R/Stest.R

In quhomology: Calculation of Homology of Quandles, Racks, Biquandles and Biracks

all_combinations <- compiler::cmpfun(function(k){
  output <- t(combn(rep(0:(k-1), 2), 2))
  output <- unique(output)
  return(output)
})

check_permutations <- compiler::cmpfun(function(B){
  C <- unique(B)
  if(all(C!=B)){
    return(FALSE)
  } else{
    return(TRUE)
  }
})

find_S_result <- compiler::cmpfun(function(x,X,S){
  for(i in 1:nrow(X)){
    if(all(X[i, ]==x)){
      match.id <- i
      break
    }
  }
  return(S[match.id, ])
})

check_YB <- compiler::cmpfun(function(S,k,X){
  for(i in 0:(k - 1)){
    for(j in 1:nrow(S)){
      LHS <- c(i, S[j, ])
      RHS <- LHS
      LHS[1:2] <- find_S_result(LHS[1:2],X,S)
      LHS[2:3] <- find_S_result(LHS[2:3],X,S)
      LHS[1:2] <- find_S_result(LHS[1:2],X,S)
      RHS[2:3] <- find_S_result(RHS[2:3],X,S)
      RHS[1:2] <- find_S_result(RHS[1:2],X,S)
      RHS[2:3] <- find_S_result(RHS[2:3],X,S)
      if(!all(LHS == RHS)){
        return(FALSE)
      }
    }
  }
  return(TRUE)
})

check_f <- compiler::cmpfun(function(S_X,k,X_squared){
  S <- unique(cbind(X_squared[, 1], S_X[, 1:2]))
  if(nrow(S)!=(k*k)){
    return(FALSE)
  } else{
    return(TRUE)
  }
})

#' @export
S_test <- compiler::cmpfun(function(k,return_result = FALSE){
  X_squared <- all_combinations(k)
  S_X <- X_squared[, 2:1]
  #here, you have to change S_X to define S
  S_X[, 2] <- up_action(X_squared[, 1], S_X[, 1], k)
  X_squared[, 2] <- down_action(S_X[, 1], X_squared[, 1], k)
  
  
  #then, check that permutations hold:
  permutations_S <- check_permutations(S_X)
  permutations_f <- check_f(S_X, k, X_squared)
  permutations_g <- check_f(X_squared, k, S_X) #ignore if not a biquandle!
  
  #and check that Yang-Baxter holds, based on S and f operation
  Yang_Baxter <- check_YB(S_X,k,X_squared)
  
  if(return_result){
    result <- c(permutations_S,permutations_f,permutations_g,Yang_Baxter)
    names(result) <- c("S permutation","f permutation", "g permutation", "Yang-Baxter")
    return(result)
  } else{
    print(paste0("The permutation checks hold that S is ", permutations_S, ", f is ",permutations_f," and g is ", permutations_g, " and that the Yang-Baxter check holds ", Yang_Baxter, "."))
  }
})