ton/ImageUtils
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

rm CondaPkg environment

Browse Source
This commit is contained in:
ton
2023-04-06 13:53:47 +07:00
parent 0a57ed7884
commit c43d949309
3329 changed files with 5725 additions and 447022 deletions
Download Patch File Download Diff File Expand all files Collapse all files

24
.CondaPkg/env/Lib/site-packages/networkx/generators/expanders.py vendored
View File

@@ -70,8 +70,8 @@ def margulis_gabber_galil_graph(n, create_using=None):
msg = "`create_using` must be an undirected multigraph."
raise nx.NetworkXError(msg)
for (x, y) in itertools.product(range(n), repeat=2):
for (u, v) in (
for x, y in itertools.product(range(n), repeat=2):
for u, v in (
((x + 2 * y) % n, y),
((x + (2 * y + 1)) % n, y),
(x, (y + 2 * x) % n),
@@ -146,22 +146,22 @@ def chordal_cycle_graph(p, create_using=None):
def paley_graph(p, create_using=None):
"""Returns the Paley (p-1)/2-regular graph on p nodes.
r"""Returns the Paley $\frac{(p-1)}{2}$ -regular graph on $p$ nodes.
The returned graph is a graph on Z/pZ with edges between x and y
if and only if x-y is a nonzero square in Z/pZ.
The returned graph is a graph on $\mathbb{Z}/p\mathbb{Z}$ with edges between $x$ and $y$
if and only if $x-y$ is a nonzero square in $\mathbb{Z}/p\mathbb{Z}$.
If p = 1 mod 4, -1 is a square in Z/pZ and therefore x-y is a square if and
only if y-x is also a square, i.e the edges in the Paley graph are symmetric.
If $p \equiv 1 \pmod 4$, $-1$ is a square in $\mathbb{Z}/p\mathbb{Z}$ and therefore $x-y$ is a square if and
only if $y-x$ is also a square, i.e the edges in the Paley graph are symmetric.
If p = 3 mod 4, -1 is not a square in Z/pZ and therefore either x-y or y-x
is a square in Z/pZ but not both.
If $p \equiv 3 \pmod 4$, $-1$ is not a square in $\mathbb{Z}/p\mathbb{Z}$ and therefore either $x-y$ or $y-x$
is a square in $\mathbb{Z}/p\mathbb{Z}$ but not both.
Note that a more general definition of Paley graphs extends this construction
to graphs over q=p^n vertices, by using the finite field F_q instead of Z/pZ.
to graphs over $q=p^n$ vertices, by using the finite field $F_q$ instead of $\mathbb{Z}/p\mathbb{Z}$.
This construction requires to compute squares in general finite fields and is
not what is implemented here (i.e paley_graph(25) does not return the true
Paley graph associated with 5^2).
not what is implemented here (i.e `paley_graph(25)` does not return the true
Paley graph associated with $5^2$).
Parameters
----------