;;poly_grobner([x^3-x^2+2,y-2*x^2+1,z-3*x+5],[x,y,z]);
;;[x^3-x^2+2,y-2*x^2+1,z-3*x+5,2*z^2+20*z-9*y+41,(-z^3)-12*z^2-45*z-104]

(in-package :5am-buchberger)


(setf fl (cdr (string->poly "[x^3-x^2+2,y-2*x^2+1,z-3*x+5]" '(x y z)))
      ref-gb (cdr (string->poly "[x^3-x^2+2,y-2*x^2+1,z-3*x+5,2*z^2+20*z-9*y+41,(-z^3)-12*z^2-45*z-104]" '(x y z))))

(format t "~S~%" (poly->string (cons :[ fl)))
(format t "~S~%" (poly->string (cons :[ ref-gb)))

(setf sp-0-1 (s-polynomial (elt fl 0) (elt fl 1)))
(format t "~S~%" (poly->string sp-0-1))

(setf sp-0-2 (s-polynomial (elt fl 0) (elt fl 2)))
(format t "~S~%" (poly->string sp-0-2))

(setf sp-1-2 (s-polynomial (elt fl 1) (elt fl 2)))
(format t "~S~%" (poly->string sp-1-2))

(setf grobner-debug::$poly_grobner_debug t)
;;(setf gb (buchberger fl))