factorization algorithm

[Jihun Yang]

let's implement this! https://en.m.wikipedia.org/wiki/Quadratic_sieve

[Jihun Yang]

algebra/algebra/polynomial/polynomial.py

Lines 168 to 201 in 1b92cc2

 def factorize(self) -> List['Polynomial']: 
     if self.degree < 2: 
         return [self] 
  
     degree = max(self.body, default=0) 
     many = degree // 2 
  
     value = [ 
         ( 
             i, 
             (v := int(self(i))), 
             divisor_function(abs(v)) * 2 if v != 0 else 1 
         ) 
         for i in range(-100, 100) 
     ] 
     value.sort(key=itemgetter(2, 1, 0)) 
     picked = value[:many] 
     picked_factor = [self._num_factor(v[1]) for v in picked] 
     checker = value[many] 
  
     for each_value in itertools.product(*picked_factor): 
         poly: Polynomial = Polynomial.from_map({ 
             x[0]: z 
             for x, z in zip(picked, each_value) 
         }) 
         if poly.degree > 0 and poly.is_integer_coefficient(): 
             if poly[poly.degree] < 0: 
                 poly = -poly 
             if self._check_this_value(checker[1], poly(checker[0])): 
                 q, r = divmod(self, poly) 
                 if r == 0: 
                     return poly.factorize() + q.factorize() 
  
     return [self] 

• 일단 지금은 classic한 방법을 사용해서 구현..
• https://en.wikipedia.org/wiki/Factorization_of_polynomials#Classical_methods