# comm_fail: Failure of commutativity and associativty using visual plots In RobinHankin/gyrogroup: The Lorentz Transform in Relativistic Physics

## Description

Relativistic addition of three-velocities is neither commutative nor associative, and the functions documented here show this visually.

## Usage

 ```1 2 3``` ```comm_fail1(u, v, bold=5, r=1) comm_fail2(u, v, bold=5, r=1) ass_fail(u, v, w, bold=5,r=1) ```

## Arguments

 `u,v,w` Three velocities. Arguments `u` and `w` are single-element three velocities, argument `v` is a vector. See the examples `bold` Integer specifying which vector element to be drawn in bold `r` Radius of dotted green circle, defaulting to 1 (corresponding to c=1). Use `NA` to suppress plotting of circle

## Value

These functions are called for their side-effect of plotting a diagram.

## Note

The vignette `lorentz` gives more details and interpretation of the diagrams

## Author(s)

Robin K. S. Hankin

## Examples

 ```1 2 3 4 5 6 7``` ```u <- as.3vel(c(0.4,0,0)) v <- seq(as.3vel(c(0.4,-0.2,0)), as.3vel(c(-0.3,0.9,0)),len=20) w <- as.3vel(c(0.8,-0.4,0)) comm_fail1(u=u, v=v) comm_fail2(u=u, v=v) ass_fail(u=u, v=v, w=w, bold=10) ```

RobinHankin/gyrogroup documentation built on Feb. 19, 2019, 3:20 a.m.