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source: branches/f4grobner/ring.lisp@ 2818

Last change on this file since 2818 was 2810, checked in by Marek Rychlik, 9 years ago

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