(original) (raw)

def mynumerator(x): if parent(x) == R: return x return numerator(x) class fastfrac: def __init__(self,top,bot=1): if parent(top) == ZZ or parent(top) == R: self.top = R(top) self.bot = R(bot) elif top.__class__ == fastfrac: self.top = top.top self.bot = top.bot * bot else: self.top = R(numerator(top)) self.bot = R(denominator(top)) * bot def reduce(self): return fastfrac(self.top / self.bot) def sreduce(self): return fastfrac(I.reduce(self.top),I.reduce(self.bot)) def iszero(self): return self.top in I and not (self.bot in I) def isdoublingzero(self): return self.top in J and not (self.bot in J) def __add__(self,other): if parent(other) == ZZ: return fastfrac(self.top + self.bot * other,self.bot) if other.__class__ == fastfrac: return fastfrac(self.top * other.bot + self.bot * other.top,self.bot * other.bot) return NotImplemented def __sub__(self,other): if parent(other) == ZZ: return fastfrac(self.top - self.bot * other,self.bot) if other.__class__ == fastfrac: return fastfrac(self.top * other.bot - self.bot * other.top,self.bot * other.bot) return NotImplemented def __neg__(self): return fastfrac(-self.top,self.bot) def __mul__(self,other): if parent(other) == ZZ: return fastfrac(self.top * other,self.bot) if other.__class__ == fastfrac: return fastfrac(self.top * other.top,self.bot * other.bot) return NotImplemented def __rmul__(self,other): return self.__mul__(other) def __div__(self,other): if parent(other) == ZZ: return fastfrac(self.top,self.bot * other) if other.__class__ == fastfrac: return fastfrac(self.top * other.bot,self.bot * other.top) return NotImplemented __truediv__ = __div__ def __pow__(self,other): if parent(other) == ZZ: return fastfrac(self.top ^ other,self.bot ^ other) return NotImplemented def isidentity(x): return x.iszero() def isdoublingidentity(x): return x.isdoublingzero() R.<ucc2,uc,ud,ux1,uy1,ux1,uy1,uz1> = PolynomialRing(QQ,8,order='invlex') I = R.ideal([ mynumerator((ux1^2+uy1^2)-(uc^2*(1+ud*ux1^2*uy1^2))) , mynumerator((ux1)-(uX1/uZ1)) , mynumerator((uy1)-(uY1/uZ1)) , mynumerator((ucc2)-(2*uc*uc)) , mynumerator((uZ1)-(1)) ]) ucc2 = fastfrac(ucc2) uc = fastfrac(uc) ud = fastfrac(ud) ux1 = fastfrac(ux1) uy1 = fastfrac(uy1) uX1 = fastfrac(uX1) uY1 = fastfrac(uY1) uZ1 = fastfrac(uZ1) uB = (((uX1+uY1)^2)) uC = ((uX1^2)) uD = ((uY1^2)) uE = ((uC+uD)) uJ = ((uE-ucc2)) uX3 = ((uc*(uB-uE)*uJ)) uY3 = ((uc*uE*(uC-uD))) uZ3 = ((uE*uJ)) ux3 = (((ux1*uy1+uy1*ux1)/(uc*(fastfrac(1)+ud*ux1*ux1*uy1*uy1)))).reduce() uy3 = (((uy1*uy1-ux1*ux1)/(uc*(fastfrac(1)-ud*ux1*ux1*uy1*uy1)))).reduce() print(isidentity((ux3^2+uy3^2)-(uc^2*(fastfrac(1)+ud*ux3^2*uy3^2)))) print(isidentity((ux3)-(uX3/uZ3))) print(isidentity((uy3)-(uY3/uZ3))) </ucc2,uc,ud,ux1,uy1,ux1,uy1,uz1>