Jacobi: Computation of the Jacobi Symbol for vli Objects

In VeryLargeIntegers: Store and Operate with Arbitrarily Large Integers

Computation of the Jacobi Symbol for vli Objects

Description

Computation of the Jacobi Symbol for vli (Very Large Integers) objects. The Jacobi Symbol is a generalization of the Legendre Symbol, not being necessary that n be a prime number.

It is needed in many algorithms of modular arithmetic, computational number theory and cryptography. For example, it is used by the present package in the Solovay-Strassen probabilistic primality test.

Usage

Jacobi(a, n)

## Default S3 method:
Jacobi(a, n)

## S3 method for class 'numeric'
Jacobi(a, n)

## S3 method for class 'vli'
Jacobi(a, n)

Arguments

a	object of class vli or 32 bits integer
n	positive odd integer; object of class vli or 32 bits integer

Value

object of class vli with value -1, 0 or 1.

Author(s)

Javier Leiva Cuadrado

Examples

x <- as.vli("342635653456")
y <- as.vli("3210591001")
Jacobi(x, y)

VeryLargeIntegers documentation built on May 31, 2023, 7:06 p.m.