https://github.com/cran/pracma
Tip revision: 392ae21a013fb3f518e8f9eb8efb458a55a2eca2 authored by HwB on 09 April 2011, 00:00:00 UTC
version 0.3-0
version 0.3-0
Tip revision: 392ae21
modpower.Rd
\name{modpower}
\alias{modpower}
\alias{modorder}
\title{
Power Function modulo m
}
\description{
Calculates powers and orders modulo \code{m}.
}
\usage{
modpower(n, k, m)
modorder(n, m)
}
\arguments{
\item{n, k, m}{Natural numbers, \code{m >= 1}.}
}
\details{
\code{modpower} calculates \code{n} to the power of \code{k} modulo
\code{m}.
\code{modorder} calculates the order of \code{n} in the multiplicative
group module \code{m}. \code{n} and \code{m} must be coprime.
Uses brute force, trick to use binary expansion and square is not more
efficient in an R implementation.
}
\value{
Natural number.
}
\note{
This function is \emph{not} vectorized.
}
\seealso{
\code{\link{primroot}}
}
\examples{
modpower(2, 100, 7) #=> 2
modpower(3, 100, 7) #=> 4
modorder(7, 17) #=> 16, i.e. 7 is a primitive root mod 17
#Gauss' table of primitive roots modulo prime numbers < 100
proots <- c(2, 2, 3, 2, 2, 6, 5, 10, 10, 10, 2, 2, 10, 17, 5, 5,
6, 28, 10, 10, 26, 10, 10, 5, 12, 62, 5, 29, 11, 50, 30, 10)
P <- primes(100)
for (i in seq(along=P)) {
cat(P[i], "\t", modorder(proots[i], P[i]), proots[i], "\t", "\n")
}
}
\keyword{ math }