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source: branches/f4grobner/ring.lisp@ 2144

Last change on this file since 2144 was 2141, checked in by Marek Rychlik, 9 years ago

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File size: 3.9 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 (:shadow "GCD" "LCM" "ZEROP" "+" "-" "*" "/" "EXPT")
37 (:export "PARSE"
38 "UNIT-FOR"
39 "ZEROP"
40 "+"
41 "-"
42 "*"
43 "+"
44 "/"
45 "EXPT"
46 "LCM"
47 "EZGCD"
48 "GCD"
49 "TOTAL-DEGREE"
50 "DIMENSION"
51 "SUGAR"
52 "DIVIDES-P"
53 "DIVIDES-LCM-P"
54 "LCM-DIVIDES-LCM-P"
55 "LCM-EQUAL-LCM-P"
56 "DIVISIBLE-BY-P"
57 "REL-PRIME-P"
58 "EQUAL-P"
59 "DEPENDS-P"
60 "TENSOR-MUL"
61 "CONTRACT"
62 "ELT"))
63
64(in-package :ring)
65
66(defgeneric unit-for (object)
67 (:method ((self number)) 1))
68
69(defgeneric zerop (object)
70 (:method ((self number)) (cl:zerop self)))
71
72(defgeneric + (x y)
73 (:method ((x number) (y number)) (cl:+ x y)))
74
75(defgeneric - (x y)
76 (:method ((x number) (y number)) (cl:- x y)))
77
78(defgeneric * (x y)
79 (:method ((x number) (y number)) (cl:* x y)))
80
81(defgeneric tensor-times (x y))
82
83(defgeneric / (x y)
84 (:method ((x number) (y number)) (cl:/ x y)))
85
86(defgeneric lcm (x y)
87 (:method ((x integer) (y integer)) (cl:lcm x y)))
88
89(defgeneric expt (x y)
90 (:method ((x integer) (y integer)) (cl:expt x y)))
91
92(defgeneric ezgcd (x y)
93 (:method ((x integer) (y integer)
94 &aux (c (cl:gcd x y)))
95 (values c (cl:/ x c) (cl:/ y c))))
96
97(defgeneric gcd (x y)
98 (:method ((x integer) (y integer))
99 (cl:gcd x y)))
100
101(defgeneric dimension (object))
102
103(defgeneric total-degree (object &optional start end))
104
105(defgeneric divides-p (object1 object2)
106 (:method ((object1 integer) (object2 integer))
107 (cl:zerop (rem object2 object1)))
108 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
109
110(defgeneric divides-lcm-p (object1 object2 object3)
111 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
112
113(defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
114 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
115
116(defgeneric lcm-equal-lcm-p (object1 object2 object3 object4)
117 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
118
119(defgeneric equal-p (object1 object2)
120 (:method ((object1 t) (object2 t)) (equalp object1 object2))
121 (:documentation "Equality using deep comparison of object slots."))
122
123(defgeneric elt (object index))
124
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