1 | ;;; -*- Mode: Lisp -*-
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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 | (defpackage "RING"
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23 | (:use :cl :copy)
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24 | (:export "RING"
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25 | "ADD-TO"
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26 | "SUBTRACT-FROM"
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27 | "MULTIPLY-BY"
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28 | "DIVIDE-BY"
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29 | "UNARY-MINUS"
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30 | "UNARY-INVERSE"
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31 | "UNIVERSAL-GCD"
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32 | "UNIVERSAL-EZGCD"
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33 | "UNIVERSAL-EQUALP"
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34 | "UNIVERSAL-ZEROP"
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35 | "MAKE-ZERO-FOR"
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36 | "MAKE-UNIT-FOR"
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37 | "->SEXP"
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38 | "RATIONAL-FIELD"
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39 | "RATIONAL-FIELD-VALUE"
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40 | "MAKE-ZERO-FOR"
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41 | "MAKE-UNIT-FOR"
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42 | "INTEGER-RING"
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43 | "INTEGER-RING-VALUE"
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44 | )
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45 | (:documentation "Defines an abstract ring class and ring operations.")
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46 | )
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47 |
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48 | (in-package "RING")
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49 |
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50 | (defclass ring () () (:documentation "An abstract ring."))
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51 |
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52 | (defgeneric multiply-by (self other)
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53 | (:documentation "Multiply SELF by OTHER."))
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54 |
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55 | (defgeneric divide-by (self other)
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56 | (:documentation "Divide SELF by OTHER."))
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57 |
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58 | (defgeneric add-to (self other)
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59 | (:documentation "Add OTHER to SELF."))
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60 |
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61 | (defgeneric subtract-from (self other)
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62 | (:documentation "Subtract OTHER from SELF."))
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63 |
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64 | (defgeneric unary-minus (self)
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65 | (:documentation "Changes SELF to its negative."))
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66 |
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67 | (defgeneric unary-inverse (self)
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68 | (:documentation "Changes SELF to the unary inverse of SELF."))
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69 |
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70 | (defgeneric universal-gcd (object other)
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71 | (:documentation "Returns GCD(OBJECT, OTHER)"))
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72 |
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73 | (defgeneric universal-ezgcd (x y)
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74 | (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
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75 | C=GCD(X,Y). It returns three values: C, X1 and Y1. The result may be obtained by
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76 | the Euclidean algorithm."))
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77 |
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78 | (defgeneric universal-equalp (self other)
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79 | (:documentation "Return T if objects SELF and OTHER are equal, NIL otherwise.")
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80 | (:method ((object1 cons) (object2 cons)) (every #'universal-equalp object1 object2))
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81 | (:method ((self number) (other number)) (= self other)))
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82 |
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83 | (defgeneric universal-zerop (self)
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84 | (:documentation "Return T if SELF is a zero in the ring it belongs to."))
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85 |
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86 | (defgeneric ->sexp (self &optional vars)
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87 | (:documentation "Convert SELF to an S-expression."))
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88 |
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89 | (defgeneric make-zero-for (self)
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90 | (:documentation "Create a zero in the ring of SELF. A fresh instance
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91 | should be returned upon every call."))
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92 |
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93 | (defgeneric make-unit-for (self)
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94 | (:documentation "Create a unit in the ring of SELF. A fresh instance
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95 | should be returned upon every call."))
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