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source: branches/f4grobner/ring.lisp@ 2850

Last change on this file since 2850 was 2839, checked in by Marek Rychlik, 9 years ago

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File size: 6.6 KB
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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(defpackage "RING"
23 (:use :cl)
24 (:export "R-PARSE"
25 "UNIT-ELEMENT"
26 "R-ZEROP"
27 "R+"
28 "R-"
29 "R*"
30 "R+"
31 "R/"
32 "R-EXPT"
33 "R-LCM"
34 "R-EZGCD"
35 "R-GCD"
36 "R-TOTAL-DEGREE"
37 "R-DIMENSION"
38 "R-EXPONENTS"
39 "R-COEFF"
40 "R-SUGAR"
41 "R-DIVIDES-P"
42 "R-DIVIDES-LCM-P"
43 "R-LCM-DIVIDES-LCM-P"
44 "R-LCM-EQUAL-LCM-P"
45 "R-REL-PRIME-P"
46 "R-EQUALP"
47 "R-CLONE"
48 "R-ELT"
49 "R->LIST"
50 "R-DIVISIBLE-BY-P"
51 "R-REL-PRIME-P"
52 "R-DEPENDS-P"
53 "R-TENSOR-PRODUCT"
54 "R-CONTRACT"
55 "R-LENGTH"
56 "MULTIPLY-BY"
57 "DIVIDE-BY"
58 "ADD-TO"
59 "SUBTRACT-FROM"
60 "UNARY-MINUS"
61 "SCALAR"
62 "INSERT-ITEM"
63 "APPEND-ITEM")
64 (:documentation
65 "Implements ring operations. These are all operations that are
66performed on the coefficients by the package, and thus the coefficient
67ring can be changed by merely redefining these operations."))
68
69(in-package :ring)
70
71(defclass scalar ()
72 ((value :initarg :value :accessor value))
73 (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))
74
75(defgeneric unit-element (class))
76
77(defgeneric r-zerop (object)
78 (:method ((self number)) (zerop self))
79 (:documentation "Tests whether a ring element is 0."))
80
81(defgeneric r+ (x y)
82 (:method ((x number) (y number)) (+ x y))
83 (:documentation "Adds ring elements."))
84
85(defgeneric r- (x y)
86 (:method ((x number) (y number)) (- x y))
87 (:documentation "Subtracts ring elements."))
88
89(defgeneric r* (x y)
90 (:method ((x number) (y number)) (* x y))
91 (:documentation "Multiplies ring elements."))
92
93(defgeneric r-tensor-product (x y)
94 (:documentation "Takes a tensor product of two objects."))
95
96(defgeneric r/ (x y)
97 (:method ((x number) (y number)) (/ x y))
98 (:documentation "Divides ring elements."))
99
100(defgeneric r-lcm (x y)
101 (:method ((x integer) (y integer)) (lcm x y))
102 (:documentation "Returns the least common multiple of ring elements."))
103
104(defgeneric r-expt (x y)
105 (:method ((x integer) (y integer)) (expt x y))
106 (:documentation "Raises X to power Y."))
107
108(defgeneric r-ezgcd (x y)
109 (:method ((x integer) (y integer)
110 &aux (c (gcd x y)))
111 (values c (/ x c) (/ y c)))
112 (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
113C=GCD(X,Y). It returns C, X1 and Y1. The result may be obtained by
114the Euclidean algorithm."))
115
116(defgeneric r-gcd (x y)
117 (:method ((x integer) (y integer))
118 (gcd x y))
119 (:documentation "Returns GCD(X,Y)."))
120
121(defgeneric r-dimension (object))
122(defgeneric r-exponents (object))
123
124(defgeneric r-coeff (object))
125(defgeneric (setf r-coeff) (new-value object))
126
127(defgeneric r-total-degree (object &optional start end))
128
129(defgeneric r-divides-p (object1 object2)
130 (:method ((object1 integer) (object2 integer))
131 (zerop (rem object2 object1)))
132 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
133
134(defgeneric r-divides-lcm-p (object1 object2 object3)
135 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
136
137(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
138 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
139
140(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
141 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
142
143(defgeneric r-equalp (object1 object2)
144 (:method (object1 object2) (equalp object1 object2))
145 (:documentation "Equality using deep comparison of object slots."))
146
147(defgeneric r-clone (object)
148 (:documentation "Performs deep copy of an object and returns the result."))
149
150(defgeneric r-elt (object index))
151
152(defgeneric (setf r-elt) (new-value object index))
153
154(defgeneric r-length (object))
155
156(defgeneric r->list (object))
157(defgeneric r-sugar (object))
158(defgeneric r-rel-prime-p (object1 object2))
159(defgeneric r-contract (object k))
160(defgeneric r-divisible-by-p (object1 object2))
161(defgeneric r-depends-p (object k))
162
163(defgeneric multiply-by (self other)
164 (:method (self other) (r* self other))
165 (:documentation "Multiply object SELF and OTHER and store the result
166into SELF. It returns SELF. For instances of a class, this operation
167may be destructive."))
168
169(defgeneric divide-by (self other)
170 (:method (self other) (r/ self other))
171 (:documentation "Divided object SELF by OTHER and store the result
172into SELF. It returns SELF. For instances of a class, this operation
173may be destructive."))
174
175(defgeneric add-to (self other)
176 (:documentation "Add to object SELF another object OTHER. For
177complex objects, it may destructively modify SELF and destructively
178modify/invalidate object OTHER. For standard classes implementing this
179method, the result should be an object which is EQ to SELF. For
180built-in classes, such as NUMBER, the returned object may not be EQ to
181the original, but it will be EQL to it.")
182 (:method (self other) (r+ self other)))
183
184(defgeneric subtract-from (self other)
185 (:documentation "Subtract from an object SELF another object OTHER.
186For complex objects, it may destructively modify SELF and
187destructively modify/invalidate object OTHER. For standard classes
188implementing this method, the result should be an object which is EQ
189to SELF. For built-in classes, such as NUMBER, the returned object may
190not be EQ to the original.")
191 (:method (self other) (r- self other)))
192
193(defgeneric unary-minus (self)
194 (:method ((x number)) (- x)))
195
196(defgeneric insert-item (self item))
197(defgeneric append-item (self item))
198
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