R function for performing Lagrangian polynomial interpolation

lagrangian_interpolation.R

# Function for performing Lagrangian polynomial interpolation https://en.wikipedia.org/wiki/Lagrange_polynomial. 
# Requires the package rSymPy https://cran.r-project.org/web/packages/rSymPy/index.html. 
# Parameters:
#   x: x values of interpolating points
#   y: values corresponding to x values
# Returns:
#   Simplified interpolated polynomial that passes through the given x and y points


lagrange.poly <- function(x, y) {
  require(rSymPy)
  
  if (length(x) != length(y)) {
    stop('x and y must be of equal length')
  }
  
  l <- list() # List to store Lagrangian polynomials L_{1,2,3,4}
  k <- 1
  
  for (i in x) {
    # Set the numerator and denominator of the Lagrangian polynomials to 1 and build them up
    num <- 1
    denom <- 1
    
    # Remove the current x value from the iterated list
    p <- x[! x %in% i]
    
    # For the remaining points, construct the Lagrangian polynomial by successively 
    # appending each x value
    for (j in p) {
      num <- paste(num, "*", "(", 'x', " - ", as.character(j), ")", sep = "", collapse = "")
      denom <- paste(denom, "*", "(", as.character(i)," - ", as.character(j), ")", sep = "", collapse = "")
    }
    
    # Set each Lagrangian polynomial in rSymPy to simplify later.
    l[k] <- paste("(", num, ")", "/", "(", denom, ")", sep = "", collapse = "")
    k <- k + 1
  }
  
  # Similar to before, we construct the final Lagrangian polynomial by successively building 
  # up the equation by iterating through the polynomials L_{1,2,3,4} and the y values 
  # corresponding to the x values.
  eq <- 0
  
  for (i in 1:length(y)) {
    eq <- paste(eq, '+', as.character(y[i]), "*", l[[i]], sep = "", collapse = "")
  }
  
  # Define x variable for rSymPy to simplify
  x <- Var('x')
  
  # Simplify the result with rSymPy and return the polynomial
  return(sympy(paste("simplify(", eq, ")")))
}

I have a value of interval censored lifetable data. I would love to use interpolation to fill in the missing values in R.