master > master: notebook - minor

- enums für Alphabete
- button layout
- refresh Knopf
- aspect ratio

notebooks/week-2.ipynb

@@ -51,8 +51,8 @@
    "source": [
     "FunctionDiagramWidget(\n",
     "    N = 2,\n",
-    "    fnames   = ['f', 'g', 'h'],\n",
-    "    setnames = ['X', 'Y', 'Z', 'W'],\n",
+    "    fnames   = ['f', 'g', 'h', 'i', 'j'],\n",
+    "    setnames = ['X', 'Y', 'Z', 'U', 'V', 'W'],\n",
     ").run();"
    ]
   },

src/maths/diagrams/sets.py

@@ -28,7 +28,7 @@ __all__ = [
 T1 = TypeVar('T1');
 T2 = TypeVar('T2');
 
-SCALE  = (1., 4.);
+SCALE  = (1., 1.5);
 OFFSET = (3., 0.);
 HMARGIN = 0.1;
 VMARGIN = 0.2;
@@ -119,15 +119,15 @@ class Functions:
         for k, f in enumerate(self.fcts):
             if k == 0:
                 comp_range = f.domain;
-                p_domain = random_points(nr_points=len(f.domain), scale=SCALE, centre=origin + k*offset);
+                p_domain = random_points(nr_points=len(f.domain), scale=SCALE, centre=origin + k*offset, tol=0.5);
             else:
                 p_domain = p_codomain;
-            p_codomain = random_points(nr_points=len(f.codomain), scale=SCALE, centre=origin + (k+1)*offset);
+            p_codomain = random_points(nr_points=len(f.codomain), scale=SCALE, centre=origin + (k+1)*offset, tol=0.5);
             # range of composition so far:
             comp_range_next = [y for x, y in f.fct if x in comp_range];
 
             if k == 0:
-                axs.scatter(p_domain[:, 0], p_domain[:, 1], label='', color='black', marker='o');
+                axs.scatter(p_domain[:, 0], p_domain[:, 1], label='', color='blue', marker='o');
                 if show_labels:
                     for i, p in enumerate(p_domain):
                         x_name = f.domain[i];
@@ -136,7 +136,7 @@ class Functions:
             for j, p in enumerate(p_codomain):
                 y = f.codomain[j];
                 marker = 'o' if (y in comp_range_next) else '.';
-                axs.scatter([p[0]], [p[1]], label='', color='black', marker=marker);
+                axs.scatter([p[0]], [p[1]], label='', color='blue', marker=marker);
                 y_name = f.codomain[j];
                 if show_labels:
                     axs.annotate(text=f'{y_name}', xy=p, textcoords='offset points', xytext=ANNOTATE_OFFSET, ha='center', size=FONTSIZE_PTS);
@@ -146,7 +146,7 @@ class Functions:
                 q = p_codomain[j];
                 x = f.domain[i];
                 if k == 0 or (x in comp_range):
-                    axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='black', linewidth=1);
+                    axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='blue', linewidth=1);
                 else:
                     axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='red', linestyle='--', linewidth=1);
 
@@ -165,6 +165,7 @@ class Functions:
 
             # update range of composition:
             comp_range = comp_range_next;
+        axs.set_aspect('equal')
         return fig, axs;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -188,7 +189,7 @@ def random_points(
     scale:     tuple[float, float] = (1., 1.),
     centre:    tuple[float, float] = (0., 0.),
     force:     bool = False,
-    tol:       float = 0.2,
+    tol:       float = 0.1,
 ) -> NDArray[Shape['*, 2'], Float]:
     theta = np.linspace(start=0, stop=2*np.pi, num=nr_points, endpoint=False);
     r_min = 0.25;

src/maths/sets/__init__.py

@@ -12,8 +12,8 @@ from src.maths.sets.random import *;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
+    'Letters',
     'random_function',
     'randomset_alphabet',
-    'randomset_greek',
     'randomset_integers',
 ];

src/maths/sets/random.py

@@ -15,9 +15,9 @@ from src.thirdparty.maths import *;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
+    'Letters',
     'randomset_integers',
     'randomset_alphabet',
-    'randomset_greek',
     'random_function',
 ];
 
@@ -25,29 +25,68 @@ __all__ = [
 # CONSTANTS / VARIABLES
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-ALPHA = 'abcdefghijklmnopqrstuvwxyz';
-GREEK = 'αβγδεζηθικλμνξοπρςτυφχψω';
+# local usage only
 T1 = TypeVar('T1');
 T2 = TypeVar('T2');
 
