Integral and differential calculus on polynomials or lists of polynomials.

Description

Performs calculus operations on polynomial objects: differentiation and indefinite or definite integration.

Usage

## S3 method for class 'polynom'
integral(expr, limits = NULL, ...)
## S3 method for class 'polylist'
integral(expr, ...)
## S3 method for class 'polynom'
deriv(expr, ...)
## S3 method for class 'polylist'
deriv(expr, ...)

Arguments

Details

integral is a local generic function. The generic function deriv is already defined in the stats package.

Value

A polynom or numeric object giving the result of the calculus operation, or list of such results. If the result is polynom the list is a polylist.

References

None

Examples

p <- poly.from.zeros(-2:5)
ip <- integral(p)
ipv <- integral(p, limits = c(-2, 5))

plot(polylist(p, deriv(p)))

x <- polynom()
H <- polylist(1, x)
for(n in 2:10)
    H[[n+1]] <- x * H[[n]] - (n-1)*H[[n-1]]

solve(deriv(H))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(PolynomF)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/PolynomF/integral.Rd_%03d_medium.png", width=480, height=480)
> ### Name: integral
> ### Title: Integral and differential calculus on polynomials or lists of
> ###   polynomials.
> ### Aliases: integral integral.polynom integral.polylist deriv.polynom
> ###   deriv.polylist
> ### Keywords: symbolmath
> 
> ### ** Examples
> 
> p <- poly.from.zeros(-2:5)
> ip <- integral(p)
> ipv <- integral(p, limits = c(-2, 5))
> 
> plot(polylist(p, deriv(p)))
> 
> x <- polynom()
> H <- polylist(1, x)
> for(n in 2:10)
+     H[[n+1]] <- x * H[[n]] - (n-1)*H[[n-1]]
> 
> solve(deriv(H))
[[1]]
[1] 0

[[2]]
numeric(0)

[[3]]
[1] 0

[[4]]
[1] -1  1

[[5]]
[1] -1.732051  0.000000  1.732051

[[6]]
[1] -2.3344142 -0.7419638  0.7419638  2.3344142

[[7]]
[1] -2.856970 -1.355626  0.000000  1.355626  2.856970

[[8]]
[1] -3.3242574 -1.8891759 -0.6167066  0.6167066  1.8891759  3.3242574

[[9]]
[1] -3.750440 -2.366759 -1.154405  0.000000  1.154405  2.366759  3.750440

[[10]]
[1] -4.1445472 -2.8024859 -1.6365190 -0.5390798  0.5390798  1.6365190  2.8024859
[8]  4.1445472

[[11]]
[1] -4.512746 -3.205429 -2.076848 -1.023256  0.000000  1.023256  2.076848
[8]  3.205429  4.512746

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>