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Jacobians of Hyperelliptic Curves
New Features:
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Two new Order functions are provided to compute the order
of a point P on a Jacobian J where the order of P or of J is bounded and where (optionally) some modular information is known
about that order.
Being able to use this extra information dramatically improves
the running time of the Order routines.
These are due to P. Gaudry.
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The function Frobenius applies the Frobenius to a point
on a Jacobian.
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The function WeilPairing computes the Weil pairing of two points
on a Jacobian defined over a finite field.
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The Order function for Jacobians over finite fields
has been rewritten by P. Gaudry.
Jacobians defined over a curve of genus 2 are treated separately.
More generally some specific algorithms are provided
to deal with some special cases.