+class Letters(Enum):
+    # 'abcdefghijklmnopqrstuvwxyz'
+    ROMAN = [chr(97 + n) for n in range(26)];
+    # 'αβγδεζηθικλμνξοπρςτυφχψω'
+    GREEK = [chr(945 + n) for n in range(25)]
+    # 'אבגדהוזחטיךכלםמןנסעףפץצקרשת' (but <—)
+    HEBREW = [chr(1488 + n) for n in range(27)];
+    SYMBOLS = [
+        r'$|0\rangle$',
+        r'$|\uparrow\rangle$',
+        r'$|\downarrow\rangle$',
+        r'$\sqrt{2}$',
+        r'$\pi$',
+        r'$e$',
+        r'$\frac{1}{137}$',
+        r'$\infty$',
+        # r'$-\infty$',
+        r'$\clubsuit$',
+        # r'$\diamondsuit$',
+        r'$\heartsuit$',
+        # r'$\spadesuit$',
+        r'$\hbar$',
+    ];
+
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # METHODS
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-def randomset_integers(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
+def randomset_integers(
+    N:       int  = -1,
+    low:     int  = 1,
+    high:    int  = 1,
+    shuffle: bool = False,
+) -> list[int]:
     if N == -1:
         N = random.randint(low, high);
-    return list(range(1, N+1));
+    values = list(range(1, N+1));
+    if shuffle:
+        return sample(values, size=N, replace=False);
+    return values;
 
-def randomset_alphabet(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
-    if N == -1:
+def randomset_alphabet(
+    mode: Letters,
+    N:       int  = -1,
+    low:     int  = 1,
+    high:    int  = 1,
+    shuffle: bool = False,
+    full:    bool = False,
+) -> list[str]:
+    letters: list[str] = mode.value;
+    if full:
+        N = len(letters);
+    elif N == -1:
+        high = min(low+1, high)
         N = random.randint(low, high);
-    return list([a for k, a in enumerate(ALPHA) if k < N]);
-
-def randomset_greek(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
-    if N == -1:
-        N = random.randint(low, high);
-    return list([a for k, a in enumerate(GREEK) if k < N]);
+    if shuffle:
+        return sample(letters, size=N, replace=False);
+    return letters[:N];
 
 def random_function(
     X: list[T1],

src/thirdparty/maths.py

@@ -9,6 +9,29 @@ from fractions import Fraction;
 import math;
 import numpy as np;
 import random;
+from typing import TypeVar;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# MODIFICATIONS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+# local usage only
+T = TypeVar('T');
+
+def sample(
+    X: list[T],
+    size: int = 1,
+    replace: bool = True,
+) -> list[T]:
+    '''
+    @inputs
+    - `X` - a list
+    - `size` <int> - desired sample size
+    - `replace` <bool> - optional replacement
+
+    @returns a sample from an uniformly distributed set.
+    '''
+    return np.random.choice(X, size=size, replace=replace).tolist();
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS
@@ -19,4 +42,5 @@ __all__ = [
     'math',
     'np',
     'random',
+    'sample',
 ];

src/widgets/function_diagrams.py

@@ -9,6 +9,7 @@ from __future__ import annotations;
 
 from src.thirdparty.types import *;
 from src.thirdparty.plots import *;
+from src.thirdparty.maths import *;
 from src.thirdparty.render import *;
 
 from src.maths.diagrams import *;
@@ -32,11 +33,13 @@ class FunctionDiagramWidget():
     N_max: int;
     fnames: list[str];
     setnames: list[str];
+    setsfrom: list[list[Any]];
 
     def __init__(
         self,
         fnames: list[str],
         setnames: list[str],
+        setsfrom: dict[str, list[Any]] | list[list[Any]] = [],
         N: Optional[int] = None,
     ):
         self.state = None;
@@ -45,6 +48,19 @@ class FunctionDiagramWidget():
         assert len(setnames) == len(fnames) + 1, f'The number of sets must be {self.N_max+1}.';
         self.fnames = fnames;
         self.setnames = setnames;
+        # fix set contents:
+        if isinstance(setsfrom, dict):
+            default = randomset_alphabet(mode=Letters.ROMAN, shuffle=True, full=True);
+            setsfrom = [ setsfrom.get(name, default) for name in setnames ];
+        if len(setsfrom) == 0:
+            setsfrom = [
+                randomset_alphabet(mode=Letters.SYMBOLS, shuffle=True, full=True),
+                randomset_alphabet(mode=Letters.ROMAN, shuffle=True, full=True),
+                randomset_alphabet(mode=Letters.HEBREW, shuffle=True, full=True),
+                randomset_alphabet(mode=Letters.GREEK, shuffle=True, full=True),
+            ];
+        n = len(setsfrom);
+        self.setsfrom = [ setsfrom[k % n] for k, name in enumerate(setnames) ];
 
