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master > master: src - methoden funktionieren

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RD 2022-10-20 22:04:06 +02:00
parent 7b237246da
commit 96684d30a8
2 changed files with 59 additions and 24 deletions
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24
src/maths/diagrams/sets.py
View File

@ -66,18 +66,24 @@ class Function(Generic[T1,T2]):
return Functions(self).draw();
class Functions:
name: str;
fcts: list[Function];
def __init__(self, *f: Function):
self.fcts = list(f);
self.name = r' \circ '.join([ fct.name[0] for fct in self.fcts ][::-1]);
def draw(self, show_labels: bool = True) -> Figure:
N = len(self.fcts);
obj = mplot.subplots(1, 1, constrained_layout=True);
fig: Figure = obj[0];
axs: Axes = obj[1];
axs.tick_params(axis='both', which='both', left=False, right=False, top=False, bottom=False, labelbottom=False, labelleft=False);
mplot.title('');
axs.tick_params(axis='both', which='both', labelbottom=False, labelleft=False);
mplot.title(f'Darstellung von ${self.name}$', fontdict={
'fontsize': 16,
'horizontalalignment': 'center',
'color': 'forestgreen',
});
mplot.xlabel('');
mplot.ylabel('');
mplot.margins(x=MARGIN, y=MARGIN);
@ -127,7 +133,7 @@ class Functions:
for j, p in enumerate(p_codomain):
y = f.codomain[j];
marker = 'o' if (y in comp_range_next) else 'x';
marker = 'o' if (y in comp_range_next) else '.';
axs.scatter([p[0]], [p[1]], label='', color='black', marker=marker);
y_name = f.codomain[j];
if show_labels:
@ -138,16 +144,16 @@ 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='g', linewidth=2);
axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='black', linewidth=1);
else:
axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='g', linestyle='--', linewidth=1);
axs.plot([p[0], q[0]], [p[1], q[1]], label='', color='red', linestyle='--', linewidth=1);
anchor = anchors[k];
fct_name, X_name, Y_name = f.name;
axs.annotate(text=f'{fct_name}', xy=anchor[0], ha='center', size=FONTSIZE_FCT);
axs.annotate(text=f'${fct_name}$', xy=anchor[0], ha='center', size=FONTSIZE_FCT);
if k == 0:
axs.annotate(text=f'{X_name}', xy=anchor[1], ha='center', size=FONTSIZE_FCT);
axs.annotate(text=f'{Y_name}', xy=anchor[2], ha='center', size=FONTSIZE_FCT);
axs.annotate(text=f'${X_name}$', xy=anchor[1], ha='center', size=FONTSIZE_FCT);
axs.annotate(text=f'${Y_name}$', xy=anchor[2], ha='center', size=FONTSIZE_FCT);
axs.add_patch(FancyArrowPatch(
anchor[3], anchor[4],
connectionstyle = 'arc3,rad=0.5',
@ -176,8 +182,6 @@ def oval(
P[-1, :] = P[0, :];
return P;
def random_points(
nr_points: int,
scale: tuple[float, float] = (1., 1.),

59
src/maths/sets/random.py
View File

@ -34,16 +34,19 @@ T2 = TypeVar('T2');
# METHODS
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def randomset_integers(low: int, high: int) -> list[int]:
N = random.randint(low, high);
def randomset_integers(N: int = -1, low: int = 1, high: int = 1) -> list[int]:
if N == -1:
N = random.randint(low, high);
return list(range(1, N+1));
def randomset_alphabet(low: int, high: int) -> list[int]:
N = random.randint(low, high);
def randomset_alphabet(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(ALPHA) if k < N]);
def randomset_greek(low: int, high: int) -> list[int]:
N = random.randint(low, high);
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]);
def random_function(
@ -52,11 +55,39 @@ def random_function(
injective: Optional[bool] = None,
surjective: Optional[bool] = None,
) -> list[tuple[T1, T2]]:
# TODO: add feature to force injectivity/surjectivity, if possible.
# m = len(X);
# n = len(Y);
# if m > n:
# injective = False;
# if m < n:
# surjective = False;
return [ (x, random.choice(Y)) for x in X ];
m = len(X);
n = len(Y);
if m == 0:
return [];
if n == 0:
raise Exception(f'Impossible to create a function with {m} elements in the domain and {n} in the codomain.');
match (injective, surjective):
case (True, _):
assert m <= n, f'Impossible to create an injective function with {m} elements in the domain and {n} in the codomain.';
Y = random.sample(Y, m);
return [(x, y) for x, y in zip(X, Y)];
case (_, True):
assert m >= n, f'Impossible to create an surjective function with {m} elements in the domain and {n} in the codomain.';
indexes = random.sample(list(range(m)), n);
g = [ (indexes[j], Y[j]) for j in range(n) ] \
+ [
(i, random.choice(Y))
for i in range(m)
if not i in indexes
];
g = sorted(g, key=lambda o: o[0]);
return [ (X[i], y) for (i, y) in g ];
case (False, _):
assert m > 1, f'Impossible to create a non-injective function with {m} elements in the domain.';
indexes = random.sample(list(range(m)), m);
g = random_function(indexes, Y);
[(i0, y0), (i1, y1)] = g[:2];
g[0] = (i0, y1);
g = sorted(g, key=lambda o: o[0]);
return [ (X[i], y) for (i, y) in g ];
case (_, False):
assert n > 1, f'Impossible to create a non-surjective function with {n} elements in the codomain.';
Y = random.sample(Y, n-1);
return random_function(X, Y);
case _:
return [ (x, random.choice(Y)) for x in X ];