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source: branches/f4grobner/ring.lisp

Last change on this file was 4550, checked in by Marek Rychlik, 8 years ago

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[4228]1;;; -*- Mode: Lisp -*-
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(defpackage "RING"
[4332]23 (:use :cl :copy)
[4228]24 (:export "RING"
[4342]25 "FIELD"
[4228]26 "ADD-TO"
27 "SUBTRACT-FROM"
28 "MULTIPLY-BY"
29 "DIVIDE-BY"
[4383]30 "ADD"
31 "SUBTRACT"
[4354]32 "MULTIPLY"
33 "DIVIDE"
[4231]34 "UNARY-MINUS"
[4246]35 "UNARY-INVERSE"
[4249]36 "UNIVERSAL-GCD"
[4228]37 "UNIVERSAL-EZGCD"
38 "UNIVERSAL-EQUALP"
39 "UNIVERSAL-ZEROP"
[4279]40 "MAKE-ZERO-FOR"
41 "MAKE-UNIT-FOR"
[4323]42 "->SEXP"
43 "RATIONAL-FIELD"
44 "RATIONAL-FIELD-VALUE"
45 "MAKE-ZERO-FOR"
46 "MAKE-UNIT-FOR"
47 "INTEGER-RING"
48 "INTEGER-RING-VALUE"
49 )
50 (:documentation "Defines an abstract ring class and ring operations.")
51 )
[4228]52
53(in-package "RING")
54
[4550]55(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
[4498]56
[4228]57(defclass ring () () (:documentation "An abstract ring."))
[4342]58(defclass field (ring) () (:documentation "An abstract ring."))
[4228]59
[4246]60(defgeneric multiply-by (self other)
[4228]61 (:documentation "Multiply SELF by OTHER."))
62
[4246]63(defgeneric divide-by (self other)
64 (:documentation "Divide SELF by OTHER."))
65
[4228]66(defgeneric add-to (self other)
67 (:documentation "Add OTHER to SELF."))
68
[4246]69(defgeneric subtract-from (self other)
[4228]70 (:documentation "Subtract OTHER from SELF."))
71
[4230]72(defgeneric unary-minus (self)
[4234]73 (:documentation "Changes SELF to its negative."))
[4230]74
[4246]75(defgeneric unary-inverse (self)
[4273]76 (:documentation "Changes SELF to the unary inverse of SELF."))
[4246]77
[4257]78(defgeneric universal-gcd (object other)
[4274]79 (:documentation "Returns GCD(OBJECT, OTHER)"))
[4228]80
[4248]81(defgeneric universal-ezgcd (x y)
82 (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
[4258]83C=GCD(X,Y). It returns three values: C, X1 and Y1. The result may be obtained by
[4373]84the Euclidean algorithm.")
85 (:method ((x t) (y t) &aux (c (universal-gcd x y)))
86 (values c (divide x c) (divide y c))))
[4248]87
[4228]88(defgeneric universal-equalp (self other)
89 (:documentation "Return T if objects SELF and OTHER are equal, NIL otherwise.")
[4447]90 (:method ((object1 null) (object2 null)) t)
[4311]91 (:method ((object1 cons) (object2 cons)) (every #'universal-equalp object1 object2))
92 (:method ((self number) (other number)) (= self other)))
[4228]93
94(defgeneric universal-zerop (self)
95 (:documentation "Return T if SELF is a zero in the ring it belongs to."))
96
[4230]97(defgeneric ->sexp (self &optional vars)
[4228]98 (:documentation "Convert SELF to an S-expression."))
[4248]99
[4278]100(defgeneric make-zero-for (self)
[4322]101 (:documentation "Create a zero in the ring of SELF. A fresh instance
102should be returned upon every call."))
[4278]103
104(defgeneric make-unit-for (self)
[4322]105 (:documentation "Create a unit in the ring of SELF. A fresh instance
106should be returned upon every call."))
[4349]107
[4376]108(defgeneric add (summand &rest more-summands)
[4379]109 (:documentation "Successively adds to SUMMAND the elements of
110MORE-SUMMANDS, using ADD-TO. The first SUMMAND must not be
111destructively modified. Instead, a copy of factor should be made and
112returned as the value of this function.")
[4373]113 (:method ((summand t) &rest more-summands)
[4382]114 "The default implementation of ADD."
[4373]115 (reduce #'add-to more-summands :initial-value (copy-instance summand))))
116
[4376]117(defgeneric subtract (minuend &rest subtrahends)
[4379]118 (:documentation "Successively subtracts SUBTRAHENDS from MINUEND,
119using SUBTRACT-FROM. MINUEND. must not be destructively modified.
[4378]120Instead, a copy of factor should be made and returned as the value of
[4379]121this function.")
[4376]122 (:method ((minuend t) &rest subtrahends)
[4382]123 "The default implementation of SUBTRACT."
[4376]124 (cond ((endp subtrahends) (unary-minus (copy-instance minuend)))
[4381]125 (t (reduce #'subtract-from subtrahends :initial-value (copy-instance minuend))))))
[4376]126
[4349]127(defgeneric multiply (factor &rest more-factors)
128 (:documentation "Successively multiplies factor FACTOR by the remaining arguments
[4352]129MORE-FACTORS, using MULTIPLY-BY to multiply two factors. FACTOR must not be destructively modified.
130Instead, a copy of factor should be made and returned as the value of this function.")
[4351]131 (:method ((factor t) &rest more-factors)
[4382]132 "The default implementation of MULTIPLY."
[4349]133 (reduce #'multiply-by more-factors :initial-value (copy-instance factor))))
134
[4354]135(defgeneric divide (numerator &rest denominators)
136 (:documentation "Successively divides NUMERATOR by elements of DENOMINATORS. The operation
137should not modify the NUMERATOR. Instead, a copy of factor should be made and returned as the value of this function.")
138 (:method ((numerator t) &rest denominators)
[4382]139 "The default implementation of DIVIDE."
[4354]140 (cond ((endp denominators)
141 (unary-inverse (copy-instance numerator)))
142 (t (reduce #'divide-by denominators :initial-value (copy-instance numerator))))))
143
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