master > master: src - clean up
- enums für Alphabete - button layout - refresh Knopf - aspect ratio
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@ -28,7 +28,7 @@ __all__ = [
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T1 = TypeVar('T1');
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T2 = TypeVar('T2');
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SCALE = (1., 4.);
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SCALE = (1., 1.5);
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OFFSET = (3., 0.);
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HMARGIN = 0.1;
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VMARGIN = 0.2;
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@ -119,15 +119,15 @@ class Functions:
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for k, f in enumerate(self.fcts):
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if k == 0:
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comp_range = f.domain;
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p_domain = random_points(nr_points=len(f.domain), scale=SCALE, centre=origin + k*offset);
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p_domain = random_points(nr_points=len(f.domain), scale=SCALE, centre=origin + k*offset, tol=0.5);
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else:
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p_domain = p_codomain;
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p_codomain = random_points(nr_points=len(f.codomain), scale=SCALE, centre=origin + (k+1)*offset);
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p_codomain = random_points(nr_points=len(f.codomain), scale=SCALE, centre=origin + (k+1)*offset, tol=0.5);
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# range of composition so far:
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comp_range_next = [y for x, y in f.fct if x in comp_range];
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if k == 0:
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axs.scatter(p_domain[:, 0], p_domain[:, 1], label='', color='black', marker='o');
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axs.scatter(p_domain[:, 0], p_domain[:, 1], label='', color='blue', marker='o');
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if show_labels:
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for i, p in enumerate(p_domain):
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x_name = f.domain[i];
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@ -136,7 +136,7 @@ class Functions:
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for j, p in enumerate(p_codomain):
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y = f.codomain[j];
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marker = 'o' if (y in comp_range_next) else '.';
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axs.scatter([p[0]], [p[1]], label='', color='black', marker=marker);
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axs.scatter([p[0]], [p[1]], label='', color='blue', marker=marker);
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y_name = f.codomain[j];
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if show_labels:
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axs.annotate(text=f'{y_name}', xy=p, textcoords='offset points', xytext=ANNOTATE_OFFSET, ha='center', size=FONTSIZE_PTS);
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@ -146,7 +146,7 @@ class Functions:
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q = p_codomain[j];
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x = f.domain[i];
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if k == 0 or (x in comp_range):
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axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='black', linewidth=1);
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axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='blue', linewidth=1);
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else:
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axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='red', linestyle='--', linewidth=1);
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@ -165,6 +165,7 @@ class Functions:
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# update range of composition:
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comp_range = comp_range_next;
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axs.set_aspect('equal')
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return fig, axs;
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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@ -188,7 +189,7 @@ def random_points(
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scale: tuple[float, float] = (1., 1.),
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centre: tuple[float, float] = (0., 0.),
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force: bool = False,
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tol: float = 0.2,
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tol: float = 0.1,
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) -> NDArray[Shape['*, 2'], Float]:
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theta = np.linspace(start=0, stop=2*np.pi, num=nr_points, endpoint=False);
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r_min = 0.25;
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@ -12,8 +12,8 @@ from src.maths.sets.random import *;
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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__all__ = [
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'Letters',
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'random_function',
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'randomset_alphabet',
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'randomset_greek',
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'randomset_integers',
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];
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@ -15,9 +15,9 @@ from src.thirdparty.maths import *;
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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__all__ = [
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'Letters',
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'randomset_integers',
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'randomset_alphabet',
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'randomset_greek',
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'random_function',
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];
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@ -25,29 +25,68 @@ __all__ = [
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# CONSTANTS / VARIABLES
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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ALPHA = 'abcdefghijklmnopqrstuvwxyz';
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GREEK = 'αβγδεζηθικλμνξοπρςτυφχψω';
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# local usage only
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T1 = TypeVar('T1');
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T2 = TypeVar('T2');
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class Letters(Enum):
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# 'abcdefghijklmnopqrstuvwxyz'
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ROMAN = [chr(97 + n) for n in range(26)];
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# 'αβγδεζηθικλμνξοπρςτυφχψω'
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GREEK = [chr(945 + n) for n in range(25)]
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# 'אבגדהוזחטיךכלםמןנסעףפץצקרשת' (but <—)
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HEBREW = [chr(1488 + n) for n in range(27)];
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SYMBOLS = [
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r'$|0\rangle$',
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r'$|\uparrow\rangle$',
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r'$|\downarrow\rangle$',
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r'$\sqrt{2}$',
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r'$\pi$',
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r'$e$',
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r'$\frac{1}{137}$',
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r'$\infty$',
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# r'$-\infty$',
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r'$\clubsuit$',
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# r'$\diamondsuit$',
