Python utils.call函数代码示例

    def _evalf_(self, n, x, parent=None, algorithm=None):
        """
        EXAMPLES::

            sage: bessel_J(0.0, 1.0)
            0.765197686557967
            sage: bessel_J(0, 1).n(digits=20)
            0.76519768655796655145
            sage: bessel_J(0.5, 1.5)
            0.649838074753747

        Check for correct rounding (:trac:`17122`)::

            sage: R = RealField(113)
            sage: a = R("8.935761195587725798762818805462843676e-01")
            sage: aa = RealField(200)(a)
            sage: for n in [-10..10]:
            ....:     b = bessel_J(R(n), a)
            ....:     bb = R(bessel_J(n, aa))
            ....:     if b != bb:
            ....:         print n, b-bb
        """
        if parent is not None:
            x = parent(x)

        try:
            return x.jn(Integer(n))
        except Exception:
            pass

        n, x = get_coercion_model().canonical_coercion(n, x)
        import mpmath
        return mpmath_utils.call(mpmath.besselj, n, x, parent=parent)

    def _evalf_(self, x, parent=None, algorithm=None):
        """
        EXAMPLES::

            sage: erf(2).n()
            0.995322265018953
            sage: erf(2).n(200)
            0.99532226501895273416206925636725292861089179704006007673835
            sage: erf(pi - 1/2*I).n(100)
            1.0000111669099367825726058952 + 1.6332655417638522934072124547e-6*I

        TESTS:

        Check that PARI/GP through the GP interface gives the same answer::

            sage: gp.set_real_precision(59)  # random
            38
            sage: print(gp.eval("1 - erfc(1)")); print(erf(1).n(200));
            0.84270079294971486934122063508260925929606699796630290845994
            0.84270079294971486934122063508260925929606699796630290845994

        Check that for an imaginary input, the output is also imaginary, see
        :trac:`13193`::

            sage: erf(3.0*I)
            1629.99462260157*I
            sage: erf(33.0*I)
            1.51286977510409e471*I
        """
        R = parent or s_parent(x)
        import mpmath
        return mpmath_utils.call(mpmath.erf, x, parent=R)

    def __call__(self, x, prec=None, coerce=True, hold=False ):
        """
        Note that the ``prec`` argument is deprecated. The precision for
        the result is deduced from the precision of the input. Convert
        the input to a higher precision explicitly if a result with higher
        precision is desired.

        EXAMPLES::

            sage: t = Ei(RealField(100)(2.5)); t
            7.0737658945786007119235519625
            sage: t.prec()
            100

            sage: Ei(1.1, prec=300)
            doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example Ei(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., Ei(1).n(300), instead.
            2.16737827956340306615064476647912607220394065907142504328679588538509331805598360907980986
        """
        if prec is not None:
            from sage.misc.misc import deprecation
            deprecation("The prec keyword argument is deprecated. Explicitly set the precision of the input, for example Ei(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., Ei(1).n(300), instead.")
            
            import mpmath
            return mpmath_utils.call(mpmath.ei, x, prec=prec)

        return BuiltinFunction.__call__(self, x, coerce=coerce, hold=hold)

 def _evalf_(self, a, b, z, parent, algorithm=None):
     """
     TESTS::
     
         sage: hypergeometric_M(1,1,1).n()
         2.71828182845905
     """
     from mpmath import hyp1f1
     return mpmath_utils.call(hyp1f1, a, b, z, parent=parent)

 def _evalf_(self, n, z, parent=None):
     """
     EXAMPLES::
     """
     import mpmath
     if isinstance(parent, Parent) and hasattr(parent, 'prec'):
         prec = parent.prec()
     else:
         prec = 53
     return mpmath_utils.call(mpmath.expint, n, z, prec=prec)

    def _evalf_(self, n, x, parent=None, algorithm=None):
        r"""
        TESTS::

            sage: zetaderiv(0, 3, hold=True).n() == zeta(3).n()
            True
            sage: zetaderiv(2, 3 + I).n()
            0.0213814086193841 - 0.174938812330834*I
        """
        from mpmath import zeta
        return mpmath_utils.call(zeta, x, 1, n, parent=parent)

    def _evalf_(self, a, z, parent=None, algorithm=None):
        """
        EXAMPLES::

            sage: struve_H(1/2,pi).n()
            0.900316316157106
            sage: struve_H(1/2,pi).n(200)
            0.9003163161571060695551991910...
        """
        import mpmath
        return mpmath_utils.call(mpmath.struveh, a, z, parent=parent)

    def _evalf_(self, n, x, parent=None, algorithm=None):
        """
        EXAMPLES::

            sage: bessel_J(0.0, 1.0)
            0.765197686557966
            sage: bessel_J(0, 1).n(digits=20)
            0.76519768655796655145
        """
        import mpmath
        return mpmath_utils.call(mpmath.besselj, n, x, parent=parent)

    def _evalf_(self, u, m, parent=None, algorithm=None):
        """
        EXAMPLES::

            sage: elliptic_eu(1,1).n()
            0.761594155955765
            sage: elliptic_eu(1,1).n(200)
            0.7615941559557648881194582...
        """
        R = parent or parent(z)
        return mpmath_utils.call(elliptic_eu_f, u, m, parent=R)

