source: branches/f4grobner/monomial.lisp@ 867

;;; -*-  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>          
;;;                                                                              
;;;  This program is free software; you can redistribute it and/or modify        
;;;  it under the terms of the GNU General Public License as published by        
;;;  the Free Software Foundation; either version 2 of the License, or           
;;;  (at your option) any later version.                                         
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;;;  This program is distributed in the hope that it will be useful,             
;;;  but WITHOUT ANY WARRANTY; without even the implied warranty of              
;;;  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               
;;;  GNU General Public License for more details.                                
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;;;  You should have received a copy of the GNU General Public License           
;;;  along with this program; if not, write to the Free Software                 
;;;  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  
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;;----------------------------------------------------------------
;; This package implements BASIC OPERATIONS ON MONOMIALS
;;----------------------------------------------------------------
;; DATA STRUCTURES: Conceptually, monomials can be represented as lists:
;;
;;      monom:  (n1 n2 ... nk) where ni are non-negative integers
;;
;; However, lists may be implemented as other sequence types,
;; so the flexibility to change the representation should be
;; maintained in the code to use general operations on sequences
;; whenever possible. The optimization for the actual representation
;; should be left to declarations and the compiler.
;;----------------------------------------------------------------
;; EXAMPLES: Suppose that variables are x and y. Then
;;
;;      Monom x*y^2 ---> (1 2)
;;
;;----------------------------------------------------------------

(defpackage "MONOMIAL"
  (:use :cl)
  (:export "MONOM"
           "EXPONENT"
           "MAKE-MONOM" 
           "MONOM-ELT" 
           "MONOM-DIMENSION" 
           "MONOM-TOTAL-DEGREE"
           "MONOM-SUGAR" 
           "MONOM-DIV"
           "MONOM-MUL" 
           "MONOM-DIVIDES-P"
           "MONOM-DIVIDES-MONOM-LCM-P"
           "MONOM-LCM-DIVIDES-MONOM-LCM-P"
           "MONOM-LCM-EQUAL-MONOM-LCM-P"
           "MONOM-DIVISIBLE-BY-P"
           "MONOM-REL-PRIME-P"
           "MONOM-EQUAL-P"
           "MONOM-LCM"
           "MONOM-GCD"
           "MONOM-DEPENDS-P"
           "MONOM-MAP"
           "MONOM-APPEND"
           "MONOM-CONTRACT"
           "MONOM-EXPONENTS"))

(in-package :monomial)

(deftype exponent ()
  "Type of exponent in a monomial."
  'fixnum)

(defstruct (monom
             ;; BOA constructor
             ;; NOTE: having a non-default constructor inhibits reading via #S(...)
             (:constructor make-monom (&key 
                                       (dimension nil dimension-suppied-p)
                                       (initial-exponents nil initial-exponents-supplied-p)
                                       (initial-exponent  nil initial-exponent-supplied-p)
                                       &aux
                                       (dim (cond (dimension-suppied-p dimension)
                                                  (initial-exponents-supplied-p (length initial-exponents))
                                                  (t (error "You must provide DIMENSION nor INITIAL-EXPONENTS"))))
                                       (exponents (cond 
                                                    ;; when exponents are supplied
                                                    (initial-exponents-supplied-p
                                                     (make-array (list dim) :initial-contents initial-exponents
                                                                 :element-type 'exponent))
                                                    ;; when all exponents are to be identical
                                                    (initial-exponent-supplied-p
                                                     (make-array (list dim) :initial-element initial-exponent
                                                                 :element-type 'exponent))
                                                    ;; otherwise, all exponents are zero
                                                    (t 
                                                     (make-array (list dim) :element-type 'exponent :initial-element 0))))))
             )
  (exponents nil :type (vector exponent *)))


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; Operations on monomials
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defun monom-dimension (m)
  (declare (type monom m))
  (length (monom-exponents m)))

(defmacro monom-elt (m index)
  "Return the power in the monomial M of variable number INDEX."
  `(elt (monom-exponents ,m) ,index))

