Python C.log方法代码示例

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
    def eval(cls, arg):
        arg = sympify(arg)

        if arg.is_Number:
            if arg is S.NaN:
                return S.NaN
            elif arg is S.Infinity:
                return S.Infinity
            elif arg is S.NegativeInfinity:
                return S.NegativeInfinity
            elif arg is S.Zero:
                return S.Zero
            elif arg is S.One:
                return C.log(sqrt(2) + 1)
            elif arg is S.NegativeOne:
                return C.log(sqrt(2) - 1)
            elif arg.is_negative:
                return -cls(-arg)
        else:
            if arg is S.ComplexInfinity:
                return S.ComplexInfinity

            i_coeff = arg.as_coefficient(S.ImaginaryUnit)

            if i_coeff is not None:
                return S.ImaginaryUnit * C.asin(i_coeff)
            else:
                if _coeff_isneg(arg):
                    return -cls(-arg)

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
    def eval(cls, arg):
        arg = sympify(arg)

        if arg.is_Number:
            if arg is S.NaN:
                return S.NaN
            elif arg is S.Infinity:
                return S.Infinity
            elif arg is S.NegativeInfinity:
                return S.NegativeInfinity
            elif arg is S.Zero:
                return S.Zero
            elif arg is S.One:
                return C.log(2**S.Half + 1)
            elif arg is S.NegativeOne:
                return C.log(2**S.Half - 1)
            elif arg.is_negative:
                return -cls(-arg)
        else:
            i_coeff = arg.as_coefficient(S.ImaginaryUnit)

            if i_coeff is not None:
                return S.ImaginaryUnit * C.asin(i_coeff)
            else:
                if arg.as_coeff_mul()[0].is_negative:
                    return -cls(-arg)

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
 def eval(cls, s):
     if s == 1:
         return C.log(2)
     z = zeta(s)
     if not z.has(zeta):
         return (1 - 2**(1 - s))*z

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]

#.........这里部分代码省略.........
            # g(x) = const
            if g is S.One and not meijerg:
                parts.append(coeff*x)
                continue

            # g(x) = expr + O(x**n)
            order_term = g.getO()

            if order_term is not None:
                h = self._eval_integral(g.removeO(), x)

                if h is not None:
                    h_order_expr = self._eval_integral(order_term.expr, x)

                    if h_order_expr is not None:
                        h_order_term = order_term.func(h_order_expr, *order_term.variables)
                        parts.append(coeff*(h + h_order_term))
                        continue

                # NOTE: if there is O(x**n) and we fail to integrate then there is
                # no point in trying other methods because they will fail anyway.
                return None

            #               c
            # g(x) = (a*x+b)
            if g.is_Pow and not g.exp.has(x) and not meijerg:
                a = Wild('a', exclude=[x])
                b = Wild('b', exclude=[x])

                M = g.base.match(a*x + b)

                if M is not None:
                    if g.exp == -1:
                        h = C.log(g.base)
                    else:
                        h = g.base**(g.exp + 1) / (g.exp + 1)

                    parts.append(coeff * h / M[a])
                    continue

            #        poly(x)
            # g(x) = -------
            #        poly(x)
            if g.is_rational_function(x) and not meijerg:
                parts.append(coeff * ratint(g, x))
                continue

            if not meijerg:
                # g(x) = Mul(trig)
                h = trigintegrate(g, x)
                if h is not None:
                    parts.append(coeff * h)
                    continue

                # g(x) has at least a DiracDelta term
                h = deltaintegrate(g, x)
                if h is not None:
                    parts.append(coeff * h)
                    continue

            if not meijerg:
                # fall back to the more general algorithm
                try:
                    h = heurisch(g, x, hints=[])
                except PolynomialError:
                    # XXX: this exception means there is a bug in the

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
 def eval(cls, s):
     if s == 1:
         return C.log(2)
     else:
         return (1-2**(1-s)) * zeta(s)

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
 def fdiff(self, argindex=1):
     n = self.args[0]
     return catalan(n)*(C.polygamma(0, n + Rational(1, 2)) - C.polygamma(0, n + 2) + C.log(4))

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
    def _eval_integral(self, f, x):
        """Calculate the anti-derivative to the function f(x).

        This is a powerful function that should in theory be able to integrate
        everything that can be integrated. If you find something, that it
        doesn't, it is easy to implement it.

        (1) Simple heuristics (based on pattern matching and integral table):

         - most frequently used functions (e.g. polynomials)
         - functions non-integrable by any of the following algorithms (e.g.
           exp(-x**2))

        (2) Integration of rational functions:

         (a) using apart() - apart() is full partial fraction decomposition
         procedure based on Bronstein-Salvy algorithm. It gives formal
         decomposition with no polynomial factorization at all (so it's fast
         and gives the most general results). However it needs much better
         implementation of RootsOf class (if fact any implementation).
         (b) using Trager's algorithm - possibly faster than (a) but needs
         implementation :)

        (3) Whichever implementation of pmInt (Mateusz, Kirill's or a
        combination of both).

          - this way we can handle efficiently huge class of elementary and
            special functions

        (4) Recursive Risch algorithm as described in Bronstein's integration
        tutorial.

          - this way we can handle those integrable functions for which (3)
            fails

        (5) Powerful heuristics based mostly on user defined rules.

         - handle complicated, rarely used cases
        """

        # if it is a poly(x) then let the polynomial integrate itself (fast)
        #
        # It is important to make this check first, otherwise the other code
        # will return a sympy expression instead of a Polynomial.
        #
        # see Polynomial for details.
        if isinstance(f, Poly):
            return f.integrate(x)

        # Piecewise antiderivatives need to call special integrate.
        if f.func is Piecewise:
            return f._eval_integral(x)

        # let's cut it short if `f` does not depend on `x`
        if not f.has(x):
            return f*x

        # try to convert to poly(x) and then integrate if successful (fast)
        poly = f.as_poly(x)

        if poly is not None:
            return poly.integrate(x).as_basic()

        # since Integral(f=g1+g2+...) == Integral(g1) + Integral(g2) + ...
        # we are going to handle Add terms separately,
        # if `f` is not Add -- we only have one term
        parts = []
        for g in make_list(f, Add):
            coeff, g = g.as_independent(x)

            # g(x) = const
            if g is S.One:
                parts.append(coeff * x)
                continue

            #               c
            # g(x) = (a*x+b)
            if g.is_Pow and not g.exp.has(x):
                a = Wild('a', exclude=[x])
                b = Wild('b', exclude=[x])

                M = g.base.match(a*x + b)

                if M is not None:
                    if g.exp == -1:
                        h = C.log(g.base)
                    else:
                        h = g.base**(g.exp+1) / (g.exp+1)

                    parts.append(coeff * h / M[a])
                    continue

            #        poly(x)
            # g(x) = -------
            #        poly(x)
            if g.is_rational_function(x):
                parts.append(coeff * ratint(g, x))
                continue

            # g(x) = Mul(trig)
#.........这里部分代码省略.........

# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import log [as 别名]
 def canonize(cls, s):
     if s == 1:
         return C.log(2)
     else:
         return (1-2**(1-s)) * zeta(s)