# transcendental: Elementary transcendental functions In onion: Octonions and Quaternions

## Description

Elementary transcendental functions: exponential and trig

## Usage

 ``` 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 28 29 30``` ```## S3 method for class 'onion' exp(x) ## S3 method for class 'onion' log(x,base=exp(1)) ## S3 method for class 'onion' sin(x) ## S3 method for class 'onion' cos(x) ## S3 method for class 'onion' tan(x) ## S3 method for class 'onion' asin(x) ## S3 method for class 'onion' acos(x) ## S3 method for class 'onion' atan(x) ## S3 method for class 'onion' sinh(x) ## S3 method for class 'onion' cosh(x) ## S3 method for class 'onion' tanh(x) ## S3 method for class 'onion' asinh(x) ## S3 method for class 'onion' acosh(x) ## S3 method for class 'onion' atanh(x) ## S3 method for class 'onion' sqrt(x) ```

## Arguments

 `x` An onionic vector `base` In `log()`, the base of the logarithm

## Details

Trig and exponential functions, and a square root. Warning: these functions do not obey all the identities that one might expect; quaternions are not commutative, and octonions are not associative. The examples section illustrates this.

## Author(s)

Robin K. S. Hankin

## Examples

 ```1 2 3 4 5 6 7 8``` ```x <- roct(3)/10 sin(x)^2 + cos(x)^2 #should be close to O1 a <- rquat(5) b <- roct(5) log(a*b) -log(a) -log(b) #zero for real or complex a & b, but not quaternions log(b*a) -log(a) -log(b) #different (and still nonzero) ```

onion documentation built on July 11, 2017, 9:04 a.m.