def Schwartzentruber(self, T, full=True, quick=True):
        r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Schwartzentruber et al. (1990) [1]_. Returns `a_alpha`, 
        `da_alpha_dT`, and `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives`  
        for more documentation. Three coefficients needed.
        
        .. math::
            \alpha = \left(c_{4} \left(- \sqrt{\frac{T}{Tc}} + 1\right) 
            - \left(- \sqrt{\frac{T}{Tc}} + 1\right) \left(\frac{T^{2} c_{3}}
            {Tc^{2}} + \frac{T c_{2}}{Tc} + c_{1}\right) + 1\right)^{2}

        References
        ----------
        .. [1] J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for 
           Non-Ideal Systems:An Easier Way," Chem. Eng., March 1990, 118-124.
        '''
        c1, c2, c3 = self.alpha_function_coeffs
        T, Tc, a = self.T, self.Tc, self.a
        a_alpha = a*((c4*(-sqrt(T/Tc) + 1) - (-sqrt(T/Tc) + 1)*(T**2*c3/Tc**2 + T*c2/Tc + c1) + 1)**2)
        if not full:
            return a_alpha
        else:
            da_alpha_dT = a*((c4*(-sqrt(T/Tc) + 1) - (-sqrt(T/Tc) + 1)*(T**2*c3/Tc**2 + T*c2/Tc + c1) + 1)*(-2*(-sqrt(T/Tc) + 1)*(2*T*c3/Tc**2 + c2/Tc) - c4*sqrt(T/Tc)/T + sqrt(T/Tc)*(T**2*c3/Tc**2 + T*c2/Tc + c1)/T))
            d2a_alpha_dT2 = a*(((-c4*(sqrt(T/Tc) - 1) + (sqrt(T/Tc) - 1)*(T**2*c3/Tc**2 + T*c2/Tc + c1) + 1)*(8*c3*(sqrt(T/Tc) - 1)/Tc**2 + 4*sqrt(T/Tc)*(2*T*c3/Tc + c2)/(T*Tc) + c4*sqrt(T/Tc)/T**2 - sqrt(T/Tc)*(T**2*c3/Tc**2 + T*c2/Tc + c1)/T**2) + (2*(sqrt(T/Tc) - 1)*(2*T*c3/Tc + c2)/Tc - c4*sqrt(T/Tc)/T + sqrt(T/Tc)*(T**2*c3/Tc**2 + T*c2/Tc + c1)/T)**2)/2)
            return a_alpha, da_alpha_dT, d2a_alpha_dT2
def Schwartzentruber(self, T, full=True, quick=True):
        r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Schwartzentruber et al. (1990) [1]_. Returns `a_alpha`, 
        `da_alpha_dT`, and `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives`  
        for more documentation. Three coefficients needed.
        
        .. math::
            \alpha = \left(c_{4} \left(- \sqrt{\frac{T}{Tc}} + 1\right) 
            - \left(- \sqrt{\frac{T}{Tc}} + 1\right) \left(\frac{T^{2} c_{3}}
            {Tc^{2}} + \frac{T c_{2}}{Tc} + c_{1}\right) + 1\right)^{2}

