source: branches/f4grobner/ring.lisp@ 2594

;;; -*-  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>          
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;;;  this program is free software; you can redistribute it and/or modify        
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(defpackage "RING"
  (:use :cl)
  (:export "R-PARSE"
           "UNIT-ELEMENT"
           "R-ZEROP"
           "R+"
           "R-"
           "R*"
           "R+"
           "R/"
           "R-EXPT"
           "R-LCM"
           "R-EZGCD"
           "R-GCD"
           "R-TOTAL-DEGREE"
           "R-DIMENSION"
           "R-EXPONENTS"
           "R-COEFF"
           "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"      
           "R-LENGTH"
           "MULTIPLY-BY"
           "ADD-TO"
           "SUBTRACT-FROM"
           "UNARY-UMINUS"
           "SCALAR"
           "INSERT-ITEM"
           "APPEND-ITEM")
  (:documentation
   "Implements ring operations.  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."))

(in-package :ring)

(defclass scalar () 
  ((value :initarg :value :accessor value))
  (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))

(defgeneric unit-element (class))

(defgeneric r-zerop (object)
  (:method ((self number)) (zerop self)))

(defgeneric r+ (x y)
  (:method ((x number) (y number)) (+ x y))) 

(defgeneric r- (x y)
  (:method ((x number) (y number)) (- x y))) 

(defgeneric r* (x y)
  (:method ((x number) (y number)) (* x y))) 

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

(defgeneric r/ (x y)
  (:method ((x number) (y number)) (/ x y))) 

(defgeneric r-lcm (x y)
  (:method ((x integer) (y integer)) (lcm x y))) 

(defgeneric r-expt (x y)
  (:method ((x integer) (y integer)) (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))
    (gcd x y)))

(defgeneric r-dimension (object))
(defgeneric r-exponents (object))
(defgeneric r-coeff (object))

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

(defgeneric r-divides-p (object1 object2)
  (:method ((object1 integer) (object2 integer))
    (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-length (object))

(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))

(defgeneric multiply-by (self other)
  (:method (self other) (r* self other)))

(defgeneric add-to (self other)
  (:method (self other) (r+ self other)))

(defgeneric subtract-from (self other)
  (:method (self other) (r- self other)))

(defgeneric unary-uminus (self))

(defgeneric insert-item (self item))
(defgeneric append-item (self item))