isomorphisms

Here's a silly-but-perhaps-provocative way to talk about calculus.

The only atom to start with is +1+1+1+1+1+1+1+… ↣ 5+5+5+5+5+5+5+…. Some people call this "to quintuple" but I'll just call it ƒ. Repeated addition of the number 5. I'm going to build up large classes of functions from this, using "meta-moves" i.e. just operating on the function.

The first meta-move I'll allow myself is to stick the +5+5+5+5… anywhere I want on the number line. Tangent picking. Also known as b in y=mx+b.

isomorphisms

# first page of www.math.sunysb.edu/~kirillov/mat552/liegroups.pdf

# However, explicitly computing the characteristic polynomial and finding the roots is a rather difficult problem.


#He must mean for general N because this seems to work for me??


require(magrittr)
require(matrixcalc)

isomorphisms

options(menu.graphics=FALSE)
options(editor='vi')
options(digits=10)
some <- car::some


#http://stackoverflow.com/questions/1448600/change-default-prompt-and-output-line-prefix-in-r
options(continue="	")

isomorphisms

#run convenience functions first....
plat <- function(space,FUN,cex=2,chroma=45,a=66,b=4,c=3){		#a,b,c are tuning parameters
		func=FUN(space)						#eval for speedup
		coleur=arg(func)%%360
		light=a+b*mod(func)+c*l(coleur)
	       	plot(space, pch=46,cex=cex, col=hcl( h=coleur, c=chroma, l=light )  )
		}

#what this function does, is plot a boring series of points with nothing on them,
# moving the REAL ACTION to the colour parameter.

isomorphisms

library(colorout)

#     The function takes numeric vectors of at most three elements each.
#     The three numbers indicate, respectively, formating, background
#     color and foreground color. If a vector has only one element, the
#     number will be used to set the foreground color; if it has two
#     elements, they will be used to set the background and foreground
#     colors.
#
#     The table below shows valid values and their meanings as both

isomorphisms

"360852405690179584","","","2013-07-26 20:01:32 +0000","<a href=""http://www.floodgap.com/software/ttytter/"" rel=""nofollow"">TTYtter</a>","Define ""clear"" Mogadishu: http://t.co/fr4NwFlMq2","","","","http://downloads.bbc.co.uk/podcasts/radio4/thpop/thpop_20130723-1000b.mp3"
"334368922310676480","","","2013-05-14 18:05:38 +0000","<a href=""http://www.floodgap.com/software/ttytter/"" rel=""nofollow"">TTYtter</a>","Romans &amp; medieval Xtians both thought women were sexually insatiable. So where did ""Lie back and think of your country"" come from? #radio4","","","",""
"334365448063823873","","","2013-05-14 17:51:49 +0000","<a href=""http://www.floodgap.com/software/ttytter/"" rel=""nofollow"">TTYtter</a>","Only within the last 200 years that a European city has overtaken the size (1mm people) of Juvenalian Rome. #radio4","","","",""
"334359389601419265","","","2013-05-14 17:27:45 +0000","<a href=""http://www.floodgap.com/software/ttytter/"" rel=""nofollow"">TTYtter</a>","ancient Romans slipping Greek into t

isomorphisms

" RATIONALE:
" _ is used all the time in programming
" - is only used for "minus −" operator
" chords hurt my hands
" I avoid naming things with _ because it hurts
" I don't mind hitting <SHIFT> for "minus"
"   because it's an operator
"   and therefore requires more thought than
"   "spacebar in a variable name".

isomorphisms

fb = function(n) {
    f = ""
    b = ""
    
    if (!n %%3) f="fizz"
    if (!n %%5) b="buzz"
    
    print(paste0(f,b))
}

isomorphisms

#with expm

require(expm)
matrix(   c(0,1,1,1),   2,2 )    -> fibonacci
c(1L,1L)    -> start

start %*% (fibonacci %*% 1337)         #1337'th term-pair in Fibonacci series

#              [,1]          [,2]
#[1,] 1.887894e+279 3.054677e+279

isomorphisms

taste <- function(soup, ladle=5L) sample.int(x=soup, size=ladle, replace=TRUE)

peek <- function(df,n=5L) df[ taste(nrow(df),n) ,   ]      #dataframe[r,c]  means "subset of dataframe row #r, column #c"

p <- function(df,n=5L)  rbind(head(df,1L), peek(df,n), tail(df,1L)) 


#SAMPLE OUTPUT
require(bigvis)
data(movies)