figsize=(6, 6))
+ax.scatter([1, 1, 2, 2], [1, 2, 1, 2], s=120, color='steelblue', zorder=3)
+setup_axes(ax, (-3, 6), (-3, 6), [1, 2, 3, 4, 5], [1, 2, 3, 4, 5])
+ax.legend([r'$\{1,\,2\} \times \{1,\,2\}$'], loc='upper center',
+          bbox_to_anchor=(0.5, -0.12), fontsize=12, frameon=True)
+ax.set_title("1.")
+plt.tight_layout()
+plt.savefig("1_kartesiche_produkte.png", dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- 2. {1, 2} × {2, 3, 4} ---
+fig, ax = plt.subplots(figsize=(6, 6))
+ax.scatter([1, 1, 1, 2, 2, 2], [2, 3, 4, 2, 3, 4], s=120, color='darkorange', zorder=3)
+setup_axes(ax, (-3, 7), (-3, 7), [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6])
+ax.legend([r'$\{1,\,2\} \times \{2,\,3,\,4\}$'], loc='upper center',
+          bbox_to_anchor=(0.5, -0.12), fontsize=12, frameon=True)
+ax.set_title("2.")
+plt.tight_layout()
+plt.savefig("2_kartesiche_produkte.png", dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- 3. {2, 3, 4} × {1, 2} ---
+fig, ax = plt.subplots(figsize=(6, 6))
+ax.scatter([2, 2, 3, 3, 4, 4], [1, 2, 1, 2, 1, 2], s=120, color='seagreen', zorder=3)
+setup_axes(ax, (-3, 7), (-3, 6), [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5])
+ax.legend([r'$\{2,\,3,\,4\} \times \{1,\,2\}$'], loc='upper center',
+          bbox_to_anchor=(0.5, -0.12), fontsize=12, frameon=True)
+ax.set_title("3.")
+plt.tight_layout()
+plt.savefig("3_kartesiche_produkte.png", dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- 4. [0, 1] × {1, 2} ---
+fig, ax = plt.subplots(figsize=(6, 6))
+x_line = np.linspace(0, 1, 100)
+ax.plot(x_line, np.ones_like(x_line), color='crimson', linewidth=3)
+ax.plot(x_line, 2 * np.ones_like(x_line), color='crimson', linewidth=3)
+ax.scatter([0, 1, 0, 1], [1, 1, 2, 2], s=60, color='crimson', zorder=3)
+setup_axes(ax, (-3, 5), (-3, 5), [0, 1, 2, 3, 4], [1, 2, 3, 4])
+ax.legend([r'$[0,\,1] \times \{1,\,2\}$'], loc='upper center',
+          bbox_to_anchor=(0.5, -0.12), fontsize=12, frameon=True)
+ax.set_title("4.")
+plt.tight_layout()
+plt.savefig("4_kartesiche_produkte.png", dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- 5. {1, 2} × [0, 1] ---
+fig, ax = plt.subplots(figsize=(6, 6))
+y_line = np.linspace(0, 1, 100)
+ax.plot(np.ones_like(y_line), y_line, color='mediumpurple', linewidth=3)
+ax.plot(2 * np.ones_like(y_line), y_line, color='mediumpurple', linewidth=3)
+ax.scatter([1, 1, 2, 2], [0, 1, 0, 1], s=60, color='mediumpurple', zorder=3)
+setup_axes(ax, (-3, 5), (-3, 5), [1, 2, 3, 4], [0, 1, 2, 3, 4])
+ax.legend([r'$\{1,\,2\} \times [0,\,1]$'], loc='upper center',
+          bbox_to_anchor=(0.5, -0.12), fontsize=12, frameon=True)
+ax.set_title("5.")
+plt.tight_layout()
+plt.savefig("5_kartesiche_produkte.png", dpi=150, bbox_inches='tight')
+plt.close()
+
+# --- 6. [0, 1] × [1, 2] ---
+fig, ax = plt.subplots(figsize=(6, 6))
+rect = plt.Rectangle((0, 1), 1, 1, linewidth=2, edgecolor='teal', facecolor='teal', alpha=0.3)
+ax.add_patch(rect)
+ax.plot([0, 1, 1, 0, 0], [1, 1, 2, 2, 1], color='teal', linewidth=2)
+setup_axes(ax, (-3, 5), (-3, 5), [0, 1, 2, 3, 4], [1, 2, 3, 4])
+ax.legend([r'$[0,\,1] \times [1,\,2]$'], loc='upper center',
+          bbox_to_anchor=(0.5, -0.12), fontsize=12, frameon=True)
+ax.set_title("6.")
+plt.tight_layout()
+plt.savefig("6_kartesiche_produkte.png", dpi=150, bbox_inches='tight')
+plt.close()
+# %%