tex-projects/LaTeX-examples
2
0
Fork 0
mirror of https://github.com/MartinThoma/LaTeX-examples.git synced 2025-04-19 11:38:05 +02:00
Code Activity

Fix Python code style

Browse source
This commit is contained in:
Martin Thoma 2015-11-20 22:36:38 +01:00
parent bd1f36e90c
commit 59b3d42774
5 changed files with 134 additions and 96 deletions
Download patch file Download diff file Expand all files Collapse all files

75
source-code/Pseudocode/Calculate-Legendre/calculateLegendre.py
View file

@ -1,75 +0,0 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
def isPrime(a):
return all(a % i for i in xrange(2, a))
# http://stackoverflow.com/a/14793082/562769
def factorize(n):
factors = []
p = 2
while True:
while(n % p == 0 and n > 0): #while we can divide by smaller number, do so
factors.append(p)
n = n / p
p += 1 #p is not necessary prime, but n%p == 0 only for prime numbers
if p > n / p:
break
if n > 1:
factors.append(n)
return factors
def calculateLegendre(a, p):
"""
Calculate the legendre symbol (a, p) with p is prime.
The result is either -1, 0 or 1
>>> calculateLegendre(3, 29)
-1
>>> calculateLegendre(111, 41) # Beispiel aus dem Skript, S. 114
-1
>>> calculateLegendre(113, 41) # Beispiel aus dem Skript, S. 114
1
>>> calculateLegendre(2, 31)
1
>>> calculateLegendre(5, 31)
1
>>> calculateLegendre(150, 1009) # http://math.stackexchange.com/q/221223/6876
1
>>> calculateLegendre(25, 1009) # http://math.stackexchange.com/q/221223/6876
1
>>> calculateLegendre(2, 1009) # http://math.stackexchange.com/q/221223/6876
1
>>> calculateLegendre(3, 1009) # http://math.stackexchange.com/q/221223/6876
1
"""
if a >= p or a < 0:
return calculateLegendre(a % p, p)
elif a == 0 or a == 1:
return a
elif a == 2:
if p%8 == 1 or p%8 == 7:
return 1
else:
return -1
elif a == p-1:
if p%4 == 1:
return 1
else:
return -1
elif not isPrime(a):
factors = factorize(a)
product = 1
for pi in factors:
product *= calculateLegendre(pi, p)
return product
else:
if ((p-1)/2)%2==0 or ((a-1)/2)%2==0:
return calculateLegendre(p, a)
else:
return (-1)*calculateLegendre(p, a)
if __name__ == "__main__":
import doctest
doctest.testmod()

94
source-code/Pseudocode/Calculate-Legendre/calculate_legendre.py Normal file
View file

@ -0,0 +1,94 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
def is_prime(a):
"""
Check if `a` is a prime number.
Parameters
----------
a : int, a >= 2
"""
return all(a % i for i in xrange(2, a))
# http://stackoverflow.com/a/14793082/562769
def factorize(n):
factors = []
p = 2
while True:
# while we can divide by smaller number, do so
while(n % p == 0 and n > 0):
factors.append(p)
n = n / p
p += 1 # p is not necessary prime, but n%p == 0 only for prime numbers
if p > n / p:
break
if n > 1:
factors.append(n)
return factors
def calculate_legendre(a, p):
"""
Calculate the legendre symbol (a, p) with p is prime.
The result is either -1, 0 or 1
>>> calculate_legendre(3, 29)
-1
>>> calculate_legendre(111, 41) # Beispiel aus dem Skript, S. 114
-1
>>> calculate_legendre(113, 41) # Beispiel aus dem Skript, S. 114
1
>>> calculate_legendre(2, 31)
1
>>> calculate_legendre(5, 31)
1
# http://math.stackexchange.com/q/221223/6876
>>> calculate_legendre(150, 1009)
1
# http://math.stackexchange.com/q/221223/6876
>>> calculate_legendre(25, 1009)
1
# http://math.stackexchange.com/q/221223/6876
>>> calculate_legendre(2, 1009)
1
# http://math.stackexchange.com/q/221223/6876
>>> calculate_legendre(3, 1009)
1
"""
if a >= p or a < 0:
return calculate_legendre(a % p, p)
elif a == 0 or a == 1:
return a
elif a == 2:
if p % 8 == 1 or p % 8 == 7:
return 1
else:
return -1
elif a == p-1:
if p % 4 == 1:
return 1
else:
return -1
elif not is_prime(a):
factors = factorize(a)
product = 1
for pi in factors:
product *= calculate_legendre(pi, p)
return product
else:
if ((p-1)/2) % 2 == 0 or ((a-1)/2) % 2 == 0:
return calculate_legendre(p, a)
else:
return (-1)*calculate_legendre(p, a)
if __name__ == "__main__":
import doctest
doctest.testmod()

18
source-code/Pseudocode/Cholesky-Zerlegung/CholeskyZerlegung.py
View file

@ -1,18 +0,0 @@
def getL(A):
n = len(A)
L = [[0 for i in range(n)] for j in range(n)]
print(L)
print("")
for k in range(n):
L[k][k] = (A[k][k] - sum([L[k][i]**2 for i in range(k)]))**0.5
for i in range(k+1, n):
L[i][k] = (A[i][k]
- sum([L[i][j]*L[k][j] for j in range(k)])) \
/ L[k][k]
print("L_%i%i = A%i%i - sum(L_...)/L_%i%i) = %i" % (i, k, i, k, k, k, L[i][k]))
return L
A = [[1,2,3],[2,8,14],[3,14,34]]
print getL(A)

22
source-code/Pseudocode/Cholesky-Zerlegung/cholesky_zerlegung.py Normal file
View file

@ -0,0 +1,22 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
def get_l(A):
n = len(A)
L = [[0 for i in range(n)] for j in range(n)]
print(L)
print("")
for k in range(n):
L[k][k] = (A[k][k] - sum([L[k][i]**2 for i in range(k)]))**0.5
for i in range(k+1, n):
L[i][k] = ((A[i][k] - sum([L[i][j]*L[k][j] for j in range(k)]))
/ L[k][k])
print("L_%i%i = A%i%i - sum(L_...)/L_%i%i) = %i" %
(i, k, i, k, k, k, L[i][k]))
return L
A = [[1, 2, 3], [2, 8, 14], [3, 14, 34]]
print(get_l(A))

21
source-code/Pseudocode/Euklidischer-Algorithmus/basiswechsel.py Normal file → Executable file
View file

@ -1,7 +1,22 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
def euklid(b, Z):
"""
Euclids algorithm to change the basis.
Returns
-------
dict
A dictionary mapping the i-th position of the new number to its value,
where higher numbers are more significant.
Examples
--------
>>> euklid(3, 5)
{1: 1, 0: 2}
"""
p = 0
while b**p <= Z:
p = p+1
@ -9,14 +24,14 @@ def euklid(b, Z):
y = {}
while Z != 0 and i > -5:
y[i] = Z // b**i
y[i] = Z // b**i
R = Z % b**i
Z = R
i = i -1
i = i - 1
return y
if __name__ == "__main__":
r = euklid(16, 15741.233)
print("Result:")
for key in sorted(r.iterkeys(),reverse=True):
for key in sorted(r.iterkeys(), reverse=True):
print "%s: %s" % (key, r[key])