The Pleasures of 'Perp Dot' Products in Sagemath

edit

Francis S. Hill, Jr. has an vector operation he calls a-Perp. It is defined as the vector perpendicular to a that is rotated 90° counterclockwise (Hill 1994:138). Wolfram also has a page on the concept here. Similar to the Normal vector, but not quite.

I wonder if there's a default Sage function, or some handy way, to do this?

Say I have vector a

a = vector(QQ, [3, 4])

and I want to get

a_Perp = vector(QQ, [-4, 3])

Hill, F. S. Jr. "The Pleasures of 'Perp Dot' Products." Ch. II.5 in Graphics Gems IV (Ed. P. S. Heckbert). San Diego: Academic Press, pp. 138-148, 1994.