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We study pseudo-arclength continuation algorithms for computing the ground state and excited-state solutions of two-dimensional spin-1 BEC.Here the chemical potential,the magnetic potential,and magnetization are used as the three components for the continuation variable.We implement the pseudo-arclength continuation algorithm until the magnetization condition is satisfied.Of particular interest here is the investigation of symmetry-breaking solutions.Some numerical experiments on Na-23 and Rb-87 are reported.