source: branches/f4grobner/monomial.lisp@ 459

;;; -*-  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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;;;  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        

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;;;  GNU General Public License for more details.                                

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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-DIVISIBLE-BY-P"

           "MONOM-REL-PRIME-P"

           "MONOM-EQUAL-P"

           "MONOM-LCM"

           "MONOM-GCD"

           "MONOM-MAP"

           "MONOM-APPEND"

           "MONOM-CONTRACT"

           "MONOM-EXPONENTS"))



(in-package :monomial)



(deftype exponent ()

  "Type of exponent in a monomial."

  'fixnum)



(deftype monom (&optional dim)

  "Type of monomial."

  `(simple-array exponent (,dim)))



;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;

;; Construction of monomials

;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;



(defmacro make-monom (dim &key (initial-contents nil initial-contents-supplied-p)

                               (initial-element 0 initial-element-supplied-p))

  "Make a monomial with DIM variables. Additional argument

INITIAL-CONTENTS specifies the list of powers of the consecutive

variables. The alternative additional argument INITIAL-ELEMENT

specifies the common power for all variables."

  ;;(declare (fixnum dim))

  `(make-array ,dim

               :element-type 'exponent

               ,@(when initial-contents-supplied-p `(:initial-contents ,initial-contents))

               ,@(when initial-element-supplied-p `(:initial-element ,initial-element))))





;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;

;; Operations on monomials

;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;



(defmacro monom-elt (m index)

  "Return the power in the monomial M of variable number INDEX."

  `(elt ,m ,index))



(defun monom-dimension (m)

  "Return the number of variables in the monomial M."

  (length m))



(defun monom-total-degree (m &optional (start 0) (end (length 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 #'+ m :start start :end end))



(defun monom-sugar (m &aux (start 0) (end (length 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-seq m1)))

  "Divide monomial M1 by monomial M2."

  (declare (type monom m1 m2 result))

  (map-into result #'- m1 m2))



(defun monom-mul (m1 m2  &aux (result (copy-seq m1)))

  "Multiply monomial M1 by monomial M2."

  (declare (type monom m1 m2 result))

  (map-into result #'+ m1 m2))



(defun monom-divides-p (m1 m2)

  "Returns T if monomial M1 divides monomial M2, NIL otherwise."

  (declare (type monom m1 m2))

  (every #'<= m1 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))) m1 m2 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))) m1 m2 m3 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))) m1 m2 m3 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 #'>= m1 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))) m1 m2))



(defun monom-equal-p (m1 m2)

  "Returns T if two monomials M1 and M2 are equal."

  (declare (type monom m1 m2))

  (every #'= m1 m2))



(defun monom-lcm (m1 m2 &aux (result (copy-seq m1)))

  "Returns least common multiple of monomials M1 and M2."

  (declare (type monom m1 m2))

  (map-into result #'max m1 m2))



(defun monom-gcd (m1 m2 &aux (result (copy-seq m1)))

  "Returns greatest common divisor of monomials M1 and M2."

  (declare (type monom m1 m2))

  (map-into result #'min m1 m2))



(defun monom-depends-p (m k)

  "Return T if the monomial M depends on variable number K."

  (declare (type monom m) (fixnum k))

  (plusp (elt m k)))



(defmacro monom-map (fun m &rest ml &aux (result `(copy-seq ,m)))

  `(map-into ,result ,fun ,m ,@ml))



(defmacro monom-append (m1 m2)

  `(concatenate 'monom ,m1 ,m2))



(defmacro monom-contract (k m)

  `(subseq ,m ,k))



(defun monom-exponents (m)

  (declare (type monom m))

  (coerce m 'list))