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numlib::order -- order of a residue class

Introduction

numlib::order(a,m) returns the order of the residue class modulo m of a in the group of units modulo m if a and m are coprime.

Call(s)

numlib::order(a, m)

Parameters

a - an integer
m - a natural number

Returns

numlib::order(a,m) returns a natural number if a is coprime to m, and FAIL if a is not coprime to m.

Related Functions

numlib::lambda, numlib::phi

Details

Example 1

We compute the order of the residue class of in the unit group modulo :

>> numlib::order(23, 2161)
                                   2160

Example 2

We compute the order of all elements in the unit group modulo :

>> map([$ 1..12],numlib::order,13)
                 [1, 12, 3, 6, 4, 12, 12, 4, 3, 6, 12, 2]

Example 3

The residue class of 7 modulo isn't a unit in the ring :

>> numlib::order(7,21)
                                   FAIL

Background

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