  We analyze wave functions constructed as a sum of product of two-electron
functions, or as a polynomial of geminals, to investigate their ability to
represent the ground state of a strongly correlated few-body system. The known
difficulty associated with variational determination of the total energy is
overcome by applying a tensor decomposition method called Waring decomposition.
Convergence speed of the total energy is compared for various polynomial types.
The result provides information bridging between geminal product wave functions
and the full-CI in the strongly correlated regime, thereby enriching knowledge
on the hierarchy of molecular orbital theories of electron pairs.