     def run(self):
         if self.N is None:
@@ -59,7 +75,7 @@ class FunctionDiagramWidget():
         cardinalities = [ kwargs[f'card_{k}'] for k in range(N+1)];
         injective = [ kwargs[f'injective_{k}'] for k in range(N)];
         surjective = [ kwargs[f'surjective_{k}'] for k in range(N)];
-        X = [ randomset_alphabet(N=card) for card in cardinalities ];
+        X = [ XX[:card] for XX, card in zip(self.setsfrom, cardinalities) ];
         comp = Functions(*[
             Function(
                 name     = (f'{self.fnames[k]}', f'{self.setnames[k]}', f'{self.setnames[k+1]}'),
@@ -85,38 +101,47 @@ class FunctionDiagramWidget():
         return;
 
     def handler_wrapper(self, N: int):
-        show_labels = widgets.Checkbox(description='Labels anzeigen?', style={'description_width': 'initial'}, visible=True);
+        button_refresh = widgets.ToggleButton(description='Neu laden');
+        button_show_labels = widgets.Checkbox(
+            description = 'Labels anzeigen?',
+            value = True,
+            style       = {
+                'description_width': 'initial',
+            },
+            visible     = True
+        );
         control_nr = widgets.IntSlider(value=N);
         controls_card = [
             widgets.IntSlider(
-                value       = None,
-                description = f'|{self.setnames[k]}|',
+                # value       = None,
+                value       = min(3,len(XX)),
+                description = f'|{setname}|',
                 min         = 1,
-                max         = 24,
+                max         = len(XX),
             )
-            for k in range(N+1)
+            for setname, XX in zip(self.setnames[:(N+1)], self.setsfrom[:(N+1)])
         ];
         controls_injective = [
             widgets.Checkbox(
-                value       = None,
-                description = f'{self.fnames[k]} injektiv?',
+                value       = False,
+                description = f'{fname} injektiv?',
                 style       = {
                     'description_width': 'initial',
                 },
                 visible     = True,
             )
-            for k in range(N)
+            for fname in self.fnames[:N]
         ];
         controls_surjective = [
             widgets.Checkbox(
-                value       = None,
-                description = f'{self.fnames[k]} surjectiv?',
+                value       = False,
+                description = f'{fname} surjectiv?',
                 style       = {
                     'description_width': 'initial',
                 },
                 visible     = True,
             )
-            for k in range(N)
+            for fname in self.fnames[:N]
         ];
         # controls_func = [None for _ in range(2*N)];
         # controls_func[::2] = controls_injective;
@@ -136,19 +161,33 @@ class FunctionDiagramWidget():
         #     for k in range(N)
         # ];
         ui = widgets.VBox(
-            [show_labels] \
+            [ button_refresh ] \
+            + [ button_show_labels ] \
             + controls_card \
             + [
-                widgets.HBox([control_injective, control_surjective])
-                for control_injective, control_surjective in zip(controls_injective, controls_surjective)
-            ]
+                widgets.HBox(
+                    [
+                        widgets.VBox(
+                            [control_injective, control_surjective],
+                            layout = {
+                                'display': 'flex',
+                                'align_items': 'stretch',
+                                'width': '100%',
+                                'overflow': 'hidden',
+                            },
+                        )
+                        for control_injective, control_surjective in zip(controls_injective, controls_surjective)
+                    ],
+                )
+            ],
         );
         display(ui);
         display(widgets.interactive_output(
             f = self.handler_plot,
-            controls = { 'N': control_nr, 'show_labels': show_labels } \
+            controls = { 'N': control_nr, 'show_labels': button_show_labels } \
                 | { f'card_{k}': controls_card[k] for k in range(N+1) } \
                 | { f'injective_{k}': controls_injective[k] for k in range(N) } \
-                | { f'surjective_{k}': controls_surjective[k] for k in range(N) }
+                | { f'surjective_{k}': controls_surjective[k] for k in range(N) } \
+                | { 'refresh': button_refresh }
         ));
         return;