source("boot.R")
box_use(./b4)
box_use(../math/sidon)

#' @export
split_sidon_8 <- function(S) {
  if (length(S) != 8) stop("Sidon 8-set must have exactly 8 elements")
  S <- sort(S)
  list(left = S[c(1, 3, 5, 7)], right = S[c(2, 4, 6, 8)])
}

#' @export
block_diag_8x8 <- function(left_block, right_block) {
  result <- matrix(rep(list(b4$zero), 64), nrow = 8, ncol = 8)
  for (i in 1:4) for (j in 1:4) {
    result[[i, j]] <- left_block[[i, j]]
    result[[i + 4, j + 4]] <- right_block[[i, j]]
  }
  result
}

#' @export
b4xb4_matrix <- function(word_left, word_right) {
  block_diag_8x8(b4$burau_matrix(word_left), b4$burau_matrix(word_right))
}