Why don't we name the functions X e^X and X logX, 'xex' and 'xlogx'? The inverses could be 'axex' and 'axlogx'. This would simplify life for those of us who only make occasional use of LambertW, and need to consult the definition each time. ----- Geometric Interpretation of the Discriminant Following up Gene's note on Discriminant = square of Vandermonde determinant ... The determinant is +- the area/volume/measure of a parallelogram/piped/? with origin 0 and each row (or each column) as a generating edge. The determinant of the matrix [ 1 2 ] [ 3 4 ] is -2, which is also the area of the parallelogram 00 - 12 - 46 - 34. (The +- depends on your sign convention, and is extinguished if you square the Vandermonde determinant.) The determinant of a V matrix is 0 whenever two roots of the related polynomial are equal. Rich