    def _evalf_(self, n, m, theta, phi, parent, **kwds):
        r"""
        TESTS::

            sage: spherical_harmonic(3 + I, 2, 1, 2).n(100)
            -0.35115433730748836508201061672 - 0.41556223397536866209990358597*I
            sage: spherical_harmonic(I, I, I, I).n()
            7.66678546069894 - 0.265754432549751*I
        """
        from mpmath import spherharm
        return mpmath_utils.call(spherharm, n, m, theta, phi, parent=parent)

    def _evalf_(self, n, z, parent=None, algorithm=None):
        """
        EXAMPLES::

            sage: N(exp_integral_e(1, 1+I))
            0.000281624451981418 - 0.179324535039359*I
            sage: exp_integral_e(1, RealField(100)(1))
            0.21938393439552027367716377546

        """
        import mpmath
        return mpmath_utils.call(mpmath.expint, n, z, parent=parent)

    def _evalf_(self, x, **kwargs):
        """
        EXAMPLES::

            sage: from sage.functions.airy import airy_ai_simple
            sage: airy_ai_simple(0.0)
            0.355028053887817
            sage: airy_ai_simple(1.0 * I)
            0.331493305432141 - 0.317449858968444*I

        We can use several methods for numerical evaluation::

            sage: airy_ai_simple(3).n(algorithm='mpmath')
            0.00659113935746072
            sage: airy_ai_simple(3).n(algorithm='mpmath', prec=100)
            0.0065911393574607191442574484080
            sage: airy_ai_simple(3).n(algorithm='scipy')  # rel tol 1e-10
            0.006591139357460719
            sage: airy_ai_simple(I).n(algorithm='scipy')  # rel tol 1e-10
            0.33149330543214117 - 0.3174498589684438*I
            
        TESTS::

            sage: parent(airy_ai_simple(3).n(algorithm='scipy'))                                          
            Real Field with 53 bits of precision
            sage: airy_ai_simple(3).n(algorithm='scipy', prec=200)
            Traceback (most recent call last):
            ...
            NotImplementedError: airy_ai not implemented for precision > 53
        """
        algorithm = kwargs.get('algorithm', 'mpmath') or 'mpmath'
        parent = kwargs.get('parent')
        if algorithm == 'scipy':
            if hasattr(parent, 'prec') and parent.prec() > 53:
                raise NotImplementedError("%s not implemented for precision > 53"%self.name())
            from sage.rings.all import RR, CC
            from sage.functions.other import real,imag
            from scipy.special import airy as airy
            if x in RR:
                y = airy(real(x))[0]
                if parent is None:
                    return RR(y)
            else:
                y = airy(complex(real(x),imag(x)))[0]
                if parent is None:
                    return CC(y)
            return parent(y)
        elif algorithm == 'mpmath':
            import mpmath
            from sage.libs.mpmath import utils as mpmath_utils
            return mpmath_utils.call(mpmath.airyai, x, parent=parent)
        else:
            raise ValueError("unknown algorithm '%s'" % algorithm)

    def __call__(self, x, prec=None, coerce=True, hold=False):
        """
        Note that the ``prec`` argument is deprecated. The precision for
        the result is deduced from the precision of the input. Convert
        the input to a higher precision explicitly if a result with higher
        precision is desired.::

            sage: t = gamma(RealField(100)(2.5)); t
            1.3293403881791370204736256125
            sage: t.prec()
            100

            sage: gamma(6, prec=53)
            doctest:...: DeprecationWarning: The prec keyword argument is deprecated. Explicitly set the precision of the input, for example gamma(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., gamma(1).n(300), instead.
            120.000000000000

        TESTS::

            sage: gamma(pi,prec=100)
            2.2880377953400324179595889091

            sage: gamma(3/4,prec=100)
            1.2254167024651776451290983034
        """
        if prec is not None:
            from sage.misc.misc import deprecation
            deprecation("The prec keyword argument is deprecated. Explicitly set the precision of the input, for example gamma(RealField(300)(1)), or use the prec argument to .n() for exact inputs, e.g., gamma(1).n(300), instead.")
            import mpmath
            return mpmath_utils.call(mpmath.gamma, x, prec=prec)

        # this is a kludge to keep
        #     sage: Q.<i> = NumberField(x^2+1)
        #     sage: gamma(i)
        # working, since number field elements cannot be coerced into SR
        # without specifying an explicit embedding into CC any more
        try:
            res = GinacFunction.__call__(self, x, coerce=coerce, hold=hold)
        except TypeError, err:
            # the __call__() method returns a TypeError for fast float arguments
            # as well, we only proceed if the error message says that
            # the arguments cannot be coerced to SR
            if not str(err).startswith("cannot coerce"):
                raise

            from sage.misc.misc import deprecation
            deprecation("Calling symbolic functions with arguments that cannot be coerced into symbolic expressions is deprecated.")
            parent = RR if prec is None else RealField(prec)
            try:
                x = parent(x)
            except (ValueError, TypeError):
                x = parent.complex_field()(x)
            res = GinacFunction.__call__(self, x, coerce=coerce, hold=hold)