library(stringr)

basisify <- function(v){
  terms <- character(0)
  for(i in seq_along(v)){
    if(v[i]!=0){
      terms <- c(terms, str_glue("{v[i]}*e({i})"))
    }
  }
  if(length(terms)==0) return("0")
  terms <- str_replace_all(terms, fixed("1*"), "")
  series <- str_flatten(terms, collapse=" + ")
  str_replace_all(series, fixed("+ -"), "- ")
}

test_vectors <- list(c(1, 2, 3),
                     c(0, 1, 2, 3),
                     c(1, 0, 3, 4),
                     c(1, 2, 0),
                     c(0, 0, 0),
                     0,
                     c(1, 1, 1),
                     c(-1, -1, -1),
                     c(-1, -2, 0, -3),
                     -1)

writeLines(sapply(test_vectors, basisify))