The shinymathexample app

First, the shinymathexample app presents the question:

The answer can the be written and checked:

It even works for mathematical/numerical equality, not just text/string equality:

Finally wrong answers are caught, too:

Exercise generation

The exercise generation code (boiled down) is something like this:

choices_x_coef <- c("a", "2*a", "3*a")
choices_x_pow <- 1:3

generate_f <- function() {
  x_coef <- sample(choices_x_coef, 1)
  x_pow <- sample(choices_x_pow, 1)
  x_part <- paste0(x_coef, "*x^", x_pow)
  eq <- ysym(x_part)
  eq
}

problem_f_eq <- generate_f()

true_ans <- list(
  x = deriv(problem_f_eq, "x")
)

output$problem <- renderUI({
  problem <- paste0("Let $$f(x) = ", tex(problem_f_eq), ".$$",
                    "Calculate the derivative with respect ", 
                    "to \\(x\\) and enter the result below.")
  
  res <- withMathJax(
    helpText(problem)
  )
  
  return(res)
})

Validation

The validation code (boiled down) is something like this:

reply <- input$answer_x

parsed_input <- iomath::prepare_input(reply)

if (inherits(parsed_input, "error")) {
  stop("Could not prepare the input (remember that I'm simple-minded!).")
}

reply_sym <- tryCatch(Ryacas::ysym(parsed_input), 
                      error = function(e) e)

if (inherits(reply_sym, "error")) {
  stop("Could not understand the input (remember that I'm simple-minded!).")
}

compare_grid <- expand.grid(
    x = seq(-10, 10, len = 6),
    a = seq(-10, 10, len = 6)
)
is_correct <- tryCatch(iomath::compare_reply_answer(reply = reply, 
                                                    answer = true_ans$x, 
                                                    compare_grid = compare_grid), 
                       error = function(e) e)

if (inherits(is_correct, "error")) {
  stop(paste0("Error: ", is_correct$message))
}

is_correct # TRUE/FALSE

Remarks

Take a look at the complete code at https://github.com/r-cas/shinymathexample.

The provided example should illustrate that it is fairly easy to make something relatively sophisticated.

Beside the central aspect of Ryacas (e.g. for derivatives etc.), iomath has the important function compare_reply_answer that compares reply to answer over the grid of values defined by compare_grid. Thus, equality of expressions are measured as point-wise equality over a finite number of points (e.g. 100) for different values of variables including an allowed tolerance.