Create binary_polinomial_factoring.sage

Author: daedalus

binary_polinomial_factoring.sage

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+#!/usr/bin/sage
+# Factoring integers representing them with polynomials with order=bits
+# Ex: 15 = 2^0 + 2^1 + 2^2 + 2^3 -> (2^0 + 2^1) * (2^0 + 2^2) -> 3*5
+# It works well with mersenne primes but not with other composites.
+
+import sys
+sys.setrecursionlimit(100000)
+
+import math
+import gmpy2
+from gmpy2 import mpz
+
+def int_to_poly(n):
+  n = mpz(n)
+  tmp="" 
+  tmp2=[] 
+  bits = n.bit_length()
+  for j in range(0,bits): 
+    b=int((n >> j) & 1) 
+    tmp = str(b) + tmp 
+    if b == 1: 
+      tmp2.append("x^%d " % (j))
+  return "+".join(tmp2)
+
+def factor_int(n,verbose=False):
+  if verbose:
+    print("converting to poly:")
+  poly = SR(int_to_poly(n))
+  if verbose:
+    print(poly)
+    print("finding factors:")
+  factored = factor(poly)
+  if verbose:
+    print(factored)
+    print("evaluating terms:")
+  factors = []
+  terms = str(factored).split(")*")
+  ls = len(terms)
+  if verbose:
+    print(ls)
+  if ls > 0:
+    for term in terms:
+      term = term.replace("(","").replace(")","")
+      if verbose:
+        print(term)
+      factors.append(sage_eval(term,{'x':2}))
+  return factors
+  
+  if __name__ == "__main__":
+    print(factor_int(Integer(sys.argv[1])))