(defun monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
  "Return the todal degree of a monomoal M. Optinally, a range
of variables may be specified with arguments START and END."
  (declare (type monom m) (fixnum start end))
  (reduce #'+ (monom-exponents m) :start start :end end))

(defun monom-sugar (m &aux (start 0) (end (monom-dimension m)))
  "Return the sugar of a monomial M. Optinally, a range
of variables may be specified with arguments START and END."
  (declare (type monom m) (fixnum start end))
  (monom-total-degree m start end))

(defun monom-div (m1 m2 &aux (result (copy-structure m1)))
  "Divide monomial M1 by monomial M2."
  (declare (type monom m1 m2))
  (map-into (monom-exponents result) #'- (monom-exponents m1) (monom-exponents m2))
  result)

(defun monom-mul (m1 m2  &aux (result (copy-structure m1)))
  "Multiply monomial M1 by monomial M2."
  (declare (type monom m1 m2 result))
  (map-into (monom-exponents result) #'+ (monom-exponents m1) (monom-exponents m2))
  result)

(defun monom-divides-p (m1 m2)
  "Returns T if monomial M1 divides monomial M2, NIL otherwise."
  (declare (type monom m1 m2))
  (every #'<= (monom-exponents m1) (monom-exponents m2)))

(defun monom-divides-monom-lcm-p (m1 m2 m3)
  "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
  (declare (type monom m1 m2 m3))
  (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z))) 
         (monom-exponents m1)
         (monom-exponents m2)
         (monom-exponents m3)))

(defun monom-lcm-divides-monom-lcm-p (m1 m2 m3 m4)
  "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
  (declare (type monom m1 m2 m3 m4))
  (every #'(lambda (x y z w) (declare (type exponent x y z w)) (<= (max x y) (max z w))) 
         (monom-exponents m1)
         (monom-exponents m2)
         (monom-exponents m3)
         (monom-exponents m4)))

(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
  "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
  (declare (type monom m1 m2 m3 m4))
  (every #'(lambda (x y z w) (declare (type exponent x y z w)) (= (max x y) (max z w)))
         (monom-exponents m1)
         (monom-exponents m2)
         (monom-exponents m3)
         (monom-exponents m4)))

(defun monom-divisible-by-p (m1 m2)
  "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
  (declare (type monom m1 m2))
   (every #'>= (monom-exponents m1) (monom-exponents m2)))

(defun monom-rel-prime-p (m1 m2)
  "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
  (declare (type monom m1 m2))
  (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y))) 
         (monom-exponents m1)
         (monom-exponents m2)))

(defun monom-equal-p (m1 m2)
  "Returns T if two monomials M1 and M2 are equal."
  (declare (type monom m1 m2))
  (every #'= (monom-exponents m1) (monom-exponents m2)))

(defun monom-lcm (m1 m2 &aux (result (copy-structure m1)))
  "Returns least common multiple of monomials M1 and M2."
  (declare (type monom m1 m2))
  (map-into (monom-exponents result) #'max 
            (monom-exponents m1)
            (monom-exponents m2))
  result)

(defun monom-gcd (m1 m2 &aux (result (copy-structure m1)))
  "Returns greatest common divisor of monomials M1 and M2."
  (declare (type monom m1 m2))
  (map-into (monom-exponents result) #'min (monom-exponents m1) (monom-exponents m2))
  result)

(defun monom-depends-p (m k)
  "Return T if the monomial M depends on variable number K."
  (declare (type monom m) (fixnum k))
  (plusp (monom-elt m k)))

(defmacro monom-map (fun m &rest ml &aux (result `(copy-structure ,m)))
  `(map-into (monom-exponents ,result) ,fun (monom-exponents ,m) ,@ml))

(defmacro monom-append (m1 m2)
  `(make-monom :exponents (concatenate 'vector (monom-exponents ,m1) (monom-exponents ,m2))))

(defmacro monom-contract (k m)
  `(setf (monom-exponents ,m) (subseq (monom-exponents ,m) ,k)))