PolynomF (version 0.94)

polynom: Constructor, coercion, predicate and print functions for polynom and polylist objects

Description

The function polynom is the constructor function for objects of the eponymous S3 class. as.polynom is the standad coercion function to the same class and is.polynom tests for inheritance from the class. polylist objects are lists of polynom objects, again with the eponymous class.

Usage

polynom(a = c(0, 1), …, eps = 0)
as.polynom(a)
is.polynom(a)
polylist(…)
as.polylist(x)
is.polylist(x)
# S3 method for polynom
print(x, variable = "x",
   digits = getOption("digits"), decreasing = FALSE, …)
# S3 method for polylist
print(x, …)

Arguments

a

Numeric coefficient vector for the constructor, specifying the coefficients of the powers from 0 to the maximum, without gaps, in that order, that is, in power series order. For the coercion and predicate functions this may be a coefficient vector, or an existing polynom object.

…

As yet, unused for polynom but may be used in future releases. With polylist, objects which are, or may be coerced to, polynom objects. With print methods, additional agruments either for the generic or for the print.polynom method.

x

Object which may be coerced to, or tested for, class polylist.

eps

Absolute tolerance below which components are considered zero.

variable

Character string giving name to be used for the independent variable.

digits

Integer giving the number of significant digits to use in the printed representation of the coefficients.

decreasing

Logical value. Should the powers appear in decreasing order?

Value

For polynom and as.polynom, an R function with class polynom. For is.polynom, a logical value

Details

polynom objects are represented as R functions with the coefficient vector held in an enclosing environment, or closure. They may be used as R functions, or as mathematical objects which behave under arithmetic and calculus operatons like polynomials.

Note that polynomials with complex coefficients are not (yet) supported. Nevertheless the root-finding methods described elsewhere will usually give complex zeros.

polylist objects are lists of polynom objects. Methods are available for dealing with all polynomials on the list simultaneously.

References

None

Examples

# NOT RUN {
x <- polynom()  # polynomial 'x'
p <- (x-1)^2 + 10*x^3 + 5*x^4
p
# 1 - 2*x + x^2 + 10*x^3 + 5*x^4 

plot(polylist(p, deriv(p), integral(p)),
    xlim = c(-2, 1), ylim = c(-10, 10))
abline(h=0, lty = "dashed", col = "grey")

print(p, variable = "z", decreasing = TRUE)

# }