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r'$\heartsuit$',
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# r'$\spadesuit$',
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r'$\hbar$',
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];
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# METHODS
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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def randomset_integers(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
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def randomset_integers(
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N: int = -1,
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low: int = 1,
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high: int = 1,
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shuffle: bool = False,
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) -> list[int]:
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if N == -1:
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N = random.randint(low, high);
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return list(range(1, N+1));
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values = list(range(1, N+1));
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if shuffle:
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return sample(values, size=N, replace=False);
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return values;
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def randomset_alphabet(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
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if N == -1:
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def randomset_alphabet(
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mode: Letters,
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N: int = -1,
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low: int = 1,
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high: int = 1,
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shuffle: bool = False,
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full: bool = False,
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) -> list[str]:
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letters: list[str] = mode.value;
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if full:
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N = len(letters);
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elif N == -1:
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high = min(low+1, high)
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N = random.randint(low, high);
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return list([a for k, a in enumerate(ALPHA) if k < N]);
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def randomset_greek(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
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if N == -1:
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N = random.randint(low, high);
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return list([a for k, a in enumerate(GREEK) if k < N]);
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if shuffle:
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return sample(letters, size=N, replace=False);
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return letters[:N];
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def random_function(
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X: list[T1],
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24
src/thirdparty/maths.py
vendored
24
src/thirdparty/maths.py
vendored
@ -9,6 +9,29 @@ from fractions import Fraction;
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import math;
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import numpy as np;
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import random;
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from typing import TypeVar;
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# MODIFICATIONS
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# local usage only
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T = TypeVar('T');
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def sample(
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X: list[T],
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size: int = 1,
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replace: bool = True,
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) -> list[T]:
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'''
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@inputs
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- `X` - a list
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- `size` <int> - desired sample size
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- `replace` <bool> - optional replacement
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@returns a sample from an uniformly distributed set.
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'''
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return np.random.choice(X, size=size, replace=replace).tolist();
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# EXPORTS
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@ -19,4 +42,5 @@ __all__ = [
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'math',
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'np',
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'random',
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'sample',
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];
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@ -9,6 +9,7 @@ from __future__ import annotations;
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from src.thirdparty.types import *;
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from src.thirdparty.plots import *;
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from src.thirdparty.maths import *;
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from src.thirdparty.render import *;
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from src.maths.diagrams import *;
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@ -32,11 +33,13 @@ class FunctionDiagramWidget():
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N_max: int;
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fnames: list[str];
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setnames: list[str];
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setsfrom: list[list[Any]];
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def __init__(
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self,
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fnames: list[str],
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setnames: list[str],
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setsfrom: dict[str, list[Any]] | list[list[Any]] = [],
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N: Optional[int] = None,
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):
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self.state = None;
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@ -45,6 +48,19 @@ class FunctionDiagramWidget():
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assert len(setnames) == len(fnames) + 1, f'The number of sets must be {self.N_max+1}.';
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self.fnames = fnames;
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self.setnames = setnames;
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# fix set contents:
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if isinstance(setsfrom, dict):
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default = randomset_alphabet(mode=Letters.ROMAN, shuffle=True, full=True);
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setsfrom = [ setsfrom.get(name, default) for name in setnames ];
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if len(setsfrom) == 0:
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setsfrom = [
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randomset_alphabet(mode=Letters.SYMBOLS, shuffle=True, full=True),
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randomset_alphabet(mode=Letters.ROMAN, shuffle=True, full=True),
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randomset_alphabet(mode=Letters.HEBREW, shuffle=True, full=True),
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randomset_alphabet(mode=Letters.GREEK, shuffle=True, full=True),
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];
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n = len(setsfrom);
