[425] | 1 | ;;; -*- mode: lisp; package: maxima; syntax: common-lisp; base: 10 -*-
|
---|
[404] | 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
---|
| 3 | ;;;
|
---|
[425] | 4 | ;;; copyright (c) 1999, 2002, 2009, 2015 marek rychlik <rychlik@u.arizona.edu>
|
---|
[404] | 5 | ;;;
|
---|
[425] | 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
|
---|
[404] | 9 | ;;; (at your option) any later version.
|
---|
| 10 | ;;;
|
---|
[425] | 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.
|
---|
[404] | 15 | ;;;
|
---|
[425] | 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.
|
---|
[404] | 19 | ;;;
|
---|
| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
---|
| 21 |
|
---|
| 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
---|
| 23 | ;;
|
---|
[425] | 24 | ;; coefficient ring operations
|
---|
[404] | 25 | ;;
|
---|
| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
---|
| 27 | ;;
|
---|
[425] | 28 | ;; these are all operations that are performed on the coefficients by
|
---|
[404] | 29 | ;; the package, and thus the coefficient ring can be changed by merely
|
---|
| 30 | ;; redefining these operations.
|
---|
| 31 | ;;
|
---|
| 32 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
|
---|
| 33 |
|
---|
[405] | 34 | (defpackage "RING"
|
---|
| 35 | (:use :cl)
|
---|
[2145] | 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"
|
---|
[2367] | 50 | "R-EXPONENTS"
|
---|
[2369] | 51 | "R-COEFF"
|
---|
[2145] | 52 | "R-SUGAR"
|
---|
| 53 | "R-DIVIDES-P"
|
---|
| 54 | "R-DIVIDES-LCM-P"
|
---|
| 55 | "R-LCM-DIVIDES-LCM-P"
|
---|
| 56 | "R-LCM-EQUAL-LCM-P"
|
---|
| 57 | "R-REL-PRIME-P"
|
---|
| 58 | "R-EQUALP"
|
---|
[2173] | 59 | "R-ELT"
|
---|
[2174] | 60 | "R->LIST"
|
---|
| 61 | "R-DIVISIBLE-BY-P"
|
---|
| 62 | "R-REL-PRIME-P"
|
---|
| 63 | "R-DEPENDS-P"
|
---|
| 64 | "R-TENSOR-PRODUCT"
|
---|
[2444] | 65 | "R-CONTRACT"
|
---|
| 66 | "R-LENGTH"
|
---|
[2476] | 67 | "MULTIPLY-BY"
|
---|
[2485] | 68 | "ADD-TO"
|
---|
| 69 | "SUBTRACT-FROM"
|
---|
| 70 | "UNARY-UMINUS"
|
---|
[2491] | 71 | "SCALAR"
|
---|
[2174] | 72 | ))
|
---|
[2131] | 73 |
|
---|
[421] | 74 | (in-package :ring)
|
---|
| 75 |
|
---|
[2496] | 76 | (defclass scalar () (value))
|
---|
[2492] | 77 |
|
---|
[2145] | 78 | (defgeneric r-unit-for (object)
|
---|
[2015] | 79 | (:method ((self number)) 1))
|
---|
[2016] | 80 |
|
---|
[2145] | 81 | (defgeneric r-zerop (object)
|
---|
[2450] | 82 | (:method ((self number)) (zerop self)))
|
---|
[2016] | 83 |
|
---|
[2145] | 84 | (defgeneric r+ (x y)
|
---|
[2450] | 85 | (:method ((x number) (y number)) (+ x y)))
|
---|
[2016] | 86 |
|
---|
[2145] | 87 | (defgeneric r- (x y)
|
---|
[2450] | 88 | (:method ((x number) (y number)) (- x y)))
|
---|
[2118] | 89 |
|
---|
[2145] | 90 | (defgeneric r* (x y)
|
---|
[2450] | 91 | (:method ((x number) (y number)) (* x y)))
|
---|
[2016] | 92 |
|
---|
[2145] | 93 | (defgeneric r-tensor-product (x y))
|
---|
[2090] | 94 |
|
---|
[2145] | 95 | (defgeneric r/ (x y)
|
---|
[2450] | 96 | (:method ((x number) (y number)) (/ x y)))
|
---|
[2016] | 97 |
