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1.4
date	2009.01.22.03.59.21;	author marek;	state Exp;
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next	1.3;

1.3
date	2009.01.19.09.24.20;	author marek;	state Exp;
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next	1.2;

1.2
date	2009.01.19.07.40.03;	author marek;	state Exp;
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next	1.1;

1.1
date	2009.01.19.06.48.00;	author marek;	state Exp;
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1.4
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@;;; -*- Mode: Lisp; Syntax: Common-Lisp; Package: Grobner; Base: 10 -*-
#|
	$Id$
  *--------------------------------------------------------------------------*
  |  Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@@math.arizona.edu)    |
  |    Department of Mathematics, University of Arizona, Tucson, AZ 85721    |
  |                                                                          |
  | Everyone is permitted to copy, distribute and modify the code in this    |
  | directory, as long as this copyright note is preserved verbatim.         |
  *--------------------------------------------------------------------------*
|#

(defpackage "COEFFICIENT-RING"
  (:export ring
	   ring-+
	   ring--
	   ring-*
	   ring-/
	   ring-gcd
	   ring-lcm
	   ring-signum
	   ring-zerop
	   ring-unit
	   ring-length
	   ring-numerator
	   ring-denominator
	   make-ring
	   *coefficient-ring*
	   *ring-of-integers*
	   *field-of-rationals*
	   field-modulo-prime
	   )
  (:use "MODULAR" "COMMON-LISP"))
    
(in-package "COEFFICIENT-RING")

#+debug(proclaim '(optimize (speed 0) (debug 3)))
#-debug(proclaim '(optimize (speed 3) (debug 0)))

(defstruct ring
  "The structure whose slots are bound to functions
performing usual ring operations. In addition to usual arithmetical
operations, bindings for other common operations
which increase efficiency of Grobner basis calculations are also
included. They are as follows:
	GCD	- greatest common divisor;
	LCM	- least common multiple;
	ZEROP	- test whether an element is zero;
	SIGNUM  - the sign of a ring element (+1, -1 or zero);
	UNIT	- the unit of the ring;
	NUMERATOR - the numerator, if a ring of fractions
	DENOMINATOR - the denominator, if a ring of fractions
	LENGTH  - an integer giving the approximate length
		of the representation; for example, for integers
		its default binding is #'integer-length;
"
  + - * / gcd lcm zerop unit length signum numerator denominator)

(defvar *ring-of-integers*
  (make-ring :+ #'+
	     :- #'-
	     :* #'*
	     :/ #'floor
	     :gcd #'gcd
	     :lcm #'lcm
	     :zerop #'zerop
	     :signum #'signum
	     :unit 1
	     :length #'integer-length
	     :numerator #'numerator
	     :denominator #'denominator)
  "Operations in the ring of integers.")

(defvar *field-of-rationals*
  (make-ring
   :+ #'+
   :- #'-
   :* #'*
   :/ #'/
   :gcd #'(lambda (&rest r) (declare (ignore r)) 1)
   :lcm #'(lambda (&rest r) (apply #'* r))
   :zerop #'zerop
   :signum #'signum
   :unit 1
   :length #'(lambda (x) (+ (integer-length (numerator x))
			    (integer-length (denominator x))))
   :numerator #'numerator
   :denominator #'denominator)
  "Operations on the field of rational numbers.")

(defun field-modulo-prime (modulus)
  "Return a RING structure with operations bound
to the arithmetical operations modulo MODULUS, which
should be a prime."
  (make-ring
   :+ #'(lambda (&rest r) (mod (apply #'+ r) modulus))
   :- #'(lambda (&rest r) (mod (apply #'- r) modulus))
   :* #'(lambda (&rest r) (mod (apply #'* r) modulus))
   :/ (make-modular-division modulus)
   :gcd #'(lambda (&rest r) (declare (ignore r)) 1)
   :lcm #'(lambda (&rest r) (mod (apply #'* r) modulus))
   :zerop #'zerop
   :signum #'(lambda (x) (if (zerop x) 0 1))
   :unit 1
   :length #'(lambda (x) (declare (ignore x)) 1)
   :numerator #'identity
   :denominator #'(lambda (x) (declare (ignore x)) 1)))


(defvar *coefficient-ring* *ring-of-integers*
  "The default RING structure, used in most operations
on the coefficients of polynomials. It should be carefully
set if rings other than the default ring is used.")

@


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;;(proclaim '(optimize (speed 0) (debug 3)))
(proclaim '(optimize (speed 3) (debug 0)))
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@d37 2
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(proclaim '(optimize (speed 0) (debug 3)))
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1.1
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	$Id: coefficient-ring.lisp,v 1.24 1997/12/13 15:56:19 marek Exp $
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