1 | #|
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2 | $Id: monom.lisp,v 1.3 2009/01/22 04:04:31 marek Exp $
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3 | *--------------------------------------------------------------------------*
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4 | | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@math.arizona.edu) |
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5 | | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
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6 | | |
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7 | | Everyone is permitted to copy, distribute and modify the code in this |
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8 | | directory, as long as this copyright note is preserved verbatim. |
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9 | *--------------------------------------------------------------------------*
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10 | |#
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11 | (defpackage "MONOM"
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12 | (:use "COMMON-LISP")
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13 | (:export monom-equal monom-divides-p monom-divisible-by-p monom-rel-prime
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14 | monom* nmonom* monom/
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15 | monom-lcm monom-gcd))
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16 |
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17 | (in-package "MONOM")
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18 |
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19 | #+debug(proclaim '(optimize (speed 0) (debug 3)))
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20 | #-debug(proclaim '(optimize (speed 3) (debug 0)))
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21 |
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22 | ;;----------------------------------------------------------------
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23 | ;; This package implements BASIC OPERATIONS ON MONOMIALS
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24 | ;;----------------------------------------------------------------
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25 | ;; DATA STRUCTURES: Monomials are represented as lists:
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26 | ;;
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27 | ;; monom: (n1 n2 ... nk) where ni are non-negative integers
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28 | ;;
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29 | ;;----------------------------------------------------------------
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30 | ;; EXAMPLES: Suppose that variables are x and y. Then
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31 | ;;
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32 | ;; Monom x*y^2 ---> (1 2)
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33 | ;;
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34 | ;;----------------------------------------------------------------
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35 |
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36 | (defun monom/ (m1 m2)
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37 | "Divide monomial M1 by monomial M2."
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38 | (mapcar #'- m1 m2))
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39 |
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40 | (defun monom* (m1 m2)
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41 | "Multiply monomial M1 by monomial M2."
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42 | (mapcar #'+ m1 m2))
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43 |
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44 | (defun nmonom* (m1 m2)
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45 | "Multiply monomials M1 and M2 - destructive version.
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46 | M1 is destructively modified, M2 is not modified."
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47 | (mapl #'(lambda (x y) (incf (car x) (car y))) m1 m2))
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48 |
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49 | (defun monom-divides-p (m1 m2)
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50 | "Returns T if monomial M1 divides monomial M2, NIL otherwise."
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51 | (every #'<= m1 m2))
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52 |
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53 | (defun monom-divisible-by-p (m1 m2)
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54 | "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
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55 | (every #'>= m1 m2))
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56 |
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57 | (defun monom-rel-prime (m1 m2)
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58 | "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
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59 | (every #'(lambda (x y) (zerop (min x y))) m1 m2))
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60 |
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61 | (defun monom-equal (m1 m2)
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62 | "Returns T if two monomials M1 and M2 are equal."
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63 | (every #'= m1 m2))
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64 |
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65 | (defun monom-lcm (m1 m2)
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66 | "Returns least common multiple of monomials M1 and M2."
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67 | (mapcar #'max m1 m2))
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68 |
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69 | (defun monom-gcd (m1 m2)
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70 | "Returns greatest common divisor of monomials M1 and M2."
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71 | (mapcar #'min m1 m2))
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