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An Addition Algorithm on the Jacobian Varieties of Curves
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The present paper computes addition on Jacobian varieties of curves using its singular plane model. Given a nonsingular curve C, let C1 be its singular (especially plane) CA model. After making clear the relationship between generalized Jacobian variety of C1 and Jacobian variety of C, we show that Arita’s algorithm for non singular CA curves also works for generalized Jacobian variety of singular CA curve C1. This means that we can compute addition on Jacobian variety of any curve (with at least one rational point) using its singular CA models.
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