(in-package :5am-division)

(let* ((f (string->poly "x^2" '(x y)))
       (y-sq (string->poly "y^2" '(x y)))
       (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
       (quotients (cdr (string->poly "[x-y,0]" '(x y))))
       (one (make-instance 'rational-field :value 1)))
  (assert (universal-equalp (multiple-value-list (normal-form f fl)) (list y-sq one 2)))
  (assert (universal-equalp (multiple-value-list (poly-pseudo-divide f fl)) (list quotients y-sq one 2)))
  ;;(assert (buchberger-criterion fl))
  )