source: branches/f4grobner/ring.lisp@ 2187

;;; -*-  mode: lisp; package: maxima; syntax: common-lisp; base: 10 -*- 

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;;;                                                                              

;;;  copyright (c) 1999, 2002, 2009, 2015 marek rychlik <rychlik@u.arizona.edu>          

;;;                                                                              

;;;  this program is free software; you can redistribute it and/or modify        

;;;  it under the terms of the gnu general public license as published by        

;;;  the free software foundation; either version 2 of the license, or           

;;;  (at your option) any later version.                                         

;;;                                                                              

;;;  this program is distributed in the hope that it will be useful,             

;;;  but without any warranty; without even the implied warranty of              

;;;  merchantability or fitness for a particular purpose.  see the               

;;;  gnu general public license for more details.                                

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;;;  you should have received a copy of the gnu general public license           

;;;  along with this program; if not, write to the free software                 

;;;  foundation, inc., 59 temple place - suite 330, boston, ma 02111-1307, usa.  

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;;

;; coefficient ring operations

;;

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;;

;; these are all operations that are performed on the coefficients by

;; the package, and thus the coefficient ring can be changed by merely

;; redefining these operations.

;;

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(defpackage "RING"

  (:use :cl)

  (:export "R-PARSE"

           "R-UNIT-FOR"

           "R-ZEROP"

           "R+"

           "R-"

           "R*"

           "R+"

           "R/"

           "R-EXPT"

           "R-LCM"

           "R-EZGCD"

           "R-GCD"

           "R-TOTAL-DEGREE"

           "R-DIMENSION"

           "R-SUGAR"

           "R-DIVIDES-P"   

           "R-DIVIDES-LCM-P"

           "R-LCM-DIVIDES-LCM-P"

           "R-LCM-EQUAL-LCM-P"

           "R-REL-PRIME-P"    

           "R-EQUALP"          

           "R-ELT"

           "R->LIST"

           "R-DIVISIBLE-BY-P"   

           "R-REL-PRIME-P"      

           "R-DEPENDS-P"        

           "R-TENSOR-PRODUCT"

           "R-CONTRACT"        

))



(in-package :ring)



(defgeneric r-unit-for (object)

  (:method ((self number)) 1))



(defgeneric r-zerop (object)

  (:method ((self number)) (cl:zerop self)))



(defgeneric r+ (x y)

  (:method ((x number) (y number)) (cl:+ x y))) 



(defgeneric r- (x y)

  (:method ((x number) (y number)) (cl:- x y))) 



(defgeneric r* (x y)

  (:method ((x number) (y number)) (cl:* x y))) 



(defgeneric r-tensor-product (x y))



(defgeneric r/ (x y)

  (:method ((x number) (y number)) (cl:/ x y))) 



(defgeneric r-lcm (x y)

  (:method ((x integer) (y integer)) (cl:lcm x y))) 



(defgeneric r-expt (x y)

  (:method ((x integer) (y integer)) (cl:expt x y))) 



(defgeneric r-ezgcd (x y)

  (:method ((x integer) (y integer)

            &aux (c (gcd x y)))

    (values c (/ x c) (/ y c))))



(defgeneric r-gcd (x y)

  (:method ((x integer) (y integer))

    (cl:gcd x y)))



(defgeneric r-dimension (object))



(defgeneric r-total-degree (object &optional start end))



(defgeneric r-divides-p (object1 object2)

  (:method ((object1 integer) (object2 integer))

    (cl:zerop (rem object2 object1)))

  (:documentation "Returns T if OBJECT1 divides OBJECT2"))



(defgeneric r-divides-lcm-p (object1 object2 object3)

  (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))



(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)

  (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))



(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)

  (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))



(defgeneric r-equalp (object1 object2)

  (:method ((object1 t) (object2 t)) (equalp object1 object2))

  (:documentation "Equality using deep comparison of object slots."))



(defgeneric r-elt (object index))

(defgeneric (setf r-elt) (new-value object index))



(defgeneric r->list (object))

(defgeneric r-sugar (object))

(defgeneric r-rel-prime-p (object1 object2))

(defgeneric r-contract (object k))

(defgeneric r-divisible-by-p (object1 object2))

(defgeneric r-depends-p (object k))