;    Copyright (C) 2006  Will M. Farr <farr@mit.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.
;
;    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.,
;    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.


(module lie-group-Rn "generics.ss"
  (require "lie-groups.ss" "manifolds.ss" "tuples.ss")
  
  (provide Rn)
  
  (define (Rn n)
    (let-values (((Rn-chart Rn)
                  (recursive-make 
                   (Rn-chart <chart>
                             :dim n
                             :chi (lambda (m) (slot-ref m 'point))
                             :chiinv (lambda (x)
                                       (make <lie-group-element>
                                             :point x
                                             :group Rn)))
                   (Rn <lie-group>
                       :standard-chart Rn-chart
                       :identity ((slot-ref Rn-chart 'chiinv) (up-unfold (lambda (i) 0) n))
                       :multiplication (let ((chi (slot-ref Rn-chart 'chi))
                                             (chiinv (slot-ref Rn-chart 'chiinv)))
                                         (lambda (g1 g2)
                                           (chiinv (+ (chi g1) (chi g2)))))
                       :inverse (let ((chi (slot-ref Rn-chart 'chi))
                                      (chiinv (slot-ref Rn-chart 'chiinv)))
                                  (lambda (g)
                                    (chiinv (- (chi g)))))))))
      Rn)))