| [404] | 1 | ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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| 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 3 | ;;;
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| 4 | ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
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| 5 | ;;;
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| 6 | ;;; This program is free software; you can redistribute it and/or modify
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| 7 | ;;; it under the terms of the GNU General Public License as published by
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| 8 | ;;; the Free Software Foundation; either version 2 of the License, or
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| 9 | ;;; (at your option) any later version.
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| 10 | ;;;
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| 11 | ;;; This program is distributed in the hope that it will be useful,
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| 12 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | ;;; GNU General Public License for more details.
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| 15 | ;;;
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| 16 | ;;; You should have received a copy of the GNU General Public License
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| 17 | ;;; along with this program; if not, write to the Free Software
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| 18 | ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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| 19 | ;;;
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| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 21 |
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| 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 23 | ;;
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| 24 | ;; Coefficient ring operations
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| 25 | ;;
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| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 27 | ;;
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| 28 | ;; These are ALL operations that are performed on the coefficients by
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| 29 | ;; the package, and thus the coefficient ring can be changed by merely
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| 30 | ;; redefining these operations.
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| 31 | ;;
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| 32 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 33 |
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| [405] | 34 | (defpackage "RING"
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| 35 | (:use :cl)
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| 36 | (:export "MAKE-RING"
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| 37 | "*RING-OF-INTEGERS*"
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| [406] | 38 | "*EXPRESSION-RING*"
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| [405] | 39 | ))
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| 40 |
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| [404] | 41 | (defstruct (ring)
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| [407] | 42 | "Defines a RING structure, whose fields
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| 43 | are common ring operations necessary to implement
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| 44 | Groebner bases."
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| [404] | 45 | (parse #'identity :type function)
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| 46 | (unit #'identity :type function)
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| 47 | (zerop #'identity :type function)
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| 48 | (add #'identity :type function)
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| 49 | (sub #'identity :type function)
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| 50 | (uminus #'identity :type function)
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| 51 | (mul #'identity :type function)
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| 52 | (div #'identity :type function)
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| 53 | (lcm #'identity :type function)
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| 54 | (ezgcd #'identity :type function)
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| 55 | (gcd #'identity :type function))
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| 56 |
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| 57 | (defparameter *ring-of-integers*
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| [408] | 58 | "Defines the ring of integers, which is an instance of RING structure."
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| [404] | 59 | (make-ring
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| 60 | :parse #'identity
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| 61 | :unit #'(lambda () 1)
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| 62 | :zerop #'zerop
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| 63 | :add #'+
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| 64 | :sub #'-
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| 65 | :uminus #'-
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| 66 | :mul #'*
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| 67 | :div #'/
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| 68 | :lcm #'lcm
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| 69 | :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
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| 70 | :gcd #'gcd)
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| 71 | "The ring of integers.")
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| 72 |
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| 73 | (defvar *expression-ring* *ring-of-integers*
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| 74 | "The ring of coefficients, over which all polynomials are assumed to
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| 75 | be defined.")
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