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source: branches/f4grobner/ring.lisp@ 2175

Last change on this file since 2175 was 2175, checked in by Marek Rychlik, 9 years ago

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File size: 4.1 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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; coefficient ring operations
25;;
26;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
27;;
28;; these are all operations that are performed on the coefficients by
29;; the package, and thus the coefficient ring can be changed by merely
30;; redefining these operations.
31;;
32;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
33
34(defpackage "RING"
35 (:use :cl)
36 (:export "R-PARSE"
37 "R-UNIT-FOR"
38 "R-ZEROP"
39 "R+"
40 "R-"
41 "R*"
42 "R+"
43 "R/"
44 "R-EXPT"
45 "R-LCM"
46 "R-EZGCD"
47 "R-GCD"
48 "R-TOTAL-DEGREE"
49 "R-DIMENSION"
50 "R-SUGAR"
51 "R-DIVIDES-P"
52 "R-DIVIDES-LCM-P"
53 "R-LCM-DIVIDES-LCM-P"
54 "R-LCM-EQUAL-LCM-P"
55 "R-DIVISIBLE-BY-P"
56 "R-REL-PRIME-P"
57 "R-EQUALP"
58 "R-DEPENDS-P"
59 "R-ELT"
60 "R->LIST"
61 "R-DIVISIBLE-BY-P"
62 "R-REL-PRIME-P"
63 "R-DEPENDS-P"
64 "R-TENSOR-PRODUCT"
65 "R-CONTRACT"
66))
67
68(in-package :ring)
69
70(defgeneric r-unit-for (object)
71 (:method ((self number)) 1))
72
73(defgeneric r-zerop (object)
74 (:method ((self number)) (cl:zerop self)))
75
76(defgeneric r+ (x y)
77 (:method ((x number) (y number)) (cl:+ x y)))
78
79(defgeneric r- (x y)
80 (:method ((x number) (y number)) (cl:- x y)))
81
82(defgeneric r* (x y)
83 (:method ((x number) (y number)) (cl:* x y)))
84
85(defgeneric r-tensor-product (x y))
86
87(defgeneric r/ (x y)
88 (:method ((x number) (y number)) (cl:/ x y)))
89
90(defgeneric r-lcm (x y)
91 (:method ((x integer) (y integer)) (cl:lcm x y)))
92
93(defgeneric r-expt (x y)
94 (:method ((x integer) (y integer)) (cl:expt x y)))
95
96(defgeneric r-ezgcd (x y)
97 (:method ((x integer) (y integer)
98 &aux (c (gcd x y)))
99 (values c (/ x c) (/ y c))))
100
101(defgeneric r-gcd (x y)
102 (:method ((x integer) (y integer))
103 (cl:gcd x y)))
104
105(defgeneric r-dimension (object))
106
107(defgeneric r-total-degree (object &optional start end))
108
109(defgeneric r-divides-p (object1 object2)
110 (:method ((object1 integer) (object2 integer))
111 (cl:zerop (rem object2 object1)))
112 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
113
114(defgeneric r-divides-lcm-p (object1 object2 object3)
115 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
116
117(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
118 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
119
120(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
121 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
122
123(defgeneric r-equalp (object1 object2)
124 (:method ((object1 t) (object2 t)) (equalp object1 object2))
125 (:documentation "Equality using deep comparison of object slots."))
126
127(defgeneric r-elt (object index))
128(defgeneric (setf r-elt) (new-value object index))
129
130(defgeneric r->list (object))
131(defgeneric r-sugar (object))
132(defgeneric r-rel-prime-p (object1 object2))
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