;;; -*-  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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;;
;; Implementations of various admissible monomial orders
;;
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(defpackage "ORDER"
  (:use :cl :monomial)
  (:export "LEX>"
	   "GRLEX>"
	   "REVLEX>"
	   "GREVLEX>"
	   "INVLEX>"
	   "MONOMIAL-ORDER"
	   "*MONOMIAL-ORDER*"
	   "REVERSE-MONOMIAL-ORDER"
	   "*PRIMARY-ELIMINATION-ORDER*"
	   "*SECONDARY-ELIMINATION-ORDER*"
	   "*ELIMINATION-ORDER*"
	   "ELIMINATION-ORDER"
	   "ELIMINATION-ORDER-1"))

(in-package :order)

;; pure lexicographic
(defun lex> (p q &optional (start 0) (end (monom-dimension  p)))
  "Return T if P>Q with respect to lexicographic order, otherwise NIL.
The second returned value is T if P=Q, otherwise it is NIL."
  (do ((i start (1+ i)))
      ((>= i end) (values nil t))
    (cond
     ((> (monom-elt p i) (monom-elt q i))
      (return-from lex> (values t nil)))
     ((< (monom-elt p i) (monom-elt q i))
      (return-from lex> (values nil nil))))))

;; total degree order , ties broken by lexicographic
(defun grlex> (p q &optional (start 0) (end (monom-dimension  p)))
  "Return T if P>Q with respect to graded lexicographic order, otherwise NIL.
The second returned value is T if P=Q, otherwise it is NIL."
  (let ((d1 (monom-total-degree p start end))
	(d2 (monom-total-degree q start end)))
    (cond
      ((> d1 d2) (values t nil))
      ((< d1 d2) (values nil nil))
      (t
	(lex> p q start end)))))


;; reverse lexicographic
(defun revlex> (p q &optional (start 0) (end (monom-dimension  p)))
  "Return T if P>Q with respect to reverse lexicographic order, NIL
otherwise.  The second returned value is T if P=Q, otherwise it is
NIL. This is not and admissible monomial order because some sets do
not have a minimal element. This order is useful in constructing other
orders."
  (do ((i (1- end) (1- i)))
      ((< i start) (values nil t))
    (cond
     ((< (monom-elt p i) (monom-elt q i))
      (return-from revlex> (values t nil)))
     ((> (monom-elt p i) (monom-elt q i))
      (return-from revlex> (values nil nil))))))


;; total degree, ties broken by reverse lexicographic
(defun grevlex> (p q &optional (start 0) (end (monom-dimension  p)))
  "Return T if P>Q with respect to graded reverse lexicographic order,
NIL otherwise. The second returned value is T if P=Q, otherwise it is NIL."
  (let ((d1 (monom-total-degree p start end))
	(d2 (monom-total-degree q start end)))
    (cond
     ((> d1 d2) (values t nil))
     ((< d1 d2) (values nil nil))
     (t
      (revlex> p q start end)))))

(defun invlex> (p q &optional (start 0) (end (monom-dimension  p)))
  "Return T if P>Q with respect to inverse lexicographic order, NIL otherwise
The second returned value is T if P=Q, otherwise it is NIL."
  (do ((i (1- end) (1- i)))
      ((< i start) (values nil t))
      (cond
	 ((> (monom-elt p i) (monom-elt q i))
	  (return-from invlex> (values t nil)))
	 ((< (monom-elt p i) (monom-elt q i))
	  (return-from invlex> (values nil nil))))))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; Some globally-defined variables holding monomial orders
;; and related macros/functions.
;;
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(defvar *monomial-order* #'lex>
  "Default order for monomial comparisons. This global variable holds
the order which is in effect when performing polynomial
arithmetic. The global order is called by the macro MONOMIAL-ORDER,
which is somewhat more elegant than FUNCALL.")

(defun monomial-order (x y)
  "Calls the global monomial order function, held by *MONOMIAL-ORDER*."
  (funcall *monomial-order* x y))

(defun reverse-monomial-order (x y)
  "Calls the inverse monomial order to the global monomial order function,
held by *MONOMIAL-ORDER*."
  (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*.")

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;;
;; Order making functions
;;
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(defun elimination-order (primary-elimination-order secondary-elimination-order k)
  "Return a predicate which compares monomials according to the
K-th elimination order. The monomial orders PRIMARY-ELIMINATION-ORDER
and SECONDARY-ELIMINATION-ORDER control the behavior on the first K
and the remaining variables, respectively."
  #'(lambda (p q &optional (start 0) (end (monom-dimension  p)))
      (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 (secondary-elimination-order q &optional (start 0) (end (monom-dimension  p)))
  "Equivalent to the function returned by the call to (ELIMINATION-ORDER NIL SECONDARY-ELIMINATION-ORDER 1)."
  (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))))