[1] | 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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