|
---|
[2145] | 98 | (defgeneric r-lcm (x y)
|
---|
[2450] | 99 | (:method ((x integer) (y integer)) (lcm x y)))
|
---|
[2016] | 100 |
|
---|
[2145] | 101 | (defgeneric r-expt (x y)
|
---|
[2450] | 102 | (:method ((x integer) (y integer)) (expt x y)))
|
---|
[2121] | 103 |
|
---|
[2145] | 104 | (defgeneric r-ezgcd (x y)
|
---|
[2016] | 105 | (:method ((x integer) (y integer)
|
---|
[2145] | 106 | &aux (c (gcd x y)))
|
---|
| 107 | (values c (/ x c) (/ y c))))
|
---|
[2017] | 108 |
|
---|
[2145] | 109 | (defgeneric r-gcd (x y)
|
---|
[2017] | 110 | (:method ((x integer) (y integer))
|
---|
[2450] | 111 | (gcd x y)))
|
---|
[2017] | 112 |
|
---|
[2145] | 113 | (defgeneric r-dimension (object))
|
---|
[2368] | 114 | (defgeneric r-exponents (object))
|
---|
[2369] | 115 | (defgeneric r-coeff (object))
|
---|
[2041] | 116 |
|
---|
[2145] | 117 | (defgeneric r-total-degree (object &optional start end))
|
---|
[2065] | 118 |
|
---|
[2145] | 119 | (defgeneric r-divides-p (object1 object2)
|
---|
[2043] | 120 | (:method ((object1 integer) (object2 integer))
|
---|
[2450] | 121 | (zerop (rem object2 object1)))
|
---|
[2062] | 122 | (:documentation "Returns T if OBJECT1 divides OBJECT2"))
|
---|
[2040] | 123 |
|
---|
[2145] | 124 | (defgeneric r-divides-lcm-p (object1 object2 object3)
|
---|
[2062] | 125 | (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
|
---|
[2070] | 126 |
|
---|
[2145] | 127 | (defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
|
---|
[2071] | 128 | (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
|
---|
[2073] | 129 |
|
---|
[2145] | 130 | (defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
|
---|
[2107] | 131 | (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
|
---|
[2133] | 132 |
|
---|
[2145] | 133 | (defgeneric r-equalp (object1 object2)
|
---|
[2133] | 134 | (:method ((object1 t) (object2 t)) (equalp object1 object2))
|
---|
[2134] | 135 | (:documentation "Equality using deep comparison of object slots."))
|
---|
[2140] | 136 |
|
---|
[2145] | 137 | (defgeneric r-elt (object index))
|
---|
[2444] | 138 |
|
---|
[2172] | 139 | (defgeneric (setf r-elt) (new-value object index))
|
---|
[2140] | 140 |
|
---|
[2444] | 141 | (defgeneric r-length (object))
|
---|
| 142 |
|
---|
[2151] | 143 | (defgeneric r->list (object))
|
---|
[2158] | 144 | (defgeneric r-sugar (object))
|
---|
[2175] | 145 | (defgeneric r-rel-prime-p (object1 object2))
|
---|
[2178] | 146 | (defgeneric r-contract (object k))
|
---|
[2179] | 147 | (defgeneric r-divisible-by-p (object1 object2))
|
---|
[2180] | 148 | (defgeneric r-depends-p (object k))
|
---|
[2475] | 149 |
|
---|
[2482] | 150 | (defgeneric multiply-by (self other)
|
---|
| 151 | (:method (self other) (r* self other)))
|
---|
[2484] | 152 |
|
---|
| 153 | (defgeneric add-to (self other)
|
---|
| 154 | (:method (self other) (r+ self other)))
|
---|
| 155 |
|
---|
| 156 | (defgeneric subtract-from (self other)
|
---|
| 157 | (:method (self other) (r- self other)))
|
---|
| 158 |
|
---|
| 159 | (defmethod unary-uminus (self))
|
---|
| 160 |
|
---|