| 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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| 34 | (defpackage "RING"
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| 35 | (:use :cl)
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| 36 | (:export "RING"
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| 37 | "RING-PARSE"
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| 38 | "RING-UNIT"
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| 39 | "RING-ZEROP"
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| 40 | "RING-ADD"
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| 41 | "RING-SUB"
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| 42 | "RING-UMINUS"
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| 43 | "RING-MUL"
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| 44 | "RING-DIV"
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| 45 | "RING-LCM"
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| 46 | "RING-EZGCD"
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| 47 | "RING-GCD"
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| 48 | "MAKE-RING"
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| 49 | "*RING-OF-INTEGERS*"
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| 50 | "*EXPRESSION-RING*"
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| 51 | ))
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| 52 |
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| 53 | (in-package :ring)
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| 54 |
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| 55 | (defstruct (ring)
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| 56 | "Defines a RING structure, whose fields
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| 57 | are common ring operations necessary to implement
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| 58 | Groebner bases."
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| 59 | (parse #'identity :type function)
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| 60 | (unit #'identity :type function)
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| 61 | (zerop #'identity :type function)
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| 62 | (add #'identity :type function)
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| 63 | (sub #'identity :type function)
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| 64 | (uminus #'identity :type function)
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| 65 | (mul #'identity :type function)
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| 66 | (div #'identity :type function)
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| 67 | (lcm #'identity :type function)
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| 68 | (ezgcd #'identity :type function)
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| 69 | (gcd #'identity :type function))
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| 70 |
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| 71 | (defparameter *ring-of-integers*
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| 72 | (make-ring
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| 73 | :parse #'identity
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| 74 | :unit #'(lambda () 1)
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| 75 | :zerop #'zerop
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| 76 | :add #'+
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| 77 | :sub #'-
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| 78 | :uminus #'-
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| 79 | :mul #'*
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| 80 | :div #'/
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| 81 | :lcm #'lcm
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| 82 | :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
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| 83 | :gcd #'gcd
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| 84 | )
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| 85 | "The ring of integers.")
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