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self.setsfrom = [ setsfrom[k % n] for k, name in enumerate(setnames) ];
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def run(self):
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if self.N is None:
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@ -59,7 +75,7 @@ class FunctionDiagramWidget():
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cardinalities = [ kwargs[f'card_{k}'] for k in range(N+1)];
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injective = [ kwargs[f'injective_{k}'] for k in range(N)];
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surjective = [ kwargs[f'surjective_{k}'] for k in range(N)];
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X = [ randomset_alphabet(N=card) for card in cardinalities ];
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X = [ XX[:card] for XX, card in zip(self.setsfrom, cardinalities) ];
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comp = Functions(*[
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Function(
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name = (f'{self.fnames[k]}', f'{self.setnames[k]}', f'{self.setnames[k+1]}'),
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@ -85,38 +101,47 @@ class FunctionDiagramWidget():
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return;
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def handler_wrapper(self, N: int):
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show_labels = widgets.Checkbox(description='Labels anzeigen?', style={'description_width': 'initial'}, visible=True);
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button_refresh = widgets.ToggleButton(description='Neu laden');
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button_show_labels = widgets.Checkbox(
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description = 'Labels anzeigen?',
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value = True,
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style = {
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'description_width': 'initial',
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},
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visible = True
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);
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control_nr = widgets.IntSlider(value=N);
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controls_card = [
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widgets.IntSlider(
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value = None,
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description = f'|{self.setnames[k]}|',
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# value = None,
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value = min(3,len(XX)),
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description = f'|{setname}|',
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min = 1,
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max = 24,
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max = len(XX),
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)
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for k in range(N+1)
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for setname, XX in zip(self.setnames[:(N+1)], self.setsfrom[:(N+1)])
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];
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controls_injective = [
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widgets.Checkbox(
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value = None,
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description = f'{self.fnames[k]} injektiv?',
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value = False,
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description = f'{fname} injektiv?',
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style = {
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'description_width': 'initial',
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},
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visible = True,
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)
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for k in range(N)
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for fname in self.fnames[:N]
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];
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controls_surjective = [
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widgets.Checkbox(
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value = None,
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description = f'{self.fnames[k]} surjectiv?',
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value = False,
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description = f'{fname} surjectiv?',
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style = {
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'description_width': 'initial',
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},
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visible = True,
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)
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for k in range(N)
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for fname in self.fnames[:N]
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];
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# controls_func = [None for _ in range(2*N)];
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# controls_func[::2] = controls_injective;
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@ -136,19 +161,33 @@ class FunctionDiagramWidget():
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# for k in range(N)
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# ];
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ui = widgets.VBox(
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[show_labels] \
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[ button_refresh ] \
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+ [ button_show_labels ] \
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+ controls_card \
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+ [
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widgets.HBox([control_injective, control_surjective])
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widgets.HBox(
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[
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widgets.VBox(
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[control_injective, control_surjective],
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layout = {
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'display': 'flex',
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'align_items': 'stretch',
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'width': '100%',
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'overflow': 'hidden',
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},
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)
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for control_injective, control_surjective in zip(controls_injective, controls_surjective)
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]
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],
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)
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],
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);
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display(ui);
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display(widgets.interactive_output(
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f = self.handler_plot,
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controls = { 'N': control_nr, 'show_labels': show_labels } \
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controls = { 'N': control_nr, 'show_labels': button_show_labels } \
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| { f'card_{k}': controls_card[k] for k in range(N+1) } \
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| { f'injective_{k}': controls_injective[k] for k in range(N) } \
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| { f'surjective_{k}': controls_surjective[k] for k in range(N) }
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| { f'surjective_{k}': controls_surjective[k] for k in range(N) } \
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| { 'refresh': button_refresh }
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));
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return;
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