Sorry for wrong language, I saw a challenge and took it. Here is the code converted back to factor, and much easier to read than the original IMO. (Concatenative programming is hard to read).

:: (basis) ( dim n -- v )
   [ 1 ]
   n
   dim [ 0 ] replicate
   [ set-nth ] keep ;

:: (bases) ( dim -- {v} )
   dim iota
   [ dim basis ] map ;

:: (grad) ( quot: ( loc -- field ) step loc -- v )
   loc length (bases)
   [ step v*n ] map
   [ loc v+ ] map
   quot
   loc quot -
   step / ;

:: grad ( quot: ( loc -- field ) loc -- v ) quot 0.01 loc (grad) ;