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source: branches/f4grobner/ring.lisp@ 2074

Last change on this file since 2074 was 2074, checked in by Marek Rychlik, 9 years ago

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[425]1;;; -*- mode: lisp; package: maxima; syntax: common-lisp; base: 10 -*-
[404]2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
[425]4;;; copyright (c) 1999, 2002, 2009, 2015 marek rychlik <rychlik@u.arizona.edu>
[404]5;;;
[425]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
[404]9;;; (at your option) any later version.
10;;;
[425]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.
[404]15;;;
[425]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.
[404]19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
[425]24;; coefficient ring operations
[404]25;;
26;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
27;;
[425]28;; these are all operations that are performed on the coefficients by
[404]29;; the package, and thus the coefficient ring can be changed by merely
30;; redefining these operations.
31;;
32;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
33
[405]34(defpackage "RING"
35 (:use :cl)
[424]36 (:export "RING"
[425]37 "RING-PARSE"
38 "RING-UNIT"
39 "RING-ZEROP"
40 "RING-ADD"
41 "RING-SUB"
42 "RING-UMINUS"
43 "RING-MUL"
44 "RING-DIV"
45 "RING-LCM"
46 "RING-EZGCD"
47 "RING-GCD"
[424]48 "MAKE-RING"
[1666]49 "+RING-OF-INTEGERS+"
[405]50 ))
51
[421]52(in-package :ring)
53
[2013]54#|
55
[404]56(defstruct (ring)
[407]57 "Defines a RING structure, whose fields
58are common ring operations necessary to implement
59Groebner bases."
[404]60 (parse #'identity :type function)
61 (unit #'identity :type function)
62 (zerop #'identity :type function)
63 (add #'identity :type function)
64 (sub #'identity :type function)
65 (uminus #'identity :type function)
66 (mul #'identity :type function)
67 (div #'identity :type function)
68 (lcm #'identity :type function)
69 (ezgcd #'identity :type function)
70 (gcd #'identity :type function))
71
[1663]72(defparameter +ring-of-integers+
[409]73 (make-ring
74 :parse #'identity
75 :unit #'(lambda () 1)
76 :zerop #'zerop
77 :add #'+
78 :sub #'-
79 :uminus #'-
80 :mul #'*
81 :div #'/
82 :lcm #'lcm
83 :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
[698]84 :gcd #'gcd
85 )
[404]86 "The ring of integers.")
[2013]87|#
88
[2059]89(defgeneric ring-parse (object)
[2014]90 (:method ((object t)) object))
[2013]91
[2059]92(defgeneric ring-unit-for (object)
[2015]93 (:method ((self number)) 1))
[2016]94
[2059]95(defgeneric ring-zerop (object)
[2016]96 (:method ((self number)) (zerop self)))
97
[2059]98(defgeneric ring-add (x y)
[2016]99 (:method ((x number) (y number)) (+ x y)))
100
[2059]101(defgeneric ring-mul (x y)
[2016]102 (:method ((x number) (y number)) (* x y)))
103
[2059]104(defgeneric ring-div (x y)
[2016]105 (:method ((x number) (y number)) (/ x y)))
106
[2059]107(defgeneric ring-lcm (x y)
[2016]108 (:method ((x integer) (y integer)) (lcm x y)))
109
[2059]110(defgeneric ring-ezgcd (x y)
[2016]111 (:method ((x integer) (y integer)
112 &aux (c (gcd x y)))
113 (values c (/ x c) (/ y c))))
[2017]114
[2059]115(defgeneric ring-gcd (x y)
[2017]116 (:method ((x integer) (y integer))
117 (gcd x y)))
118
[2065]119(defgeneric dimension (object))
[2041]120
[2068]121(defgeneric total-degree (object &optional start end))
[2065]122
[2057]123(defgeneric divides-p (object1 object2)
[2043]124 (:method ((object1 integer) (object2 integer))
[2062]125 (zerop (rem object2 object1)))
126 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
[2040]127
[2056]128(defgeneric divides-lcm-p (object1 object2 object3)
[2062]129 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
[2070]130
[2071]131(defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
132 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
[2073]133
[2074]134(defun lcm-equal-lcm-p (object1 object2 object3 object4)
135 "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."
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