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We consider trigonometric solutions of WDVV equations and derive geometricconditions when a collection of vectors with multiplicities determines such asolution. We incorporate these conditions into the notion of trigonometricVeselov system ($\vee$-system) and we determine all trigonometric$\vee$-systems with up to five vectors. We show that generalizedCalogero-Moser-Sutherland operator admits a factorized eigenfunction if andonly if it corresponds to the trigonometric $\vee$-system; this inverts aone-way implication observed by Veselov for the rational solutions.

Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems