Calculating The Jacobi Symbol
The above formulas lead to an efficient algorithm for calculating the Jacobi symbol, analogous to the Euclidean algorithm for finding the GCD of two numbers. (This should not be surprising in light of rule 3)).
The "numerator" is reduced modulo the "denominator" using rule 2). Any multiples of 2 are pulled out using rule 4) and calculated using rule 8). The symbol is flipped using rule 6), and the algorithm recurses until the "numerator" is 1 (covered by rule 4)) or 2 (covered by rule 8)), or the "numerator" equals the "denominator" (rule 3)).
Read more about this topic: Jacobi Symbol
Famous quotes containing the words calculating the, calculating, jacobi and/or symbol:
“What our children have to fear is not the cars on the highways of tomorrow but our own pleasure in calculating the most elegant parameters of their deaths.”
—J.G. (James Graham)
“I know that the right kind of leader for the Labour Party is a kind of desiccated calculating machine.”
—Aneurin Bevan (1897–1960)
“During the long ages of class rule, which are just beginning to cease, only one form of sovereignty has been assigned to all men—that, namely, over all women. Upon these feeble and inferior companions all men were permitted to avenge the indignities they suffered from so many men to whom they were forced to submit.”
—Mary Putnam Jacobi (1842–1906)
“The glance is natural magic. The mysterious communication established across a house between two entire strangers, moves all the springs of wonder. The communication by the glance is in the greatest part not subject to the control of the will. It is the bodily symbol of identity with nature. We look into the eyes to know if this other form is another self, and the eyes will not lie, but make a faithful confession what inhabitant is there.”
—Ralph Waldo Emerson (1803–1882)