Operator overloading and class definition in R: Use a different base field/corpus

Question

(I'm using the word "field" in the mathematical sense; base fields/corpora which R already uses include the real and complex numbers.)

I'm interested in allowing some other base fields/corpora (like F₅, which is modular arithmetic in base 5). To do that I would need to

1. define a new data type
2. overload the relevant operators (+, *, and maybe more)
3. maybe something else? e.g., integrate with other functionality?

So, how does one define a new data type or overload operators in R?

Answer 1

I found Hadley Wickham's devtools wiki an invaluable resource for getting started with classes in R. In particular, read the sections on:

• S3 classes
• S4 classes

Here is a starting point that illustrates some of the concepts in S3 classes. Let's call your new class f5. At a minimum, you would probably want to create methods for:

• Coercion: as.f5
• Test: is.f5
• Some basic operators: +.f5
• A class to handle printing: print.f5

Some code (using digitsBase in package GLDEX to do the base conversion):

library(GLDEX)

as.f5 <- function(x){
  if(!inherits(x, "f5")) class(x) <- c("f5", class(x))
  x
}

is.f5 <- function(x){
  inherits(x, "f5")
}

`+.f5` <- function(e1, e2){
  NextMethod(e1, e2)
}

print.f5 <- function(x, ...){
  # Next line from ?GLDEX::digitsBase
  b2ch <- function(db) noquote(gsub("^0+(.{1,})$"," \1", 
                           apply(db, 2, paste, collapse = "")))

  cat("Base 5:\n")
  cat(b2ch(digitsBase(x, 5)))
  invisible(x)
}


x <- as.f5(0:10)
y <- as.f5(5)

x + y

Base 5:
10 11 12 13 14 20 21 22 23 24 30

Answer 2

I interpreted your question a bit differently than @Andrie, but he has already done a bunch of the needed S3 class work. I thought you wanted to develop group operations on a group with five elements, or perhaps a ring. You would then want a "+" operation with an identity element == 0 and perhaps a "*" operation with an identity element == 1.

If you wanted the nonnegative integers mapped into this, you would use the modulo arithmetic operators, %% and perhaps %/%:

?Ops
as.g5 <- function(x){
  if(!inherits(x, "g5")) class(x) <- c("g5", class(x))
  x %% 5
}

print.g5 <- function(x, ...){

  cat("G5 equivalent:\n")
  cat(x %% 5)
  invisible(x)
}

If you wanted two operators you might be looking for:

 `+.g5` <- function(e1, e2){
   NextMethod(e1 ,e2) %% 5
 }

 `*.g5` <- function(e1, e2){
   NextMethod(e1 ,e2) %% 5
 }
 x <- as.g5(0:10)
 y <- as.g5(5)

 x + y
#G5 equivalent:
#0 1 2 3 4 0 1 2 3 4 0
 y <- as.g5(2)
 x * y
#G5 equivalent:
#0 2 4 1 3 0 2 4 1 3 0

It's also possible to use these operation on "volatile" versions of vectors:

 as.g5(1:10) * as.g5(1:10)
# G5 equivalent:
# 1 4 4 1 0 1 4 4 1 0