Galois / commutators / Abel-Ruffini / Boas Katz / Vladimir I. Arnol'd

Abel-Ruffini.R

#start with six random coefficients for the quintic + a constant
start <- complex( modulus=1+rnorm(6,sd=.1), argument=1:6 )
twiddler <- function(x) complex(modulus=1, argument=x)

#there’s some bogus R nonsense about c() and list() coming…
swirl <- list(start)

#twiddle the 6 inputs around
for (j in 1:326/8) { swirl <- c( swirl, list( start + c(0,-8*twiddler(j)*j,0,8*twiddler(j)*j,0,0) ) ) }

#change the zeroes to twiddle the other coefficients


require(magrittr)    #as if you didn't already!
require(animation)



#you can replace this with just the 'for' loop for testing
saveGIF({ 
  for (swoop in swirl) { 
    #side by side
    par(mfrow=c(1,2));
    
    #organising the plots with aesthetic stuff on a second line; is that more readable?
    plot( swoop, pch=19, main='coefficients',
    xlim=c(-3,3), ylim=c(-3,3), col=rgb(0,0,0, 1-1:6/10) );
    
    #polyroot finds the answers for you, and so is in some sense the "main part" of this script. If I feed polyroot(1,2,-3) it solves x² + 2x − 3 = 0.
    polyroot( swoop ) %>% plot(pch=19, cex=2
    
    col=rainbow(5), main='solutions',
    xlim=c(-3,2), ylim=c(-3,5) )
    
    }}, interval=.03, movie.name='Abel-Ruffini.5.clown-balls.gif', ani.width=700, ani.height=300)