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