class Gaussian_Integer(): #入力定義 def __init__(self,Real_part=0,Imaginary_part=0): self.re=Real_part self.im=Imaginary_part #表示定義 def __str__(self): s="" s=Gaussian_Integer.__strmake(s,self.re,"") s=Gaussian_Integer.__strmake(s,self.im,"i") if s=="": return "0" else: return s def __strmake(self,coefficient,axis): if coefficient==0: return self else: if self=="": if axis=="": self+=str(coefficient) else: if coefficient==1:self+=axis elif coefficient==-1:self+="-"+axis else:self+=str(coefficient)+axis else: if coefficient>0: if coefficient==1:self+="+"+axis else:self+="+"+str(coefficient)+axis else: if coefficient==-1:self+="-"+axis else:self+=str(coefficient)+axis return self #四則演算定義 #加法 def __add__(self,other): if isinstance(other,Gaussian_Integer): return Gaussian_Integer(self.re+other.re,self.im+other.im) else: return Gaussian_Integer(self.re+other,self.im) def __radd__(self,other): if isinstance(other,int): return Gaussian_Integer(self.re+other,self.im) #減法 def __sub__(self,other): return self+(-other) def __rsub__(self,other): if isinstance(other,int): return (-self)+other #乗法 def __mul__(self,other): a,b=self.re,self.im if isinstance(other,Gaussian_Integer): c,d=other.re,other.im return Gaussian_Integer(a*c-b*d,a*d+b*c) else: return Gaussian_Integer(other*a,other*b) def __rmul__(self,other): if isinstance(other,int): a,b=self.re,self.im return Gaussian_Integer(other*a,other*b) #除法 def __truediv__(self,other): pass def __rtruediv__(self,other): pass def __floordiv__(self,other): if isinstance(other,int): other=Gaussian_Integer(other,0) a,b=self.re,self.im c,d=other.re,other.im n=other.norm() p=(2*(a*c+b*d)+n)//(2*n) q=(2*(b*c-a*d)+n)//(2*n) return Gaussian_Integer(p,q) def __mod__(self,other): return self-other*(self//other) #比較演算子 def __eq__(self,other): if isinstance(other,Gaussian_Integer): return (self.re==other.re) and (self.im==other.im) else: return (self-other)==Gaussian_Integer(0,0) def __bool__(self): return not(self==0) #その他 def conjugate(self): return Gaussian_Integer(self.re,-self.im) def __abs__(self): import math return math.sqrt(self.norm()) def norm(self): return self.re*self.re+self.im*self.im #実数から複素数に変換 def Real_to_Complex(self): pass #正負判定 #要約 #逆数 def __inverse(self): pass #符号 def __pos__(self): return self def __neg__(self): return Gaussian_Integer(-self.re,-self.im) #最大公約数 def gcd(x,y): """Gauss整数 x,yの最大公約数を求める. x,y:Gauss整数 """ if x.norm()