(uiop:define-package :st-buchberger/src/ideal
 (:mix :cl)
 (:mix-reexport :st-buchberger/src/groebner)
 (:export #:ideal #:make-ideal #:basis #:member-p))

(in-package #:st-buchberger/src/ideal)

(defclass ideal ()
  ((ring
    :initarg :ring
    :initform (error "You must specify a ring for the polynomial ideal.")
    :accessor ring)
   (generators
    :initarg :generators
    :initform (error "You must provide a set of generators for the ideal.")
    :accessor generators)
   (cached-basis)))

(defun make-ideal (&rest generators)
  "Create a new ideal generated by the elements contained in the
GENERATORS list."
  (when generators
    (let* ((g (first generators))
           (base-ring (base-ring g)))
      (unless (every (lambda (x) (eq x base-ring))
                     (mapcar #'base-ring (rest generators)))
        (error "Every generator must belong to the same ring."))
      (make-instance 'ideal
                     :ring base-ring
                     :generators (make-array (length generators)
                                             :element-type (class-of g)
                                             :initial-contents generators)))))

(defmethod print-object ((ideal ideal) stream)
  (print-unreadable-object (ideal stream :type t)
    (format stream "~@{~S ~S~^ ~}"
            :ring (slot-value ideal 'ring)
            :generators (slot-value ideal 'generators))))

(defgeneric basis (ideal)
  (:documentation "Returns an array of generators for `ideal'."))

(defmethod basis ((ideal ideal))
  (with-slots (cached-basis) ideal
    (setf cached-basis (reduced-groebner (generators ideal)))
    cached-basis))

(defgeneric member-p (element ideal))

(defmethod member-p ((element ring-element) (ideal ideal))
  (with-slots (generators cached-basis) ideal
    (unless (and (slot-boundp ideal 'cached-basis) cached-basis)
      (setf cached-basis (basis ideal)))
    (ring-zero-p (ring-mod element cached-basis))))