In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. More generally there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduced by André Weil (1940) for Jacobians of curves, who gave an abstract algebraic definition; the corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function.
Read more about Weil Pairing: Formulation, Generalisation To Abelian Varieties, Applications
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“The mysteries of faith are degraded if they are made into an object of affirmation and negation, when in reality they should be an object of contemplation.”
—Simone Weil (1909–1943)
“Through man, and woman, and sea, and star,
Saw the dance of nature forward far;
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Saw musical order, and pairing rhymes.”
—Ralph Waldo Emerson (1803–1882)