Copyright 2006 Massachusetts Institute of Technology.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Image saved on Wednesday June 21, 2006 at 10:31:10 PM
  Release 7.7.90.+                 || Microcode 14.17 || Runtime 15.6
  SF 4.41                          || LIAR 4.117      || Edwin 3.116
  ScmUtils Mechanics . Winter 2006
;You are in an interaction window of the Edwin editor.
;Type C-h for help.  C-h m will describe some commands.

(cd "/usr/local/scmutils/src/calculus")
;Value: #[pathname 12 "/usr/local/scmutils/src/calculus/"]

;Value: spacetime

;Value: (rectangular spacetime)

;Value: (spherical spacetime)

;Value: spacetime-rectangular

;Value: spacetime-spherical

;Value: (rectangular spacetime)

(clobbering t)
(clobbering d/dt)
(clobbering dt)
;Value: (spherical spacetime)

;Value: r-event

;Value: s-event

;Value: dT

;Value: dX

;Value: dY

;Value: dZ

;Value: dR

;Value: dTheta

;Value: dPhi

;Value: Schwarzschild-metric

;Value: S-metric

;Value: Gam


#| Result:
(down
 (down
  (up
   0
   (+ (/ (* G M) (expt r0 2))
      (/ (* -2 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 3))))
   0
   0)
  (up (/ (* -1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 2)) (* G M r0))) 0 0 0)
  (up 0 0 0 0)
  (up 0 0 0 0))
 (down (up (/ (* -1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 2)) (* G M r0))) 0 0 0)
       (up 0 (/ (* 1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 2)) (* G M r0))) 0 0)
       (up 0 0 (/ 1 r0) 0)
       (up 0 0 0 (/ 1 r0)))
 (down (up 0 0 0 0)
       (up 0 0 (/ 1 r0) 0)
       (up 0 (+ (* -1 r0) (/ (* 2 G M) (expt c 2))) 0 0)
       (up 0 0 0 (/ (cos theta0) (sin theta0))))
 (down
  (up 0 0 0 0)
  (up 0 0 0 (/ 1 r0))
  (up 0 0 0 (/ (cos theta0) (sin theta0)))
  (up
   0
   (+ (* -1 r0 (expt (sin theta0) 2)) (/ (* 2 G M (expt (sin theta0) 2)) (expt c 2)))
   (* -1 (sin theta0) (cos theta0))
   0)))
|#process time: 561770 (520480 RUN + 41290 GC); real time: 563907
;Unspecified return value

;Value: Gamma1

process time: 435060 (385240 RUN + 49820 GC); real time: 436181
;Value: Gamma-comma


