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The pairing mechanism in high-temperature superconducting cuprates remains an open challenging problem.In this talk,I will give a brief introduction on the numerical techniques used in our study,and then present numerical results for the one-band and three-band Hubbard models with and without electron-phonon interaction.Our simulations show that while antiferromagnetic spin correlation and dominant d-wave pairing can be well established in the electronic models,it is difficult to realize the long-range superconducting order in such models.