[425] | 1 | ;;; -*- mode: lisp; package: maxima; syntax: common-lisp; base: 10 -*-
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[404] | 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 3 | ;;;
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[425] | 4 | ;;; copyright (c) 1999, 2002, 2009, 2015 marek rychlik <rychlik@u.arizona.edu>
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[404] | 5 | ;;;
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[425] | 6 | ;;; this program is free software; you can redistribute it and/or modify
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| 7 | ;;; it under the terms of the gnu general public license as published by
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| 8 | ;;; the free software foundation; either version 2 of the license, or
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[404] | 9 | ;;; (at your option) any later version.
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| 10 | ;;;
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[425] | 11 | ;;; this program is distributed in the hope that it will be useful,
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| 12 | ;;; but without any warranty; without even the implied warranty of
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| 13 | ;;; merchantability or fitness for a particular purpose. see the
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| 14 | ;;; gnu general public license for more details.
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[404] | 15 | ;;;
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[425] | 16 | ;;; you should have received a copy of the gnu general public license
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| 17 | ;;; along with this program; if not, write to the free software
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| 18 | ;;; foundation, inc., 59 temple place - suite 330, boston, ma 02111-1307, usa.
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[404] | 19 | ;;;
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| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 21 |
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| 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 23 | ;;
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[425] | 24 | ;; coefficient ring operations
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[404] | 25 | ;;
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| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 27 | ;;
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[425] | 28 | ;; these are all operations that are performed on the coefficients by
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[404] | 29 | ;; the package, and thus the coefficient ring can be changed by merely
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| 30 | ;; redefining these operations.
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| 31 | ;;
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| 32 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 33 |
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[405] | 34 | (defpackage "RING"
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| 35 | (:use :cl)
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[2096] | 36 | (:export "PARSE"
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| 37 | "UNIT-FOR"
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[2097] | 38 | "ZEROP"
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| 39 | "ADD"
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| 40 | "SUB"
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| 41 | "UMINUS"
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| 42 | "MUL"
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| 43 | "DIV"
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| 44 | "LCM"
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| 45 | "EZGCD"
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| 46 | "GCD"
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[405] | 47 | ))
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| 48 |
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[421] | 49 | (in-package :ring)
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| 50 |
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[2100] | 51 | (defgeneric unit-for (object)
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[2015] | 52 | (:method ((self number)) 1))
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[2016] | 53 |
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[2100] | 54 | (defgeneric zerop (object)
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| 55 | (:method ((self number)) (cl:zerop self)))
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[2016] | 56 |
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[2100] | 57 | (defgeneric add (x y)
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[2016] | 58 | (:method ((x number) (y number)) (+ x y)))
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| 59 |
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[2100] | 60 | (defgeneric mul (x y)
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[2016] | 61 | (:method ((x number) (y number)) (* x y)))
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| 62 |
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[2100] | 63 | (defgeneric tensor-mul (x y))
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[2090] | 64 |
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[2100] | 65 | (defgeneric div (x y)
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[2016] | 66 | (:method ((x number) (y number)) (/ x y)))
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| 67 |
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[2100] | 68 | (defgeneric lcm (x y)
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| 69 | (:method ((x integer) (y integer)) (cl:lcm x y)))
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[2016] | 70 |
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[2100] | 71 | (defgeneric ezgcd (x y)
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[2016] | 72 | (:method ((x integer) (y integer)
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| 73 | &aux (c (gcd x y)))
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| 74 | (values c (/ x c) (/ y c))))
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[2017] | 75 |
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[2100] | 76 | (defgeneric gcd (x y)
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[2017] | 77 | (:method ((x integer) (y integer))
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[2100] | 78 | (cl:gcd x y)))
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[2017] | 79 |
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[2065] | 80 | (defgeneric dimension (object))
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[2041] | 81 |
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[2068] | 82 | (defgeneric total-degree (object &optional start end))
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[2065] | 83 |
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[2057] | 84 | (defgeneric divides-p (object1 object2)
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[2043] | 85 | (:method ((object1 integer) (object2 integer))
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[2062] | 86 | (zerop (rem object2 object1)))
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| 87 | (:documentation "Returns T if OBJECT1 divides OBJECT2"))
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[2040] | 88 |
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[2056] | 89 | (defgeneric divides-lcm-p (object1 object2 object3)
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[2062] | 90 | (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
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[2070] | 91 |
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[2071] | 92 | (defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
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| 93 | (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
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[2073] | 94 |
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[2094] | 95 | (defmethod lcm-equal-lcm-p (object1 object2 object3 object4)
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[2093] | 96 | "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise.")
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