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Beispiele für Kartesisches Produkt

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Sandro Zimmermann 2026-11-01 17:53:36 +01:00
parent 8d96c0e202
commit 69934aabb7
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#%%
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()
# %%