source: branches/f4grobner/ring.lisp@ 3163

;;; -*-  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        

;;;  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.                                         

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;;;  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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(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-CLONE"

           "R-ELT"

           "R->LIST"

           "R-DIVISIBLE-BY-P"   

           "R-REL-PRIME-P"      

           "R-DEPENDS-P"        

           "LEFT-TENSOR-PRODUCT-BY"

           "RIGHT-TENSOR-PRODUCT-BY"

           "LEFT-CONTRACT"

           "R-LENGTH"

           "MULTIPLY-BY"

           "DIVIDE-BY"

           "ADD-TO"

           "SUBTRACT-FROM"

           "UNARY-MINUS"

           "SCALAR"

           "SCALAR-COEFF"

           "INSERT-ITEM"

           "APPEND-ITEM"

           "COPY-INSTANCE")

  (:shadowing-import-from 

   #+openmcl-native-threads #:ccl 

   #+cmu #:pcl

   #+sbcl #:sb-pcl 

   #+lispworks #:hcl 

   #+allegro #:mop 

   #+clisp #:clos

   #:class-slots #:slot-definition-name)

  (: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 () 

  ((coeff :initarg :coeff :accessor scalar-coeff))

  (:default-initargs :coeff nil)

  (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))



(defgeneric unit-element (class))



(defgeneric r-zerop (object)

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

  (:documentation "Tests whether a ring element is 0."))



(defgeneric r+ (x y)

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

  (:documentation "Adds ring elements.")) 



(defgeneric r- (x y)

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

  (:documentation "Subtracts ring elements.")) 



(defgeneric r* (x y)

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

  (:documentation "Multiplies ring elements.")) 



(defgeneric left-tensor-product-by (self other)

  (:documentation "Takes a tensor product of SELF with OTHER, where

OTHER is the left factor."))



(defgeneric right-tensor-product-by (self other)

  (:documentation "Takes a tensor product of SELF with OTHER, where

OTHER is the right factor."))



(defgeneric r/ (x y)

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

  (:documentation "Divides ring elements.")) 



(defgeneric r-lcm (x y)

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

  (:documentation "Returns the least common multiple of ring elements.")) 



(defgeneric r-expt (x y)

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

  (:documentation "Raises X to power Y.")) 



(defgeneric r-ezgcd (x y)

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

            &aux (c (gcd x y)))

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

  (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,

C=GCD(X,Y).  It returns C, X1 and Y1. The result may be obtained by

the Euclidean algorithm."))



(defgeneric r-gcd (x y)

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

    (gcd x y))

  (:documentation "Returns GCD(X,Y)."))



(defgeneric r-dimension (object))

(defgeneric r-exponents (object))



(defgeneric r-coeff (object))

(defgeneric (setf r-coeff) (new-value 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 object2) (equalp object1 object2))

  (:method ((object1 list) (object2 list))

    (every #'r-equalp object1 object2))

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



(defgeneric r-elt (object index)

  (:documentation "Access a part of an object OBJECT with index INDEX."))



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

  (:documentation "A setter of a part of an object OBJECT with index INDEX."))



(defgeneric r-length (object))



(defgeneric r->list (object))

(defgeneric r-sugar (object))

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

(defgeneric left-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))

  (:documentation "Multiply object SELF and OTHER and store the result

into SELF.  It returns SELF. For instances of a class, this operation

may be destructive."))



(defgeneric divide-by (self other)

  (:method (self other) (r/ self other))

  (:documentation "Divided object SELF by OTHER and store the result

into SELF.  It returns SELF. For instances of a class, this operation

may be destructive."))



(defgeneric add-to (self other)

  (:documentation "Add to object SELF another object OTHER.  For

complex objects, it may destructively modify SELF and destructively

modify/invalidate object OTHER. For standard classes implementing this

method, the result should be an object which is EQ to SELF. For

built-in classes, such as NUMBER, the returned object may not be EQ to

the original, but it will be EQL to it.")

  (:method (self other) (r+ self other)))



(defgeneric subtract-from (self other)

  (:documentation "Subtract from an object SELF another object OTHER.

For complex objects, it may destructively modify SELF and

destructively modify/invalidate object OTHER. For standard classes

implementing this method, the result should be an object which is EQ

to SELF. For built-in classes, such as NUMBER, the returned object may

not be EQ to the original.")

  (:method (self other) (r- self other)))



(defgeneric unary-minus (self)

  (:method ((x number)) (- x)))



(defgeneric insert-item (self item))

(defgeneric append-item (self item))



;; Source: http://stackoverflow.com/questions/11067899/is-there-a-generic-method-for-cloning-clos-objects

;; NOTE: This is a shallow copy. Add an around method for classes which need deep copy of the slots.

(defgeneric copy-instance (object &rest initargs &key &allow-other-keys)

  (:documentation "Makes and returns a shallow copy of OBJECT.



  An uninitialized object of the same class as OBJECT is allocated by

  calling ALLOCATE-INSTANCE.  For all slots returned by

  CLASS-SLOTS, the returned object has the

  same slot values and slot-unbound status as OBJECT.



  REINITIALIZE-INSTANCE is called to update the copy with INITARGS.")

  (:method ((object standard-object) &rest initargs &key &allow-other-keys)

    (let* ((class (class-of object))

           (copy (allocate-instance class)))

      (dolist (slot-name (mapcar #'slot-definition-name (class-slots class)))

        (when (slot-boundp object slot-name)

          (setf (slot-value copy slot-name)

                (slot-value object slot-name))))

      (apply #'reinitialize-instance copy initargs))))



#|

;; A stripped-down version of shallow copy

;; Source: http://stackoverflow.com/questions/11067899/is-there-a-generic-method-for-cloning-clos-objects

(defun shallow-copy-object (original)

  (let* ((class (class-of original))

         (copy (allocate-instance class)))

    (dolist (slot (mapcar #'slot-definition-name (class-slots class)))

      (when (slot-boundp original slot)

        (setf (slot-value copy slot)

              (slot-value original slot))))

    copy))

|#