How to convert equation from R code into readable text? - r

Question

I have defined multiple different functions, each containing one equation each, like so:
catalanFormula <- function(n){
return( (factorial(2 * n)) / ((factorial(n + 1)) * factorial(n)) )
}
triangularFormula <- function(n){
return( (n * (n+1)) / 2 )
}
I am then plotting each function using the plot() function from base R. What I want to do is be able to include the equation in my plot as a label or text, but in a way that is easily understandable. I know I can use LaTeX to write each equation manually, but I was wondering if there is a package or method anyone knows of that can deparse a mathematical equation in R and turn it into a standard readable mathematical equation. The only math occurring is factorials, multiplication, division, exponents, addition, and subtraction.
For example, I want to convert
(factorial(2 * n)) / ((factorial(n + 1)) * factorial(n))
into something that looks like this.
Then, be able to use the output within the text() function of base R plotting.

Answer 1

With the Ryacas package you can transform a math expression to its corresponding LaTeX code. But the factorial must be given as !:
library(Ryacas)
eq <- yac_symbol("(2 * n)! / ((n + 1)! * n!)")
tex(eq)
# "\\frac{\\left( 2 n\\right) !}{\\left( n + 1\\right) ! n!}"
Another possibility is to call Python from R and use the pytexit library:
from pytexit import py2tex
py2tex("math.factorial(2 * n) / ((factorial(n + 1)) * factorial(n))")
# $$\frac{\operatorname{factorial}\left(2n\right)}{\operatorname{factorial}\left(n+1\right) \operatorname{factorial}\left(n\right)}$$
You can also take a look at PyLaTeX and lax.

Answer 2

Here's a base R function that will walk the abstract syntax tree to replace the factorial and / functions with the corresponding ?plotmath markup so you can add them to R plots.
returnToPlotmath <- function(fun) {
swap <- function(x) {
if (class(x) %in% c("call","(")) {
x <- as.list(x)
if (as.character(x[[1]])=="/") {
x[[1]] = quote(frac)
x[[2]] = swap(x[[2]])
x[[3]] = swap(x[[3]])
} else if (as.character(x[[1]])=="factorial") {
x[[1]] = quote(`*`)
if (is.call(x[[2]])) {
x[[2]] = as.call(list(quote(`(`), x[[2]]))
} else {
x[[2]] = swap(x[[2]])
}
x[[3]] = "!"
} else if (as.character(x[[1]])=="*") {
if(is.call(x[[2]]) | is.call(x[[3]])) {
x[[1]] = quote(`%.%`)
x[[2]] = swap(x[[2]])
x[[3]] = swap(x[[3]])
}
} else {
x[[2]] = swap(x[[2]])
if (length(x)==3) x[[3]] = swap(x[[3]])
}
return(as.call(x))
} else {
return(x)
}
}
body_exprs <- body(fun)[[2]]
swap(body_exprs[[length(body_exprs)]])
}
This does assume that the return is the last statement in the function body {} block. You can get the expression with
returnToPlotmath(catalanFormula)
# frac(((2 * n) * "!"), (((n + 1) * "!") %.% (n * "!")))
returnToPlotmath(triangularFormula)
# frac((n %.% (n + 1)), 2)
And you can add them to plot titles and such
plot(main=returnToPlotmath(catalanFormula), 1, 1)
plot(main=returnToPlotmath(triangularFormula), 1, 1)
This solution is highly specific to the functions you need to transform. But it could be extended if needed.

Answer 3

The expr2latex() function from simsalapar parses expressions to LaTeX, and can be extended to include the factorial symbol with a minor addition to the code:
expr2latex2 <- function(expr) {
L <- length(expr)
c.BinTable <- simsalapar:::c.BinTable
if(!L) "" else {
Symb <- is.symbol(expr)
F <- if(Symb) expr else expr[[1]]
cF <- simsalapar:::mDeparse(F)
FF <- simsalapar:::renderAtom(F, Len=L, d.a = cF)
if(Symb && L != 1)
stop("is.symbol(.), but length(.) = ", L, " != 1")
else if(!Symb && typeof(expr) != "language" && L != 1)
stop("is not language nor symbol), but length(.) = ", L, " != 1")
switch(L,
## length 1:
FF,
{ ## length 2: e.g. "- 1", "+ x", "!TRUE", "~ ff",
#browser()
rhs <- expr2latex2(expr[[2]])
if (cF == "bold") paste0("\\mathbf{", rhs, "}")
else if(cF == "italic") paste0("\\mathit{", rhs, "}")
else if(cF == "factorial") paste0("(",rhs,")!") #extra case added in for factorial
else if(!simsalapar:::isOp(cF)) # not a binary operator ==> "function call":
paste0(FF,"(",rhs,")") ## e.g. "O(n)"
else if(cF == "{") paste0("{", rhs, "}")
else if(cF == "(") paste0("(", rhs, ")")
else paste(FF, rhs)
},
{ ## length 3:
lhs <- expr2latex2(expr[[2]])
rhs <- expr2latex2(expr[[3]])
if(cF == "[") ## subscript
paste0(lhs, "_{", rhs, "}")
else if(cF == "~") ## space
paste(lhs, "\\", rhs)
## not treated, as plotmath() does neither :
## else if(cF == "[[")
## paste0(lhs, "[[", rhs, "]]")
else if(cF %in% c.BinTable)
paste(lhs, simsalapar:::getTab(cF, simsalapar:::BinTable), rhs)
else if(cF %in% c.RelTable)
paste(lhs, simsalapar:::getTab(cF, simsalapar:::RelTable), rhs)
else if(simsalapar:::isOp(cF)) ## e.g. U + x
paste(lhs, FF, rhs)
else ## log(x, 2)
paste0(FF, "(", lhs, ",", rhs, ")")
},
## length >=4 : F(a, b, c, ...)
stop("length(expr) = ",L," (>= 4); not yet implemented") # TODO MM
)## end{switch}
}
}
original function
expr2latex( quote( (factorial(2 * n)) / ((factorial(n + 1)) * factorial(n)) ) )
#[1] "(factorial(2 n)) / ((factorial(n + 1)) factorial(n))"
revised treatment of factorials
expr2latex2( quote( (factorial(2 * n)) / ((factorial(n + 1)) * factorial(n)) ) )
#[1] "((2 n)!) / (((n + 1)!) (n)!)"