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source: branches/f4grobner/ring.lisp@ 2594

Last change on this file since 2594 was 2523, checked in by Marek Rychlik, 9 years ago

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File size: 4.7 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-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-UMINUS"
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
78(defgeneric r+ (x y)
79 (:method ((x number) (y number)) (+ x y)))
80
81(defgeneric r- (x y)
82 (:method ((x number) (y number)) (- x y)))
83
84(defgeneric r* (x y)
85 (:method ((x number) (y number)) (* x y)))
86
87(defgeneric r-tensor-product (x y))
88
89(defgeneric r/ (x y)
90 (:method ((x number) (y number)) (/ x y)))
91
92(defgeneric r-lcm (x y)
93 (:method ((x integer) (y integer)) (lcm x y)))
94
95(defgeneric r-expt (x y)
96 (:method ((x integer) (y integer)) (expt x y)))
97
98(defgeneric r-ezgcd (x y)
99 (:method ((x integer) (y integer)
100 &aux (c (gcd x y)))
101 (values c (/ x c) (/ y c))))
102
103(defgeneric r-gcd (x y)
104 (:method ((x integer) (y integer))
105 (gcd x y)))
106
107(defgeneric r-dimension (object))
108(defgeneric r-exponents (object))
109(defgeneric r-coeff (object))
110
111(defgeneric r-total-degree (object &optional start end))
112
113(defgeneric r-divides-p (object1 object2)
114 (:method ((object1 integer) (object2 integer))
115 (zerop (rem object2 object1)))
116 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
117
118(defgeneric r-divides-lcm-p (object1 object2 object3)
119 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
120
121(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
122 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
123
124(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
125 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
126
127(defgeneric r-equalp (object1 object2)
128 (:method ((object1 t) (object2 t)) (equalp object1 object2))
129 (:documentation "Equality using deep comparison of object slots."))
130
131(defgeneric r-elt (object index))
132
133(defgeneric (setf r-elt) (new-value object index))
134
135(defgeneric r-length (object))
136
137(defgeneric r->list (object))
138(defgeneric r-sugar (object))
139(defgeneric r-rel-prime-p (object1 object2))
140(defgeneric r-contract (object k))
141(defgeneric r-divisible-by-p (object1 object2))
142(defgeneric r-depends-p (object k))
143
144(defgeneric multiply-by (self other)
145 (:method (self other) (r* self other)))
146
147(defgeneric add-to (self other)
148 (:method (self other) (r+ self other)))
149
150(defgeneric subtract-from (self other)
151 (:method (self other) (r- self other)))
152
153(defgeneric unary-uminus (self))
154
155(defgeneric insert-item (self item))
156(defgeneric append-item (self item))
157
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