def a_alpha_and_derivatives(self, T, full=True, quick=True):
        r'''Method to calculate `a_alpha` and its first and second
        derivatives for this EOS. Returns `a_alpha`, `da_alpha_dT`, and 
        `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives` for more 
        documentation. Uses the set values of `Tc`, `m`, and `a`.
        
        .. math::
            a\alpha = a \left(m \left(- \sqrt{\frac{T}{Tc}} + 1\right)
            + 1\right)^{2}
        
            \frac{d a\alpha}{dT} = \frac{a m}{T} \sqrt{\frac{T}{Tc}} \left(m
            \left(\sqrt{\frac{T}{Tc}} - 1\right) - 1\right)

            \frac{d^2 a\alpha}{dT^2} = \frac{a m \sqrt{\frac{T}{Tc}}}{2 T^{2}}
            \left(m + 1\right)
        '''
        a, Tc, m = self.a, self.Tc, self.m
        sqTr = (T/Tc)**0.5
        a_alpha = a*(m*(1. - sqTr) + 1.)**2
        if not full:
            return a_alpha
        else:
            da_alpha_dT = -a*m*sqTr*(m*(-sqTr + 1.) + 1.)/T
            d2a_alpha_dT2 =  a*m*sqTr*(m + 1.)/(2.*T*T)
            return a_alpha, da_alpha_dT, d2a_alpha_dT2
def a_alpha_and_derivatives(self, T, full=True, quick=True):
        r'''Method to calculate `a_alpha` and its first and second
        derivatives for this EOS. Returns `a_alpha`, `da_alpha_dT`, and 
        `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives` for more 
        documentation. Uses the set values of `Tc`, `m`, and `a`.
        
        .. math::
            a\alpha = a \left(m \left(- \sqrt{\frac{T}{Tc}} + 1\right)
            + 1\right)^{2}
        
            \frac{d a\alpha}{dT} = \frac{a m}{T} \sqrt{\frac{T}{Tc}} \left(m
            \left(\sqrt{\frac{T}{Tc}} - 1\right) - 1\right)

            \frac{d^2 a\alpha}{dT^2} = \frac{a m \sqrt{\frac{T}{Tc}}}{2 T^{2}}
            \left(m + 1\right)
        '''
        a, Tc, m = self.a, self.Tc, self.m
        sqTr = (T/Tc)**0.5
        a_alpha = a*(m*(1. - sqTr) + 1.)**2
        if not full:
            return a_alpha
        else:
            da_alpha_dT = -a*m*sqTr*(m*(-sqTr + 1.) + 1.)/T
            d2a_alpha_dT2 =  a*m*sqTr*(m + 1.)/(2.*T*T)
            return a_alpha, da_alpha_dT, d2a_alpha_dT2
def a_alpha_and_derivatives ( self , T , full = True , quick = True ) : a , Tc , m = self . a , self . Tc , self . m sqTr = ( T / Tc ) ** 0.5 a_alpha = a * ( m * ( 1. - sqTr ) + 1. ) ** 2 if not full : return a_alpha else : da_alpha_dT = - a * m * sqTr * ( m * ( - sqTr + 1. ) + 1. ) / T d2a_alpha_dT2 = a * m * sqTr * ( m + 1. ) / ( 2. * T * T ) return a_alpha , da_alpha_dT , d2a_alpha_dT2
r'''Method to calculate `a_alpha` and its first and second
        derivatives for this EOS. Returns `a_alpha`, `da_alpha_dT`, and 
        `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives` for more 
        documentation. Uses the set values of `Tc`, `m`, and `a`.
        
        .. math::
            a\alpha = a \left(m \left(- \sqrt{\frac{T}{Tc}} + 1\right)
            + 1\right)^{2}
        
            \frac{d a\alpha}{dT} = \frac{a m}{T} \sqrt{\frac{T}{Tc}} \left(m
            \left(\sqrt{\frac{T}{Tc}} - 1\right) - 1\right)

            \frac{d^2 a\alpha}{dT^2} = \frac{a m \sqrt{\frac{T}{Tc}}}{2 T^{2}}
            \left(m + 1\right)
r Method to calculate a_alpha and its first and second derivatives for this EOS . Returns a_alpha da_alpha_dT and d2a_alpha_dT2 . See GCEOS . a_alpha_and_derivatives for more documentation . Uses the set values of Tc m and a . .. math :: a \ alpha = a \ left ( m \ left ( - \ sqrt { \ frac { T } { Tc }} + 1 \ right ) + 1 \ right ) ^ { 2 } \ frac { d a \ alpha } { dT } = \ frac { a m } { T } \ sqrt { \ frac { T } { Tc }} \ left ( m \ left ( \ sqrt { \ frac { T } { Tc }} - 1 \ right ) - 1 \ right )