Python basic.C類代碼示例

    def _eval_expand_complex(self, *args):
        if self.exp.is_Integer:
            exp = self.exp
            re, im = self.base.as_real_imag()
            if exp >= 0:
                base = re + S.ImaginaryUnit * im
            else:
                mag = re ** 2 + im ** 2
                base = re / mag - S.ImaginaryUnit * (im / mag)
                exp = -exp
            return (base ** exp).expand()
        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()

            r = (re ** 2 + im ** 2) ** S.Half
            t = C.atan2(im, re)

            rp, tp = r ** self.exp, t * self.exp

            return rp * C.cos(tp) + rp * C.sin(tp) * S.ImaginaryUnit
        else:
            return C.re(self) + S.ImaginaryUnit * C.im(self)

def evalf_log(expr, prec, options):
    arg = expr.args[0]
    workprec = prec+10
    xre, xim, xacc, _ = evalf(arg, workprec, options)

    if xim:
        # XXX: use get_abs etc instead
        re = evalf_log(C.log(C.abs(arg, evaluate=False), evaluate=False), prec, options)
        im = mpf_atan2(xim, xre or fzero, prec)
        return re[0], im, re[2], prec

    imaginary_term = (mpf_cmp(xre, fzero) < 0)

    re = mpf_log(mpf_abs(xre), prec, round_nearest)
    size = fastlog(re)
    if prec - size > workprec:
        # We actually need to compute 1+x accurately, not x
        arg = C.Add(S.NegativeOne,arg,evaluate=False)
        xre, xim, xre_acc, xim_acc = evalf_add(arg, prec, options)
        prec2 = workprec - fastlog(xre)
        re = mpf_log(mpf_add(xre, fone, prec2), prec, round_nearest)

    re_acc = prec

    if imaginary_term:
        return re, mpf_pi(prec), re_acc, prec
    else:
        return re, None, re_acc, None

def get_integer_part(expr, no, options, return_ints=False):
    """
    With no = 1, computes ceiling(expr)
    With no = -1, computes floor(expr)

    Note: this function either gives the exact result or signals failure.
    """

    # The expression is likely less than 2^30 or so
    assumed_size = 30
    ire, iim, ire_acc, iim_acc = evalf(expr, assumed_size, options)

    # We now know the size, so we can calculate how much extra precision
    # (if any) is needed to get within the nearest integer
    if ire and iim:
        gap = max(fastlog(ire)-ire_acc, fastlog(iim)-iim_acc)
    elif ire:
        gap = fastlog(ire)-ire_acc
    elif iim:
        gap = fastlog(iim)-iim_acc
    else:
        # ... or maybe the expression was exactly zero
        return None, None, None, None

    margin = 10

    if gap >= -margin:
        ire, iim, ire_acc, iim_acc = evalf(expr, margin+assumed_size+gap, options)

    # We can now easily find the nearest integer, but to find floor/ceil, we
    # must also calculate whether the difference to the nearest integer is
    # positive or negative (which may fail if very close)
    def calc_part(expr, nexpr):
        nint = int(to_int(nexpr, round_nearest))
        expr = C.Add(expr, -nint, evaluate=False)
        x, _, x_acc, _ = evalf(expr, 10, options)
        check_target(expr, (x, None, x_acc, None), 3)
        nint += int(no*(mpf_cmp(x or fzero, fzero) == no))
        nint = from_int(nint)
        return nint, fastlog(nint) + 10

    re, im, re_acc, im_acc = None, None, None, None

    if ire:
        re, re_acc = calc_part(C.re(expr, evaluate=False), ire)
    if iim:
        im, im_acc = calc_part(C.im(expr, evaluate=False), iim)

    if return_ints:
        return int(to_int(re or fzero)), int(to_int(im or fzero))
    return re, im, re_acc, im_acc

    def as_real_imag(self, deep=True, **hints):
        from sympy.core.symbol import symbols
        from sympy.polys.polytools import poly
        from sympy.core.function import expand_multinomial
        if self.exp.is_Integer:
            exp = self.exp
            re, im = self.base.as_real_imag(deep=deep)
            a, b = symbols('a, b', dummy=True)
            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 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**a*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 = (re**2 + im**2)**S.Half
            t = C.atan2(im, re)

            rp, tp = r**self.exp, t*self.exp

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

            if deep:
                hints['complex'] = False
                return (C.re(self.expand(deep, complex=False)),
                C.im(self. expand(deep, **hints)))
            else:
                return (C.re(self), C.im(self))

 def _eval_subs(self, old, new):
     if self==old: return new
     if isinstance(old, self.__class__) and self.base==old.base:
         coeff1,terms1 = self.exp.as_coeff_terms()
         coeff2,terms2 = old.exp.as_coeff_terms()
         if terms1==terms2: return new ** (coeff1/coeff2) # (x**(2*y)).subs(x**(3*y),z) -> z**(2/3*y)
     if old.func is C.exp:
         coeff1,terms1 = old.args[0].as_coeff_terms()
         coeff2,terms2 = (self.exp * C.log(self.base)).as_coeff_terms()
         if terms1==terms2: return new ** (coeff1/coeff2) # (x**(2*y)).subs(exp(3*y*log(x)),z) -> z**(2/3*y)
     return self.base._eval_subs(old, new) ** self.exp._eval_subs(old, new)

    def as_real_imag(self, deep=True):
        """Performs complex expansion on 'self' and returns a tuple
           containing collected both real and imaginary parts. This
           method can't be confused with re() and im() functions,
           which does not perform complex expansion at evaluation.

           However it is possible to expand both re() and im()
           functions and get exactly the same results as with
           a single call to this function.

           >>> from sympy import symbols, I

           >>> x, y = symbols('xy', real=True)

           >>> (x + y*I).as_real_imag()
           (x, y)

           >>> from sympy.abc import z, w

           >>> (z + w*I).as_real_imag()
           (-im(w) + re(z), im(z) + re(w))

        """
        return (C.re(self), C.im(self))

 def _eval_expand_complex(self, deep=True, **hints):
         return C.re(self) + C.im(self)*S.ImaginaryUnit

 def _eval_derivative(self, s):
     dbase = self.base.diff(s)
     dexp = self.exp.diff(s)
     return self * (dexp * C.log(self.base) + dbase * self.exp / self.base)

 def _eval_as_leading_term(self, x):
     if not self.exp.has(x):
         return self.base.as_leading_term(x) ** self.exp
     return C.exp(self.exp * C.log(self.base)).as_leading_term(x)

 def _eval_power(self, exp):
     return C.exp(exp)

 def _eval_expand_complex(self, *args):
     func = self.func(*[ a._eval_expand_complex(*args) for a in self.args ])
     return C.re(func) + S.ImaginaryUnit * C.im(func)

 def _eval_expand_complex(self, deep=True, **hints):
     if deep:
         func = self.func(*[ a.expand(deep, **hints) for a in self.args ])
     else:
         func = self.func(*self.args)
     return C.re(func) + S.ImaginaryUnit * C.im(func)

 def __abs__(self):
     return C.abs(self)

 def as_real_imag(self, deep=True):
     return (C.re(self), C.im(self))

 def _eval_expand_complex(self, *args):
     return C.re(self) + C.im(self)*S.ImaginaryUnit