Exemplo n.º 1
0
Arquivo: power.py Projeto: Maihj/sympy
    def as_real_imag(self, deep=True, **hints):
        from sympy.polys.polytools import poly

        if self.exp.is_Integer:
            exp = self.exp
            re, im = self.base.as_real_imag(deep=deep)
            if not im:
                return self, S.Zero
            a, b = symbols('a b', cls=Dummy)
            if exp >= 0:
                if re.is_Number and im.is_Number:
                    # We can be more efficient in this case
                    expr = expand_multinomial(self.base**exp)
                    return expr.as_real_imag()

                expr = poly(
                    (a + b)**exp)  # a = re, b = im; expr = (a + b*I)**exp
            else:
                mag = re**2 + im**2
                re, im = re/mag, -im/mag
                if re.is_Number and im.is_Number:
                    # We can be more efficient in this case
                    expr = expand_multinomial((re + im*S.ImaginaryUnit)**-exp)
                    return expr.as_real_imag()

                expr = poly((a + b)**-exp)

            # Terms with even b powers will be real
            r = [i for i in expr.terms() if not i[0][1] % 2]
            re_part = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
            # Terms with odd b powers will be imaginary
            r = [i for i in expr.terms() if i[0][1] % 4 == 1]
            im_part1 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
            r = [i for i in expr.terms() if i[0][1] % 4 == 3]
            im_part3 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])

            return (re_part.subs({a: re, b: S.ImaginaryUnit*im}),
            im_part1.subs({a: re, b: im}) + im_part3.subs({a: re, b: -im}))

        elif self.exp.is_Rational:
            # NOTE: This is not totally correct since for x**(p/q) with
            #       x being imaginary there are actually q roots, but
            #       only a single one is returned from here.
            re, im = self.base.as_real_imag(deep=deep)
            r = Pow(Pow(re, 2) + Pow(im, 2), S.Half)
            t = C.atan2(im, re)

            rp, tp = Pow(r, self.exp), t*self.exp

            return (rp*C.cos(tp), rp*C.sin(tp))
        else:

            if deep:
                hints['complex'] = False

                expanded = self.expand(deep, **hints)
                if hints.get('ignore') == expanded:
                    return None
                else:
                    return (C.re(expanded), C.im(expanded))
            else:
                return (C.re(self), C.im(self))
Exemplo n.º 2
0
    def as_real_imag(self, deep=True, **hints):
        from sympy.polys.polytools import poly

        if self.exp.is_Integer:
            exp = self.exp
            re, im = self.base.as_real_imag(deep=deep)
            if not im:
                return self, S.Zero
            a, b = symbols('a b', cls=Dummy)
            if exp >= 0:
                if re.is_Number and im.is_Number:
                    # We can be more efficient in this case
                    expr = expand_multinomial(self.base**exp)
                    return expr.as_real_imag()

                expr = poly(
                    (a + b)**exp)  # a = re, b = im; expr = (a + b*I)**exp
            else:
                mag = re**2 + im**2
                re, im = re/mag, -im/mag
                if re.is_Number and im.is_Number:
                    # We can be more efficient in this case
                    expr = expand_multinomial((re + im*S.ImaginaryUnit)**-exp)
                    return expr.as_real_imag()

                expr = poly((a + b)**-exp)

            # Terms with even b powers will be real
            r = [i for i in expr.terms() if not i[0][1] % 2]
            re_part = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
            # Terms with odd b powers will be imaginary
            r = [i for i in expr.terms() if i[0][1] % 4 == 1]
            im_part1 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])
            r = [i for i in expr.terms() if i[0][1] % 4 == 3]
            im_part3 = Add(*[cc*a**aa*b**bb for (aa, bb), cc in r])

            return (re_part.subs({a: re, b: S.ImaginaryUnit*im}),
            im_part1.subs({a: re, b: im}) + im_part3.subs({a: re, b: -im}))

        elif self.exp.is_Rational:
            # NOTE: This is not totally correct since for x**(p/q) with
            #       x being imaginary there are actually q roots, but
            #       only a single one is returned from here.
            re, im = self.base.as_real_imag(deep=deep)
            r = Pow(Pow(re, 2) + Pow(im, 2), S.Half)
            t = C.atan2(im, re)

            rp, tp = Pow(r, self.exp), t*self.exp

            return (rp*C.cos(tp), rp*C.sin(tp))
        else:

            if deep:
                hints['complex'] = False

                expanded = self.expand(deep, **hints)
                if hints.get('ignore') == expanded:
                    return None
                else:
                    return (C.re(expanded), C.im(expanded))
            else:
                return (C.re(self), C.im(self))