(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.<uk,uc,ud,ux2,uy2,ux1,uy1,ux1,uy1,uz1,ux2,uy2,uz2> = PolynomialRing(QQ,13,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((ux2^2+uy2^2)-(uc^2*(1+ud*ux2^2*uy2^2))) , mynumerator((ux2)-(uX2/uZ2)) , mynumerator((uy2)-(uY2/uZ2)) , mynumerator((uk*uc)-(1)) , mynumerator((uZ2)-(1)) ]) J = I + R.ideal([0 , uX1-uX2 , uY1-uY2 , uZ1-uZ2 ]) uk = fastfrac(uk) uc = fastfrac(uc) ud = fastfrac(ud) ux2 = fastfrac(ux2) uy2 = fastfrac(uy2) ux1 = fastfrac(ux1) uy1 = fastfrac(uy1) uX1 = fastfrac(uX1) uY1 = fastfrac(uY1) uZ1 = fastfrac(uZ1) uX2 = fastfrac(uX2) uY2 = fastfrac(uY2) uZ2 = fastfrac(uZ2) uA = ((uX1)) uB = ((uY1)) uC = ((uZ1*uX2)) uD = ((uZ1*uY2)) uE = ((uA*uB)) uF = ((uC*uD)) uG = ((uE+uF)) uH = ((uE-uF)) uJ = (((uA-uC)*(uB+uD)-uH)) uK = (((uA+uD)*(uB+uC)-uG)) uX3 = ((uG*uJ)) uY3 = ((uH*uK)) uZ3 = ((uk*uJ*uK)) ux3 = (((ux1*uy2+uy1*ux2)/(uc*(fastfrac(1)+ud*ux1*ux2*uy1*uy2)))).reduce() uy3 = (((uy1*uy2-ux1*ux2)/(uc*(fastfrac(1)-ud*ux1*ux2*uy1*uy2)))).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))) unified = True uX4 = uX3 uY4 = uY3 uZ4 = uZ3 ux4 = (((ux1*uy1+uy1*ux1)/(uc*(fastfrac(1)+ud*ux1*ux1*uy1*uy1)))).reduce() uy4 = (((uy1*uy1-ux1*ux1)/(uc*(fastfrac(1)-ud*ux1*ux1*uy1*uy1)))).reduce() if unified: unified = isdoublingidentity((ux4^2+uy4^2)-(uc^2*(fastfrac(1)+ud*ux4^2*uy4^2))) if unified: unified = isdoublingidentity((ux4)-(uX4/uZ4)) if unified: unified = isdoublingidentity((uy4)-(uY4/uZ4)) if unified: print("Unified") </uk,uc,ud,ux2,uy2,ux1,uy1,ux1,uy1,uz1,ux2,uy2,uz2>