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numlib::mroots -- modular roots of polynomials

Introduction

For a univariate polynomial P over the integers and for a natural number m the function call numlib::mroots(P,m) returns the sorted list of all integers such that if such integers exist; otherwise numlib::mroots(P,m) returns FAIL.

Call(s)

numlib::mroots(P,m)

Parameters

P - a univariate polynomial over the integers
m - a natural number

Returns

numlib::mroots returns either a list of nonnegative integers or FAIL.

Related Functions

numlib::lincongruence, numlib::msqrts

Details

Example 1

Defining a polynomial

>> P := poly(3*T^7 + 2*T^2 + T - 17, [T])
                              7      2
                      poly(3 T  + 2 T  + T - 17, [T])

and computing its roots modulo :

>> numlib::mroots(P, 1751)
                     [221, 260, 612, 736, 1127, 1496]

The polynomial P does'nt have roots modulo :

>> numlib::mroots(P, 1994)
                                   FAIL

Background




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