#| Result:
(down
 (down (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
       (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
       (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
       (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0)))
 (down
  (down
   (up
    0
    (+ (/ (* -2 G M) (expt r0 3))
       (/ (* 6 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4))))
    0
    0)
   (up
    (+
     (/
      (* -1/2 G M (expt c 2))
      (+ (* 1/4 (expt c 4) (expt r0 3))
         (* -1 G M (expt c 2) (expt r0 2))
         (* (expt G 2) (expt M 2) r0)))
     (/
      (* 1/2 (expt G 2) (expt M 2))
      (+ (* 1/4 (expt c 4) (expt r0 4))
         (* -1 G M (expt c 2) (expt r0 3))
         (* (expt G 2) (expt M 2) (expt r0 2)))))
    0
    0
    0)
   (up 0 0 0 0)
   (up 0 0 0 0))
  (down
   (up
    (+
     (/
      (* -1/2 G M (expt c 2))
      (+ (* 1/4 (expt c 4) (expt r0 3))
         (* -1 G M (expt c 2) (expt r0 2))
         (* (expt G 2) (expt M 2) r0)))
     (/
      (* 1/2 (expt G 2) (expt M 2))
      (+ (* 1/4 (expt c 4) (expt r0 4))
         (* -1 G M (expt c 2) (expt r0 3))
         (* (expt G 2) (expt M 2) (expt r0 2)))))
    0
    0
    0)
   (up
    0
    (+
     (/
      (* 1/2 G M (expt c 2))
      (+ (* 1/4 (expt c 4) (expt r0 3))
         (* -1 G M (expt c 2) (expt r0 2))
         (* (expt G 2) (expt M 2) r0)))
     (/
      (* -1/2 (expt G 2) (expt M 2))
      (+ (* 1/4 (expt c 4) (expt r0 4))
         (* -1 G M (expt c 2) (expt r0 3))
         (* (expt G 2) (expt M 2) (expt r0 2)))))
    0
    0)
   (up 0 0 (/ -1 (expt r0 2)) 0)
   (up 0 0 0 (/ -1 (expt r0 2))))
  (down (up 0 0 0 0) (up 0 0 (/ -1 (expt r0 2)) 0) (up 0 -1 0 0) (up 0 0 0 0))
  (down (up 0 0 0 0)
        (up 0 0 0 (/ -1 (expt r0 2)))
        (up 0 0 0 0)
        (up 0 (* -1 (expt (sin theta0) 2)) 0 0)))
 (down
  (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
  (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
  (down (up 0 0 0 0)
        (up 0 0 0 0)
        (up 0 0 0 0)
        (up 0 0 0 (/ -1 (expt (sin theta0) 2))))
  (down
   (up 0 0 0 0)
   (up 0 0 0 0)
   (up 0 0 0 (/ -1 (expt (sin theta0) 2)))
   (up
    0
    (+ (* -2 r0 (sin theta0) (cos theta0))
       (/ (* 4 G M (sin theta0) (cos theta0)) (expt c 2)))
    (+ 1 (* -2 (expt (cos theta0) 2)))
    0)))
 (down (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
       (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
       (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
       (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))))
|#process time: 810550 (725840 RUN + 84710 GC); real time: 812352
;Unspecified return value

;Value: Gamma-comma1

;Value: Riemann-tensor1

;Value: R


#| Result:
(down
 (down
  (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
  (down
   (up
    0
    (+ (/ (* -2 G M) (expt r0 3))
       (/ (* 4 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4))))
    0
    0)
   (up (/ (* G M) (+ (* -1/2 (expt c 2) (expt r0 3)) (* G M (expt r0 2)))) 0 0 0)
   (up 0 0 0 0)
   (up 0 0 0 0))
  (down
   (up
    0
    0
    (+ (/ (* G M) (expt r0 3))
       (/ (* -2 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4))))
    0)
   (up 0 0 0 0)
   (up (/ (* G M) (* (expt c 2) r0)) 0 0 0)
   (up 0 0 0 0))
  (down
   (up
    0
    0
    0
    (+ (/ (* G M) (expt r0 3))
       (/ (* -2 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4)))))
   (up 0 0 0 0)
   (up 0 0 0 0)
   (up (/ (* G M (expt (sin theta0) 2)) (* (expt c 2) r0)) 0 0 0)))
 (down
  (down
   (up
    0
    (+ (/ (* 2 G M) (expt r0 3))
       (/ (* -4 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4))))
    0
    0)
   (up (/ (* -1 G M) (+ (* -1/2 (expt c 2) (expt r0 3)) (* G M (expt r0 2)))) 0 0 0)
   (up 0 0 0 0)
   (up 0 0 0 0))
  (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
  (down
   (up 0 0 0 0)
   (up 0 0 (/ (* 1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 3)) (* G M (expt r0 2)))) 0)
   (up 0 (/ (* G M) (* (expt c 2) r0)) 0 0)
   (up 0 0 0 0))
  (down
   (up 0 0 0 0)
   (up 0 0 0 (/ (* 1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 3)) (* G M (expt r0 2)))))
   (up 0 0 0 0)
   (up 0 (/ (* G M (expt (sin theta0) 2)) (* (expt c 2) r0)) 0 0)))
 (down
  (down
   (up
    0
    0
    (+ (/ (* -1 G M) (expt r0 3))
       (/ (* 2 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4))))
    0)
   (up 0 0 0 0)
   (up (/ (* -1 G M) (* (expt c 2) r0)) 0 0 0)
   (up 0 0 0 0))
  (down
   (up 0 0 0 0)
   (up 0
       0
       (/ (* -1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 3)) (* G M (expt r0 2))))
       0)
   (up 0 (/ (* -1 G M) (* (expt c 2) r0)) 0 0)
   (up 0 0 0 0))
  (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))
  (down (up 0 0 0 0)
        (up 0 0 0 0)
        (up 0 0 0 (/ (* 2 G M) (* (expt c 2) r0)))
        (up 0 0 (/ (* -2 G M (expt (sin theta0) 2)) (* (expt c 2) r0)) 0)))
 (down
  (down
   (up
    0
    0
    0
    (+ (/ (* -1 G M) (expt r0 3))
       (/ (* 2 (expt G 2) (expt M 2)) (* (expt c 2) (expt r0 4)))))
   (up 0 0 0 0)
   (up 0 0 0 0)
   (up (/ (* -1 G M (expt (sin theta0) 2)) (* (expt c 2) r0)) 0 0 0))
  (down
   (up 0 0 0 0)
   (up 0
       0
       0
       (/ (* -1/2 G M) (+ (* -1/2 (expt c 2) (expt r0 3)) (* G M (expt r0 2)))))
   (up 0 0 0 0)
   (up 0 (/ (* -1 G M (expt (sin theta0) 2)) (* (expt c 2) r0)) 0 0))
  (down (up 0 0 0 0)
        (up 0 0 0 0)
        (up 0 0 0 (/ (* -2 G M) (* (expt c 2) r0)))
        (up 0 0 (/ (* 2 G M (expt (sin theta0) 2)) (* (expt c 2) r0)) 0))
  (down (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0) (up 0 0 0 0))))
|#process time: 2079430 (1839230 RUN + 240200 GC); real time: 2085584
;Unspecified return value

