(module lie-group-Rn-test "generics.ss"
  (require "test.ss" "lie-group-Rn.ss" "lie-groups.ss" "tuples.ss" "manifolds.ss")
  
  (provide lie-group-Rn-test-suite)
   
  (define R6 (Rn 6))
  (define R6-chart (slot-ref R6 'standard-chart))
  
  (define R6-chi (slot-ref R6-chart 'chi))
  (define R6-chiinv (slot-ref R6-chart 'chiinv))

  (define-named-coordinates (x y z u v w) R6-chart)
  
  (define lie-group-Rn-test-suite
    (test-suite
     "lie-groups.ss test suite"
     (test-case 
      "(* g g^-1) ?=? identity"
      (let ((g (R6-chiinv (up 1 2 3 4 5 6))))
        (check-equals? (R6-chi (* g (/ g)))
                       (R6-chi (slot-ref R6 'identity)))))
     (test-case
      "Extend d/dx equals d/dx"
      (let ((ext (natural-extension R6)))
        (let ((ed/dx (ext d/dx))
              (e (slot-ref R6 'identity)))
          (let ((d/dxc ((vector-field->component-field d/dx R6-chart) e))
                (ed/dxc ((vector-field->component-field ed/dx R6-chart) e)))
            (check-equals? d/dxc ed/dxc))
          (let ((m (R6-chiinv (up 23 578 82 02 5234 876))))
            (let ((d/dxc ((vector-field->component-field d/dx R6-chart) m))
                  (ed/dxc ((vector-field->component-field ed/dx R6-chart) m)))
              (check-equals? d/dxc ed/dxc))))))
     (test-case
      "Is R6 abelian?"
      (let ((f (structure-constants R6 R6-chart)))
        (check-equals? f
                       (* f 0)))))))