integer2 http://www.openmath.org/cd http://www.openmath.org/cd/integer2.ocd 2006-07-11 2004-07-11 0 1 experimental This CD holds a collection of basic modular arithmetic for integers. modulo_relation This symbol represents a univariate function, whose argument should be an integer. When applied to an integer m, it denotes the equivalence relation of being equal modulo m on Z. divides This symbol represents a bivariate Boolean function, whose arguments should be integers. When applied to integers a and b, it denotes the property that a divides b. For two integers a and b, the number a divides b if and only, in the magma Z with multiplication, a is a left divisor of b. eqmod This symbol represents a Boolean valued trivariate function, whose arguments should be integers. When applied to integers a, b, m, it denotes the Boolean evalue of the assertion that a and b are equal modulo m. neqmod This symbol represents a Boolean valued trivariate function, whose arguments should be integers. When applied to integers a, b, m, it denotes the Boolean evalue of the assertion that a and b are not equal modulo m. class This symbol represents a bivariate function, whose arguments should be integers. If a, m are integers, then class(a,m) denotes the residue class a mod m in setname2.Zm. euler This symbol denotes the univariate Euler totient function. If m is an integer, then euler(m) denotes the order of the multiplicative group of invertible elements in the residue class ring Z/mZ. ord This symbol denotes a binary function. Its first argument shoud be a prime number p, the second an integer n. When applied to p and n, it represents the highest power of p occurring in a factorization of n. There are two factors 2 in 60: 2 60 2