Legendre transforms for type A n and B n V -systems.

The Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations have a rich structure related to the theory of Frobenius manifolds, with many known families of solutions. A Legendre transformation is a symmetry of the WDVV equations, introduced by Dubrovin. We explicitly compute the results of a Legendre transformation applied to An - and Bn -type multi-parameter rational solutions, relating them to known and new trigonometric solutions. [ABSTRACT FROM AUTHOR]