# Univariate polynomial objects in R

### Description

A package to implement a class of objects that behave like univariate polynomails. Arithmetic operations (addition, subtraction, multiplication, division, remainder, raising to a non-negative integer power) are supported in a natural way. The objects also act as R functions. This package is a successor to the ‘polynom’ package, but has a simpler and more convenient representation for the objects. Like ‘polynom’ it uses S3 classes and methods.

### Details

Package: | PolynomF |

Type: | Package |

Version: | 1.0 |

Date: | 2008-05-05 |

License: | GPL-2 |

LazyLoad: | yes |

The constructor function `polynom`

is used to create polynomial
objects from their coefficient vector, in power series order. Once
polynomials are constructed they may used as objects in arithmetic
operations, integration and differentiation, and as R functions that
evaluate the polynomial either at a numeric or complex vector, or at
another polynomial, i.e. substituting one polynomial into
another. Facilities are also provided for graphical presentation and
calculation of complex zeros.

The constructor function `polylist`

may be used to create a
*list* of polynomial objects. Operations on `polylist`

objects include simultaneous graphical display of all components and
coercion to function. The function may then be used to evaluate all
all polynomials on the list simultaneously at the same argument.

### Author(s)

Bill Venables, with some code inherited from the original `package`

by Bill Venables and Kurt Hornik.

Maintainer: <Bill.Venables@gmail.com>

### References

None.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
x <- polynom()
p <- (x-1)^2 + 1
p
plot(p)
pv <- p(-3:4); pv
p1 <- p(p-1); p1;
plot(polylist(p, p1))
## Hermite polynomials to degree 10
H <- polylist(1, x)
for(n in 2:10)
H[[n+1]] <- x*H[[n]] - (n-1)*H[[n-1]]
H
### normalisation to unit length
for(n in 1:11)
H[[n]] <- H[[n]]*exp(-lgamma(n)/2)
plot(H, xlim = c(-3,3))
## orthogonality relationship check:
f <- function(i,j) stats::integrate(function(z)
dnorm(z)*H[[i+1]](z)*H[[j+1]](z), -Inf, Inf)
f(2,3)
f(4,4)
``` |