        References
        ----------
        .. [1] J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for 
           Non-Ideal Systems:An Easier Way," Chem. Eng., March 1990, 118-124.
        '''
        c1, c2, c3 = self.alpha_function_coeffs
        T, Tc, a = self.T, self.Tc, self.a
        a_alpha = a*((c4*(-sqrt(T/Tc) + 1) - (-sqrt(T/Tc) + 1)*(T**2*c3/Tc**2 + T*c2/Tc + c1) + 1)**2)
        if not full:
            return a_alpha
        else:
            da_alpha_dT = a*((c4*(-sqrt(T/Tc) + 1) - (-sqrt(T/Tc) + 1)*(T**2*c3/Tc**2 + T*c2/Tc + c1) + 1)*(-2*(-sqrt(T/Tc) + 1)*(2*T*c3/Tc**2 + c2/Tc) - c4*sqrt(T/Tc)/T + sqrt(T/Tc)*(T**2*c3/Tc**2 + T*c2/Tc + c1)/T))
            d2a_alpha_dT2 = a*(((-c4*(sqrt(T/Tc) - 1) + (sqrt(T/Tc) - 1)*(T**2*c3/Tc**2 + T*c2/Tc + c1) + 1)*(8*c3*(sqrt(T/Tc) - 1)/Tc**2 + 4*sqrt(T/Tc)*(2*T*c3/Tc + c2)/(T*Tc) + c4*sqrt(T/Tc)/T**2 - sqrt(T/Tc)*(T**2*c3/Tc**2 + T*c2/Tc + c1)/T**2) + (2*(sqrt(T/Tc) - 1)*(2*T*c3/Tc + c2)/Tc - c4*sqrt(T/Tc)/T + sqrt(T/Tc)*(T**2*c3/Tc**2 + T*c2/Tc + c1)/T)**2)/2)
            return a_alpha, da_alpha_dT, d2a_alpha_dT2
def Schwartzentruber ( self , T , full = True , quick = True ) : c1 , c2 , c3 = self . alpha_function_coeffs T , Tc , a = self . T , self . Tc , self . a a_alpha = a * ( ( c4 * ( - sqrt ( T / Tc ) + 1 ) - ( - sqrt ( T / Tc ) + 1 ) * ( T ** 2 * c3 / Tc ** 2 + T * c2 / Tc + c1 ) + 1 ) ** 2 ) if not full : return a_alpha else : da_alpha_dT = a * ( ( c4 * ( - sqrt ( T / Tc ) + 1 ) - ( - sqrt ( T / Tc ) + 1 ) * ( T ** 2 * c3 / Tc ** 2 + T * c2 / Tc + c1 ) + 1 ) * ( - 2 * ( - sqrt ( T / Tc ) + 1 ) * ( 2 * T * c3 / Tc ** 2 + c2 / Tc ) - c4 * sqrt ( T / Tc ) / T + sqrt ( T / Tc ) * ( T ** 2 * c3 / Tc ** 2 + T * c2 / Tc + c1 ) / T ) ) d2a_alpha_dT2 = a * ( ( ( - c4 * ( sqrt ( T / Tc ) - 1 ) + ( sqrt ( T / Tc ) - 1 ) * ( T ** 2 * c3 / Tc ** 2 + T * c2 / Tc + c1 ) + 1 ) * ( 8 * c3 * ( sqrt ( T / Tc ) - 1 ) / Tc ** 2 + 4 * sqrt ( T / Tc ) * ( 2 * T * c3 / Tc + c2 ) / ( T * Tc ) + c4 * sqrt ( T / Tc ) / T ** 2 - sqrt ( T / Tc ) * ( T ** 2 * c3 / Tc ** 2 + T * c2 / Tc + c1 ) / T ** 2 ) + ( 2 * ( sqrt ( T / Tc ) - 1 ) * ( 2 * T * c3 / Tc + c2 ) / Tc - c4 * sqrt ( T / Tc ) / T + sqrt ( T / Tc ) * ( T ** 2 * c3 / Tc ** 2 + T * c2 / Tc + c1 ) / T ) ** 2 ) / 2 ) return a_alpha , da_alpha_dT , d2a_alpha_dT2
r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Schwartzentruber et al. (1990) [1]_. Returns `a_alpha`, 
        `da_alpha_dT`, and `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives`  
        for more documentation. Three coefficients needed.
        
        .. math::
            \alpha = \left(c_{4} \left(- \sqrt{\frac{T}{Tc}} + 1\right) 
            - \left(- \sqrt{\frac{T}{Tc}} + 1\right) \left(\frac{T^{2} c_{3}}
            {Tc^{2}} + \frac{T c_{2}}{Tc} + c_{1}\right) + 1\right)^{2}

        References
        ----------
        .. [1] J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for 
           Non-Ideal Systems:An Easier Way," Chem. Eng., March 1990, 118-124.
r Method to calculate a_alpha and its first and second derivatives according to Schwartzentruber et al . ( 1990 ) [ 1 ] _ . Returns a_alpha da_alpha_dT and d2a_alpha_dT2 . See GCEOS . a_alpha_and_derivatives for more documentation . Three coefficients needed . .. math :: \ alpha = \ left ( c_ { 4 } \ left ( - \ sqrt { \ frac { T } { Tc }} + 1 \ right ) - \ left ( - \ sqrt { \ frac { T } { Tc }} + 1 \ right ) \ left ( \ frac { T^ { 2 } c_ { 3 }} { Tc^ { 2 }} + \ frac { T c_ { 2 }} { Tc } + c_ { 1 } \ right ) + 1 \ right ) ^ { 2 }