test_that("Test suite aae.R; orbit()", {
  expect_true(all(unlist(orbit(id, 1:3)) == 1:3))

  a1 <- orbit(as.cycle(c("(123)", "(23)", "(1234567)", "(234567)", "(13)(45)(67)(89)")), 1)
  a2 <- list(c(1, 2, 3), 1, c(1, 2, 3, 4, 5, 6, 7), 1, c(1, 3))
  expect_true(identical(a1, a2))

  expect_true(all(sapply(1:9, function(i) {
    i %in% orbit(as.cycle("(45)(126)"), 1:9)[[i]]
  })))
  expect_true(all(sapply(1:9, function(i) {
    i %in% orbit(as.cycle("(45)"), 1:9)[[i]]
  })))

  checker1 <- function(a, n) {
    expect_true(all(unlist(lapply(orbit(a, n), function(x) {
      n %in% x
    }))))
  }

  includes_id <- as.cycle(c("", "(123)", ""))
  for (i in 1:5) {
    checker1(includes_id, i)
  }

  for (i in 1:2) {
    for (n in 1:9) {
      checker1(rperm(), n)
    }
  }
})