Coerce Scalar Polynomials to Character Strings — as_txt

This utility coerces a scalar polynomial (given by the vector of real coefficients) or a scalar Laurent polynomial to a character string. If the vector should be interpreted as a Laurent polynomial, the minimal degree should be given in the argument laurent described below. The following "formats" are implemented.

syntax = "txt" returns a simple text representation,
syntax = "TeX" renders the coefficients to string in "TeX" syntax and
syntax = "expression" gives a string which may be rendered to an R expression with parse. This expression may be used to evaluate the polynomial and for annotating plots, see plotmath and the examples below.

Usage

as_txt_scalarpoly(
  coefs,
  syntax = c("txt", "TeX", "expression"),
  x = "z",
  laurent = FALSE
)

Arguments

coefs: Vector of doubles (complex elements are not allowed) representing a univariate polynomial (first element corresponds to power zero). When it represents a Laurent polynomial, the first element corresponds to the minimal degree.
syntax: (character string) determines the format of the output string.
x: (character string) polynomial variable.
laurent: Boolean or integer. Default set to FALSE. If one deals with Laurent polynomials, an integer corresponding to the minimal degree of the Laurent polynomial should be supplied.

Value

Character string used for printing univariate (Laurent) polynomials.

Examples

coefs = c(1, 2.3, 0, -1, 0)

as_txt_scalarpoly(coefs, syntax = 'txt', x = 'x')
#> [1] "1 + 2.3x - x^3"
as_txt_scalarpoly(coefs, syntax = 'TeX', x = '\\alpha')
#> [1] "1 + 2.3\\alpha - \\alpha^{3}"
as_txt_scalarpoly(coefs, syntax = 'expression', x = 'z')
#> [1] "1 + 2.3*z - z^{3}"
as_txt_scalarpoly(coefs = sample((-10):10, 7, replace = TRUE), 
                  syntax = 'txt', x = 'x', 
                  laurent = -3)
#> [1] "7x^-3 - 9x^-2 - 7x^-1 + 3 - 9x + 3x^2 + 3x^3"

if (FALSE) {
# the case syntax = "expression" may be used e.g. as follows

# make_polyfun creates a "closure" which evaluates the polynomial at given points
# note that this simple version does not work for zero polynomials!
make_polyfun = function(coefs) {
  expr = parse(text = as_txt_scalarpoly(coefs, 'expression', 'x'))
  fun = function(x) {
    return(eval(expr))
  }
  return(fun)
}

a = make_polyfun(coefs)
a(1)   # return the value  of the polynomial at x = 1
a(1:5) # return the values of the polynomial at x = 1,2,3,4,5

# create a plot
x_grid = seq(from = -1, to = 1, length.out = 101)
plot(x_grid, a(x_grid), type = 'l', xlab = 'x', ylab = 'a(x)',
     main = parse(text = paste('a(x) == ',
          as_txt_scalarpoly(coefs, syntax = 'expression', x = 'x'))))
}