test_that("Test suite aaa.R", {
  id <- cycle(list(list()))
  expect_true(is.id(id))


  a1 <- c(
    3L, 14L, 9L, 18L, 10L, 19L, 4L, 17L, 12L, 7L, 5L, 15L, 1L,
    16L, 8L, 13L, 11L, 2L, 6L, 20L
  )

  problem <- as.word(a1)
  problem * problem


  j1 <- c(12L, 11L, 1L, 9L, 7L, 2L, 3L, 8L, 17L, 15L, 18L, 5L, 6L, 13L, 16L, 4L, 14L, 10L, 19L, 20L)
  j2 <- c(11L, 12L, 14L, 3L, 10L, 8L, 9L, 13L, 20L, 16L, 6L, 2L, 17L, 15L, 7L, 1L, 18L, 5L, 4L, 19L)
  v1 <- as.word(j1)
  v2 <- as.word(j2)
  word_prod_single(v1, v2)

  # to create an identity cyclist, use list(c()).

  b1 <- cycle(list(list(1:2, 3:5, 6:10, 11:15)))
  b2 <- b1 + as.cycle(100:119)

  w <- list(c(1), c(2, 5, 3), c(4))
  x <- list(c(1), c(2, 5, 3), c(4, 7))
  y <- list(c(4, 6), c(2, 5, 1), c(8, 3))
  z <- list(c(4, 6, 8, 2, 3, 1, 7, 9, 5))


  # following returns cyclists:
  nicify_cyclist(x)
  nicify_cyclist(y)
  nicify_cyclist(z)

  thing1 <- cycle(list(nicify_cyclist(x), nicify_cyclist(y), nicify_cyclist(z), list(c())))
  thing2 <- cycle(list(x, y, z, list(c())))


  ww <- word(matrix(replicate(12, sample(9)), ncol = 9, byrow = TRUE))
  xx <- word(matrix(replicate(12, sample(9)), ncol = 9, byrow = TRUE))
  jj <- ww
  size(jj) <- 10

  expect_true(all(sgn(ww) * sgn(xx) == sgn(ww * xx)))
  identical(as.word(as.cycle(xx)), xx)



  expect_true(all(inverse(thing1) * thing1 == id))
  expect_true(all(thing1 * inverse(thing1) == id))


  a <- as.word(thing1)
  a[1] <- a[2]


  as.cycle(1:9)


  # combine cyclists using cycle(list(x,y,z))

  z1 <- list(c(3, 17), 39, c(10, 14, 5, 8, 11), c(18, 12), c(16, 7, 19, 13, 15, 4, 20, 9, 6, 1), 32, 22)
  z2 <- list(1:4, 10:11, 20:33)

  fish <- cycle(list(x, y, z))


  x2 <- c(7, 9, 3, 5, 8, 6, 1, 4, 2)

  x3 <- rbind(
    a = c(5L, 8L, 4L, 6L, 3L, 9L, 1L, 7L, 2L),
    b = c(2L, 5L, 3L, 9L, 1L, 7L, 6L, 4L, 8L),
    c = c(9L, 5L, 7L, 1L, 4L, 3L, 8L, 6L, 2L),
    d = 1:9,
    e = c(1L, 2L, 3L, 5L, 4L, 6L, 7L, 8L, 9L)
  )

  x4 <- cbind(x3, matrix(11:20, 5, 2))

  id <- cycle(list(list()))

  xjj <- cycle(list(
    list(c(1, 2, 4), c(3, 6)),
    list(c(1, 2), c(3, 4, 5, 6, 7)),
    list(c(1, 2, 4), c(3, 6)),
    list(c(1, 2, 4), c(3, 16)),
    list(c(1, 2, 4), c(3, 6)),
    list(c(1, 2, 4), c(3, 6)),
    list(), # empty!
    list(c(1, 2, 4), c(3, 56)),
    list(c(1, 2, 4), c(3, 56), 20:21)
  ))


  cl3 <- list(c(3, 25, 1), 5:10, c(17, 19))


  x3 <- word(x3)
  # x3^6


  shape_cyclist(list(list()))

  data(megaminx)
  m <- megaminx
  p <- megaminx
  m[1] <- id
  m[2] <- as.cycle(1:10)
  m[3] <- id
  m[4] <- as.cycle(1:40)

  m[6] * m[7]


  expect_true(all(p * inverse(p) == id))
  expect_true(all(inverse(p) * p == id))

  expect_true(all(p == p^1))
  expect_true(all(p^2 == p * p^1))
  expect_true(all(p^3 == p * p^2))
  expect_true(all(p^4 == p * p^3))
  expect_true(all(p^5 == p * p^4))


  rep(m, 0)
  sgn(thing1)



  o1 <- rperm(31, 20)
  o2 <- rperm(31, 20)
  o3 <- rperm(31, 20)

  expect_true(all(o1^(o2 * o3) == (o1^o2)^o3))

  trim(as.word(id))
  trim(word(col(matrix(0, 4, 5))))

  nothing <- word(col(matrix(0, 4, 5)))
  trim(nothing)


  o1[1] <- id # former bug



  ## check Hall-Witt:

  x <- rperm(100, 7)
  y <- rperm(100, 8)
  z <- rperm(100, 9)

  uu <- # should be the identity
    commutator(commutator(x, y), z^x) *
      commutator(commutator(z, x), y^z) *
      commutator(commutator(y, z), x^y)

  expect_true(all(is.id(uu)))

  ## Following is the same test more compactly written:
  expect_true(all(is.id(.[.[x, y], z^x] * .[.[z, x], y^z] * .[.[y, z], x^y])))



  ## bug in shapepart:
  options(warn = 4)
  shapepart(allperms(5))


  ## bug in sgn(), issue #4:
  expect_true(sgn(as.cycle("(12)(34)")) == 1)


  ## test for permutation matrix making sense:

  a <- rperm(1, 14)
  b <- rperm(1, 14)
  pa <- perm_matrix(a)
  pb <- perm_matrix(b)

  expect_true(is.perm_matrix(pa))
  expect_true(is.perm_matrix(pb))
  expect_true(is.perm_matrix(pa %*% pb))
  expect_true(is.perm_matrix(pb %*% pa))

  expect_true(is.perm_matrix(solve(pa)))
  expect_true(is.perm_matrix(solve(pb)))

  expect_true(all(pa == t(solve(pa))))
  expect_true(all(pb == t(solve(pb))))

  expect_true(all(solve(pa) == perm_matrix(inverse(a))))
  expect_true(all(solve(pb) == perm_matrix(inverse(b))))
  expect_true(all(crossprod(pa, pb) == perm_matrix(inverse(a) * b)))
})