;;; -*- mode: lisp; package: maxima; syntax: common-lisp; base: 10 -*- ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; ;;; copyright (c) 1999, 2002, 2009, 2015 marek rychlik ;;; ;;; this program is free software; you can redistribute it and/or modify ;;; it under the terms of the gnu general public license as published by ;;; the free software foundation; either version 2 of the license, or ;;; (at your option) any later version. ;;; ;;; this program is distributed in the hope that it will be useful, ;;; but without any warranty; without even the implied warranty of ;;; merchantability or fitness for a particular purpose. see the ;;; gnu general public license for more details. ;;; ;;; you should have received a copy of the gnu general public license ;;; along with this program; if not, write to the free software ;;; foundation, inc., 59 temple place - suite 330, boston, ma 02111-1307, usa. ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ;; coefficient ring operations ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;; ;; these are all operations that are performed on the coefficients by ;; the package, and thus the coefficient ring can be changed by merely ;; redefining these operations. ;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; (defpackage "RING" (:use :cl) (:export "RING" "RING-PARSE" "RING-UNIT" "RING-ZEROP" "RING-ADD" "RING-SUB" "RING-UMINUS" "RING-MUL" "RING-DIV" "RING-LCM" "RING-EZGCD" "RING-GCD" "MAKE-RING" "+RING-OF-INTEGERS+" )) (in-package :ring) #| (defstruct (ring) "Defines a RING structure, whose fields are common ring operations necessary to implement Groebner bases." (parse #'identity :type function) (unit #'identity :type function) (zerop #'identity :type function) (add #'identity :type function) (sub #'identity :type function) (uminus #'identity :type function) (mul #'identity :type function) (div #'identity :type function) (lcm #'identity :type function) (ezgcd #'identity :type function) (gcd #'identity :type function)) (defparameter +ring-of-integers+ (make-ring :parse #'identity :unit #'(lambda () 1) :zerop #'zerop :add #'+ :sub #'- :uminus #'- :mul #'* :div #'/ :lcm #'lcm :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c))) :gcd #'gcd ) "The ring of integers.") |# (defgeneric ring-parse (object) (:method ((object t)) object)) (defgeneric ring-unit-for (object) (:method ((self number)) 1)) (defgeneric ring-zerop (object) (:method ((self number)) (zerop self))) (defgeneric ring-add (x y) (:method ((x number) (y number)) (+ x y))) (defgeneric ring-mul (x y) (:method ((x number) (y number)) (* x y))) (defgeneric ring-div (x y) (:method ((x number) (y number)) (/ x y))) (defgeneric ring-lcm (x y) (:method ((x integer) (y integer)) (lcm x y))) (defgeneric ring-ezgcd (x y) (:method ((x integer) (y integer) &aux (c (gcd x y))) (values c (/ x c) (/ y c)))) (defgeneric ring-gcd (x y) (:method ((x integer) (y integer)) (gcd x y))) (defgeneric dimension (object)) (defgeneric total-degree (object &optional start end)) (defgeneric divides-p (object1 object2) (:method ((object1 integer) (object2 integer)) (zerop (rem object2 object1))) (:documentation "Returns T if OBJECT1 divides OBJECT2")) (defgeneric divides-lcm-p (object1 object2 object3) (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise.")) (defgeneric lcm-divides-lcm-p (object1 object2 object3 object4) (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise.")) (defun lcm-equal-lcm-p (object1 object2 object3 object4) "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."