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https://github.com/wangjksjtu/python_NumTheory
https://github.com/wangjksjtu/python_NumTheory
Last synced: 3 months ago
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- Host: GitHub
- URL: https://github.com/wangjksjtu/python_NumTheory
- Owner: wangjksjtu
- Created: 2017-05-07T03:50:57.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2017-06-04T04:32:31.000Z (over 7 years ago)
- Last Synced: 2024-05-22T19:31:53.530Z (9 months ago)
- Language: Python
- Size: 7.81 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
- awesome-scs - 2017 - python_NumTheory
README
## python_NumTheory
A python library that realizes the basic algorthims in number theory
### Functions ###
def isPrime(n): # judge if a positive integer is a prime
def countPrime(a, b, c = 1): # count number of primes in [a, b], c is interval
def getAllPrime(a, b, c = 1): # get all primes in [a, b], c is interval
def getResidue(n, mode = 0): # get residue of a positive integer
def EuclidDivision(a, b, mode = 0): # finish euclid division
def greatestCommonDivisor(a, b): # get the greatest common divisor of two integers
def greatestCommonDivisor_n(a): # get the greatest common divisor of n integers (a is a list)
def leastCommonMultiple(a, b): # get the least common multiple of two integers
def leastCommonMultiple_n(a): # get the least common multiple of n integers (a is a list)
def isCoprime(a, b): # judge if a and b are coprime
def getReciprocal(a, m) # get reciprocal of a mod m
def decompose(a): # decompose an integer in violence
def getStandardDecomposition(a): # get standard decomposition expression in violence
def Bezout(a, b): # Bezout theory
def binaryLinearDiophantineEquation(a, b, c): # get answer of binary linear diophantine equation
def quickPow(a, b, m): # quick pow implementaion
def quadraticResidue_prime(p): # get quadratic residues of a prime
def quadraticNonResidue_prime(p): # get quadratic non-residues of a prime
def quadraticResidue_prime_pair(p): # get quadratic residue-pair of a prime
def EllipticCurveEquation(a, b, c, d, p): # solve elliptic curve equation
def Legendre(a, p): # caculate Legendre symbol
def Jacobi(a, p): # caculate Jacobi symbol
def NaiveModSquareEquation(a, m): # solve mod-square equation in violence
def ModSquareEquation(a, m): # solve mod-square equation
def NaiveSquarePEquation(p): # solve square p equation in violence
def EulerFunction(m): # implement euler function
def getSimplifySurplus(m): # get simplify surplus set of m
def isPrimaryRoot(g, p): # judge if g is primary root of p
def getAllPrimaryRoot_naive(p): # get all primary root in violence
def getAllPrimaryRoot(p): # get all primary root
def FermatPseudoprime(size, probability = 0.0001): # generate Fermat pseudoprime
def EulerPseudoprime(size, probability = 0.0001): # generate Euler pseudoprime
### Attentions ###
+ There are not user friendly documents now.
+ There are still some alogorithms unfinished.
+ I will update this repo if I have free time and I think it's worth doing so.
### Later Work ###
+ def SquarePEquation(p):
+ def Even_fractions(x):
+ def getAllPrimaryRoot_n(p, a):
+ related useful functions
+ other algorithms such as RSA.
### Contact me ###
+ [email protected]
+ [email protected]