Updates

Added some infor in the readme, Added the unit_test.py, added some
examples and made some minor modifications in pyprime.

README.md

@@ -14,14 +14,14 @@ Algorithm developped :
 - Fermat's test (based on Fermat's theorem)
 - Prime generating functions
 
-## Math
+# Math
 
 Here are a bit of information to help understand some of the algorithms
 
 Congruence :
 ------------
  "`≡`" means congruent, `a ≡ b (mod m)` implies that 
-`m/(a-b), ∃ k ∈ Z` that verifies `a = kn + b`
+`m / (a-b), ∃ k ∈ Z` that verifies `a = kn + b`
 
  which implies:
 
@@ -35,10 +35,15 @@ Fermart's Theorem
 
 Miller rabin
 ------------ 
- Take a random `a∈{1,...,n−1}` and `n > 2`, </br>
+ Take a random `a ∈ {1,...,n−1}` and `n > 2`, </br>
  Find `d` and `s` such as with `n - 1 = 2^s * d` (with d odd) </br>
  if `(a^d)^2^r ≡ 1 mod n` for all `r` in `0` to `s-1` </br>
  Then `n` is prime.
 
  The test output is false of 1/4 of the "a values" possible in `n`, 
- so the test is repeated t times.
+ so the test is repeated t times.
+
+
+Strong Pseudoprime
+-------------------
+A strong [pseudoprime](http:https://mathworld.wolfram.com/StrongPseudoprime.html) to a base `a` is an odd composite number `n` with `n-1 = d·2^s` (for d odd) for which either `a^d = 1(mod n)` or `a^(d·2^r) = -1(mod n)` for some `r = 0, 1, ..., s-1` </br>

src/examples.py

@@ -3,10 +3,15 @@
 Created on Tue Mar 21 13:23:52 2017
 
 @author: sylhare
+
 """
 
 import pyprime as p
+import unit_test as ut
 
+#Demo of Grphical Prime functions
+p.sacksPlot()
+p.ulamPlot()
 
 #Demo of the Primarity testing functions
 print(p.isPrime(7))
@@ -17,6 +22,6 @@
 print(p.genPrimes(7))
 print(p.findPrimes(2, 7, p.fermat))
 
-#Demo of Grphical Prime functions
-p.sacksPlot()
-p.ulamPlot()
+#Demo of the unit_test functions
+print(ut.carmiTest(p.isPrime))
+print(ut.ppTest(p.isPrime))

src/pyprime.py

@@ -172,7 +172,7 @@ def sacks(upper=1000, primeTest=pyprime):
  theta = math.sqrt(i) * 2 * math.pi #i=1 theta= 2pi for a given i, angle=(i*theta)/1 
  r = math.sqrt(i) 
 
- if primeTest(i) == True:
+ if primeTest(i):
  pricoo.append((theta,r)) 
  else:
  coord.append((theta,r))

src/unit_test.py

@@ -0,0 +1,81 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Feb 14 11:34:49 2017
+
+@author: Sylhare
+
+"""
+
+
+#Carmichael number often trigger false positive for the fermat algorithm
+__carmichael = [561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341]
+
+#The key is the base, the list is the pseudoprimes of that base
+__pseudoPrimes = {2: [2047, 3277, 4033, 4681, 8321], 
+ 3: [121, 703, 1891, 3281, 8401, 8911],
+ 4: [341, 1387, 2047, 3277, 4033, 4371],
+ 5: [781, 1541, 5461, 5611, 7813],
+ 6: [217, 481, 1111, 1261, 2701],
+ 7: [25, 325, 703, 2101, 2353, 4525],
+ 8: [9, 65, 481, 511, 1417, 2047],
+ 9: [91, 121, 671, 703, 1541, 1729]}
+
+def ppTest(function):
+ """
+ Test the function on a couple of pseudo primes numbers
+ 
+ Returns a string with all the results
+ True - passes the test
+ False - fails the test
+ 
+ """
+ results = {}
+ status = "\nPseudo Primes Test:\n"
+
+ for key in __pseudoPrimes:
+ results[key] = functionTest(function, __pseudoPrimes[key])
+ status += "[" + passTest(results[key]) + "]: PseudoPrime #" \
+ + str(key) + "\n"
+
+ return status
+
+def carmiTest(function):
+ """
+ Test the function on the carmichael numbers
+ Fermat and millerRabin usually fail this test
+ 
+ Returns a string with the result
+ True - passes the test
+ False - fails the test
+ 
+ """
+ results = functionTest(function, __carmichael)
+ status = "\nCarmichael Test:\n"
+ status += "[" + passTest(results) + "]: Carmichael" 
+
+ return status 
+
+def functionTest(function, src):
+ """
+ Take a function and a source list of numbers to test on the function 
+ 
+ Returns a list of tuples (the number tested, it's own result)
+ """
+ results = []
+ for n in src:
+ results.append((n, function(n)))
+
+ return results
+
+def passTest(results):
+ """
+ For Prime testing functions, in order to pass the test,
+ the results should be a list of False 
+ 
+ Return OK when pass the test, FAIL otherwise 
+ """
+ for n in results:
+ if n[1]:
+ return "FAIL"
+
+ return " OK "