Now, introduce the ordered pair of real numbers â = (a, b) called a dual scalar. Let the addition and subtraction of these numbers be componentwise, and define multiplication as a ^ ^ c ^ ^ = ( a , b ) ( c , d ) = ( a c , a d + b c ) . The multiplication of a screw S = (S, V) by the dual scalar â = (a, b) is computed componentwise to be, a ^ ^ S = ( a , b ) ( S , V ) = ( a S , a V + b S ) .