;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- 
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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>		 
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(in-package :grobner)

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;;
;; Order making functions
;;
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(defvar *monomial-order* #'lex>
  "Default order for monomial comparisons")

(defmacro monomial-order (x y)
  `(funcall *monomial-order* ,x ,y))

(defun reverse-monomial-order (x y)
  (monomial-order y x))

(defvar *primary-elimination-order* #'lex>)

(defvar *secondary-elimination-order* #'lex>)

(defvar *elimination-order* nil
  "Default elimination order used in elimination-based functions.
If not NIL, it is assumed to be a proper elimination order. If NIL,
we will construct an elimination order using the values of
*PRIMARY-ELIMINATION-ORDER* and *SECONDARY-ELIMINATION-ORDER*.")

(defun elimination-order (k)
  "Return a predicate which compares monomials according to the
K-th elimination order. Two variables *PRIMARY-ELIMINATION-ORDER*
and *SECONDARY-ELIMINATION-ORDER* control the behavior on the first K
and the remaining variables, respectively."
  (declare (type fixnum k))
  #'(lambda (p q &optional (start 0) (end (monom-dimension  p)))
      (declare (type monom p q) (type fixnum start end))
      (multiple-value-bind (primary equal)
	   (funcall *primary-elimination-order* p q start k)
	 (if equal
	     (funcall *secondary-elimination-order* p q k end)
	   (values primary nil)))))

(defun elimination-order-1 (p q &optional (start 0) (end (monom-dimension  p)))
  "Equivalent to the function returned by the call to (ELIMINATION-ORDER 1)."
  (declare (type monom p q) (type fixnum start end))
  (cond
   ((> (monom-elt p start) (monom-elt q start)) (values t nil))
   ((< (monom-elt p start) (monom-elt q start)) (values nil nil))
   (t (funcall *secondary-elimination-order* p q (1+ start) end))))