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polynomial <- function(coef = c(0, 1)) {
a <- as.numeric(coef)
while ((la <- length(a)) > 1 && a[la] == 0) a <- a[-la]
structure(a, class = "polynomial")
}
as.polynomial <- function(p) {
if (is.polynomial(p)) p else polynomial(p)
}
is.polynomial <- function(p) {
inherits(p, "polynomial")
}
Ops.polynomial <- function(e1, e2) {
if (missing(e2))
return(switch(.Generic,
`+` = e1,
`-` = polynomial(NextMethod(.Generic)),
stop("unsupported unary operation")))
e1 <- unclass(e1)
e2 <- unclass(e2)
l1 <- length(e1)
l2 <- length(e2)
e1.op.e2 <- switch(.Generic,
`+` = , `-` = {
e1 <- c(e1, rep.int(0, max(0, l2 - l1)))
e2 <- c(e2, rep.int(0, max(0, l1 - l2)))
NextMethod(.Generic)
},
`*` = if (l1 == 1 || l2 == 1) {
e1 * e2
} else {
m <- outer(e1, e2)
as.vector(tapply(m, row(m) + col(m), sum))
},
`/` = {
if (l2 == 0) stop("unsupported polynomial division")
if (l2 == 1) e1/e2 else {
p <- rev(e1)
q <- rev(e2)
r <- rep.int(0, length(p))
i <- 0
while (length(p) >= l2) {
i <- i + 1
d <- p[1]/q[1]
r[i] <- d
p[1:l2] <- p[1:l2] - d * q
p <- p[-1]
}
if (i == 0) 0 else r[i:1]
}
},
`^` = {
if (l2 != 1 || e2 < 0 || e2%%1 != 0) stop("unsupported polynomial power")
switch(as.character(e2), `0` = 1, `1` = e1, {
p <- q <- polynomial(e1)
for (i in 2:e2) p <- p * q
as.numeric(p)
})
},
`%%` = {
if (l2 == 1) 0 else {
p <- rev(e1)
q <- rev(e2)
while (length(p) >= l2) {
d <- p[1]/q[1]
p[1:l2] <- p[1:l2] - d * q
p <- p[-1]
}
if (length(p) == 0) 0 else rev(p)
}
},
`==` = return(l1 == l2 && all(e1 == e2)),
`!=` = return(l1 != l2 || any(e1 != e2)),
stop("unsupported operation on polynomials"))
polynomial(e1.op.e2)
}
Summary.polynomial <- function(..., na.rm = FALSE) {
ok <- switch(.Generic,
sum = , prod = TRUE,
FALSE)
if (!ok)
stop(gettextf("Generic '%s' not defined for \"%s\" objects.", .Generic, .Class))
switch(.Generic,
sum = accumulate("+", as.polynomial(0), polylist(...)),
prod = accumulate("*", as.polynomial(1), polylist(...)))
}
Math.polynomial <- function(x, ...) {
switch(.Generic,
round = , signif = , floor = , ceiling = , trunc = polynomial(NextMethod(.Generic)),
stop(paste(.Generic, "unsupported for polynomials")))
}
as.character.polynomial <- function(x, decreasing = FALSE, ...) {
p <- unclass(x)
lp <- length(p) - 1
names(p) <- 0:lp
p <- p[p != 0]
if (length(p) == 0)
return("0")
if (decreasing)
p <- rev(p)
signs <- ifelse(p < 0, "- ", "+ ")
signs[1] <- if (signs[1] == "- ")
"-" else ""
np <- names(p)
p <- as.character(abs(p))
p[p == "1" & np != "0"] <- ""
pow <- paste("x^", np, sep = "")
pow[np == "0"] <- ""
pow[np == "1"] <- "x"
stars <- rep.int("*", length(p))
stars[p == "" | pow == ""] <- ""
paste(signs, p, stars, pow, sep = "", collapse = " ")
}
print.polynomial <- function(x, digits = getOption("digits"), decreasing = FALSE, ...) {
p <- as.character.polynomial(signif(x, digits = digits), decreasing = decreasing)
pc <- nchar(p)
ow <- max(35, getOption("width"))
m2 <- 0
while (m2 < pc) {
m1 <- m2 + 1
m2 <- min(pc, m2 + ow)
if (m2 < pc)
while (substring(p, m2, m2) != " " && m2 > m1 + 1) m2 <- m2 - 1
cat(substring(p, m1, m2), "\n")
}
invisible(x)
}
as.function.polynomial <- function(x, ...) {
a <- rev(coef(x))
w <- as.name("w")
v <- as.name("x")
ex <- call("{", call("<-", w, 0))
for (i in seq_along(a)) {
ex[[i + 2]] <- call("<-", w, call("+", a[1], call("*", v, w)))
a <- a[-1]
}
ex[[length(ex) + 1]] <- w
f <- function(x) NULL
body(f) <- ex
f
}
poly.orth <- function(x, degree = length(unique(x)) - 1, norm = TRUE) {
at <- attr(poly(x, degree), "coefs")
a <- at$alpha
N <- at$norm2
x <- polynomial()
p <- list(polynomial(0), polynomial(1))
for (j in 1:degree) p[[j + 2]] <- (x - a[j]) * p[[j + 1]] - N[j + 1]/N[j] * p[[j]]
p <- p[-1]
if (norm) {
sqrtN <- sqrt(N[-1])
for (j in 1 + 0:degree) p[[j]] <- p[[j]]/sqrtN[j]
}
class(p) <- "polylist"
p
}
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