Ops.onion: Arithmetic Ops Group Methods for Octonions

Description

Allows arithmetic operators to be used for octonion calculations, such as addition, multiplication, division, integer powers, etc.

Usage

# S3 method for onion
Ops(e1, e2)
OprodO(oct1, oct2)
HprodH(quat1, quat2)
R_OprodO(oct1, oct2)
R_HprodH(quat1, quat2)
AprodA(A, B, ur=getOption("use.R"))
AsumA(A, B)
Apower(A, B)
AequalsA(A, B)
AprodS(A, scalar)
Ainv(A)
Aneg(A)
Amassage(A, B)
harmonize(A, B)

Arguments

e1,e2, A, B

Objects of class “onion”

oct1,oct2

Octonionic vectors

quat1,quat2

Quaternionic vectors

scalar

Scalar vector

In function AprodA(), Boolean with default FALSE meaning to use the c implementation; and TRUE meaning to use the interpreted R function. See details section

Value

An object of the appropriate (ie biggest) class as went in, as per harmonize().

The only non obvious ones are Amassage(), which is used by the other functions to massage the two arguments into being the same length, thus emulating recycling.

The other one is harmonize() that coerces scalars into quaternions and quaternions into octonions if necessary, returning a list of two octonions or two quaternions of the same length, for passing to functions like AprodA().

None of these functions are really intended for the end user: use the ops as shown in the examples section.

Details

The function Ops.onion() passes unary and binary arithmetic operators (“+”, “-”, “*”, and “/”) to the appropriate specialist function.

The most interesting operator is “*”, which is passed to AprodA(). This function is sensitive to the value of option use.R. If this is TRUE, then arguments are passed, via Amassage(), to either R_HprodH() (for quaternions), or R_OprodO() (for octonions). If option use.R is anything other than TRUE (including being unset, which is the default), the massaged arguments are passed to HprodH() or OprodO(). This is what the user usually wants: it is much faster than using the R_ functions.

The relative performance of, say, OprodO() vs R_OprodO(), will be system dependent but on my little Linux system (Fedora; 256MB) OprodO() runs more than three hundred times faster than R_OprodO(). Your mileage may vary; see examples section for using options() to set argument ur.

Examples

Run this code

# NOT RUN {
x <- octonion(Re=1  , il=1:3, k=3:1)
y <- octonion(Re=1:3,  i=1  ,il=3:1)
z <- octonion(Re=3:1,  j=1  ,jl=1:3)
x*9
x+y
x*y
x/y

# }