Nothing
monic.polynomials <- function( monic.recurrences )
{
###
### This function returns a list with n+1 elements
### containing the order k monic polynomials for orders k=0,1,...,n
###
### Parameter
### monic.recurrences = a data frame containing the parameters a and b
###
np1 <- nrow( monic.recurrences )
n <- np1 - 1
polynomials <- as.list( rep( NULL, np1 ) )
p.0 <- polynomial( c(1) )
polynomials[[1]] <- p.0
a <- monic.recurrences$a
b <- monic.recurrences$b
j <- 0
while( j < n ) {
aj <- a[j+1]
bj <- b[j+1]
monomial <- polynomial( c( -aj, 1 ) )
if ( j == 0 ) {
p.jp1 <- monomial
}
else {
p.jm1 <- polynomials[[j]]
p.j <- polynomials[[j+1]]
p.jp1 <- monomial * p.j - bj * p.jm1
}
polynomials[[j+2]] <- p.jp1
j <- j + 1
}
return( polynomials )
}
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