;Value: R1

;Value: Ricci-tensor1

;Value: Ricci


#| Result:
(down (down 0 0 0 0) (down 0 0 0 0) (down 0 0 0 0) (down 0 0 0 0))
|#process time: 77580 (68300 RUN + 9280 GC); real time: 77739
;Unspecified return value

;Value: 5721677

;Value: 31

;Value: 118289650

;Value: 1059142

(517218 4302 (??? value-expression))
(0 1393665 (??? coords))
(339598 1512386 (??? point))
(0 1 (??? coords))
(0 0 (??? point))
(0 0 Riemann-tensor)
(0 0 t:covariant-derivative)
(0 1 Christoffel)
(0 1 invert-metric)
(0 2 contract)
(0 797 tensor-product)
(131 130 coefficient-structure->tensor-field)
(256 6 tensor-field->coefficient-structure)
(0 2 t:comma)
(520 7 ff->tf)
(516 4 vf->tf)
(521519 1 memoized-abstract-structure-function)
(4911180 138468 memoized-simplify)
(0 0 complex-rules)
(0 0 exp-expand)
(0 0 exp-contract)
(0 0 exp->sincos)
(0 0 sincos->exp2)
(0 0 sincos->exp1)
(68222 28308 sincos-random)
(81130 15395 flush-obvious-ones)
(78297 18228 split-high-degree-sines)
(68089 28436 split-high-degree-cosines)
(0 0 cos^2->sin^2)
(68166 28359 sin^2->cos^2)
(0 0 contract-expt-trig)
(0 0 contract-multiangle)
(0 0 expand-multiangle)
(68553 146165 angular-parity)
(68264 28261 sincos->trig)
(6 138528 trig->sincos)
(0 0 canonicalize-partials)
(0 0 log-expand)
(0 0 log-contract)
(0 0 logexp->specfun)
(0 0 specfun->logexp)
(74809 50800 sqrt-contract)
(156294 213491 sqrt-expand)
(0 0 special-trig)
(396086 237786 universal-reductions)
(0 0 diff:cosh)
(0 0 diff:sinh)
(0 1044288 diff:atan2)
(0 0 diff:atan1)
(0 1044288 diff:acos)
(0 0 diff:asin)
(0 696832 diff:cos)
(348416 696832 diff:sin)
(0 0 diff:log)
(0 0 diff:exp)
(0 0 diff:expt)
(12 520 diff:power)
(0 1044468 diff:sqrt)
(0 0 diff:invert)
(0 0 diff:negate)
(0 1044468 diff:/)
(696844 6269300 diff:*)
(0 0 diff:-)
(12 2089188 diff:+)
;Value: done