Multi variate Taylor Expansion

taylor-expansion.egi

(define $∇
  (lambda [$f $xs]
    (generate-tensor
      1#(∂/∂ f (nth %1 xs))
      {(length xs)})))

(define $nabla ∇)

(define $taylor-expansion2
  (lambda [$f $xs $as]
    (map2 *
          (map 1#(/ 1 (fact %1)) nats0)
;          (map (substitute (zip xs as) $) 
               (iterate (Op.* (∇ $ xs) (V.* (generate-tensor 1#h_%1 {(length xs)}) $)) f))))

(define $taylor-expansion3
  (lambda [$f $xs $as]
    (iterate (Op.* (∇ $ xs) (V.* (generate-tensor 1#h_%1 {(length xs)}) $)) f)))

(define $Op.* compose)