def _rewrite_sin(m_n, s, a, b):
 from sympy import expand_mul, pi, ceiling, gamma
 (m, n) = m_n
 m = expand_mul((m / pi))
 n = expand_mul((n / pi))
 r = ceiling((((- m) * a) - n.as_real_imag()[0]))
 return (gamma((((m * s) + n) + r)), gamma((((1 - n) - r) - (m * s))), (((-1) ** r) * pi))

def _rewrite_sin ( m_n , s , a , b ) : from sympy import expand_mul , pi , ceiling , gamma ( m , n ) = m_n m = expand_mul ( ( m / pi ) ) n = expand_mul ( ( n / pi ) ) r = ceiling ( ( ( ( - m ) * a ) - n . as_real_imag ( ) [ 0 ] ) ) return ( gamma ( ( ( ( m * s ) + n ) + r ) ) , gamma ( ( ( ( 1 - n ) - r ) - ( m * s ) ) ) , ( ( ( - 1 ) ** r ) * pi ) )
re-write the sine function sin as gamma functions .