source: branches/f4grobner/monom.lisp@ 2472

;;; -*-  Mode: Lisp -*- 
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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.                                         
;;;                                                                              
;;;  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 "MONOM"
  (:use :cl :ring)
  (:export "MONOM"
           "EXPONENT"
           "MAKE-MONOM-VARIABLE"))

(in-package :monom)

(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))

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

(defclass monom ()
  ((dimension          :initarg :dimension :accessor r-dimension)
   (exponents :initarg :exponents :accessor r-exponents))
  (:default-initargs :dimension nil :exponents nil :exponent nil))

(defmethod print-object ((self monom) stream)
  (format stream "#<MONOM DIMENSION=~A EXPONENTS=~A>"
          (r-dimension self)
          (r-exponents self)))

(defmethod shared-initialize :after ((self monom) slot-names
                                     &key 
                                       dimension
                                       exponents
                                       exponent
                                     &allow-other-keys
                                       )
  (if (eq slot-names t) (setf slot-names '(dimension exponents)))
  (dolist (slot-name slot-names)
    (case slot-name
      (dimension 
       (cond (dimension 
              (setf (slot-value self 'dimension) dimension))
             (exponents
              (setf (slot-value self 'dimension) (length exponents)))
             (t 
              (error "DIMENSION or EXPONENTS must not be NIL"))))
      (exponents  
       (cond 
         ;; when exponents are supplied
         (exponents
          (let ((dim (length exponents)))
            (when (and dimension (/= dimension dim))
              (error "EXPONENTS must have length DIMENSION")) 
            (setf (slot-value self 'dimension) dim
                  (slot-value self 'exponents) (make-array dim :initial-contents exponents))))
         ;; when all exponents are to be identical
         (t
          (let ((dim (slot-value self 'dimension)))
            (setf (slot-value self 'exponents)
                  (make-array (list dim) :initial-element (or exponent 0)
                              :element-type 'exponent)))))))))

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

(defmethod r-coeff ((m monom))
  "A MONOM can be treated as a special case of TERM,
where the coefficient is 1."
  1)
  
(defmethod r-elt ((m monom) index)
  "Return the power in the monomial M of variable number INDEX."
  (with-slots (exponents)
      m
    (elt exponents index)))

(defmethod (setf r-elt) (new-value (m monom) index)
  "Return the power in the monomial M of variable number INDEX."
  (with-slots (exponents)
      m
    (setf (elt exponents index) new-value)))

(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-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 fixnum start end))
  (with-slots (exponents)
      m
    (reduce #'+ exponents :start start :end end)))


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

(defmethod r* ((m1 monom) (m2 monom))
  "Multiply monomial M1 by monomial M2."
  (with-slots ((exponents1 exponents) dimension)
      m1
    (with-slots ((exponents2 exponents))
        m2
      (let* ((exponents (copy-seq exponents1)))
        (map-into exponents #'+ exponents1 exponents2)
        (make-instance 'monom :dimension dimension :exponents exponents)))))


(defmethod r/ ((m1 monom) (m2 monom))
  "Divide monomial M1 by monomial M2."
  (with-slots ((exponents1 exponents) (dimension1 dimension))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (let* ((exponents (copy-seq exponents1))
             (dimension dimension1))
        (map-into exponents #'- exponents1 exponents2)
        (make-instance 'monom :dimension dimension :exponents exponents)))))

(defmethod r-divides-p ((m1 monom) (m2 monom))
  "Returns T if monomial M1 divides monomial M2, NIL otherwise."
  (with-slots ((exponents1 exponents))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (every #'<= exponents1 exponents2))))


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


(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
  "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) (<= (max x y) (max z w))) 
         m1 m2 m3 m4))
         
(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
  "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
  (with-slots ((exponents1 exponents))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (with-slots ((exponents3 exponents))
          m3
        (with-slots ((exponents4 exponents))
            m4
          (every 
           #'(lambda (x y z w) (= (max x y) (max z w)))
           exponents1 exponents2 exponents3 exponents4))))))

(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
  "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
  (with-slots ((exponents1 exponents))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (every #'>= exponents1 exponents2))))

(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
  "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
  (with-slots ((exponents1 exponents))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))


(defmethod r-equalp ((m1 monom) (m2 monom))
  "Returns T if two monomials M1 and M2 are equal."
  (with-slots ((exponents1 exponents))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (every #'= exponents1 exponents2))))

(defmethod r-lcm ((m1 monom) (m2 monom)) 
  "Returns least common multiple of monomials M1 and M2."
  (with-slots ((exponents1 exponents) (dimension1 dimension))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (let* ((exponents (copy-seq exponents1))
             (dimension dimension1))
        (map-into exponents #'max exponents1 exponents2)
        (make-instance 'monom :dimension dimension :exponents exponents)))))


(defmethod r-gcd ((m1 monom) (m2 monom))
  "Returns greatest common divisor of monomials M1 and M2."
  (with-slots ((exponents1 exponents) (dimension1 dimension))
      m1
    (with-slots ((exponents2 exponents))
        m2
      (let* ((exponents (copy-seq exponents1))
             (dimension dimension1))
        (map-into exponents #'min exponents1 exponents2)
        (make-instance 'monom :dimension dimension :exponents exponents)))))

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

(defmethod r-tensor-product ((m1 monom) (m2 monom))
  (with-slots ((exponents1 exponents) (dimension1 dimension))
      m1
    (with-slots ((exponents2 exponents) (dimension2 dimension))
        m2
      (make-instance 'monom 
                     :dimension (+ dimension1 dimension2)
                     :exponents (concatenate 'vector exponents1 exponents2)))))

(defmethod r-contract ((m monom) k)
  "Drop the first K variables in monomial M."
  (declare (fixnum k))
  (with-slots (dimension exponents) 
      m
    (setf dimension (- dimension k)
          exponents (subseq exponents k))))

(defun make-monom-variable (nvars pos &optional (power 1)
                            &aux (m (make-instance 'monom :dimension nvars)))
  "Construct a monomial in the polynomial ring
RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
which represents a single variable. It assumes number of variables
NVARS and the variable is at position POS. Optionally, the variable
may appear raised to power POWER. "
  (declare (type fixnum nvars pos power) (type monom m))
  (with-slots (exponents)
      m
    (setf (elt exponents pos) power)
    m))

(defmethod r->list ((m monom))
  "A human-readable representation of a monomial M as a list of exponents."  
  (coerce (r-exponents m) 'list))