blarg

1 files changed, 53 insertions, 2 deletions

diff --git a/work/calculus_play.scm b/work/calculus_play.scm
index 7a043df..fe8a322 100644
--- a/work/calculus_play.scm
+++ b/work/calculus_play.scm
@@ -1,6 +1,56 @@
 
-;;; Jan 26th
+;;; Jan 29th
+
+(load "~/thesis/scmutils/src/calculus/load.scm")
+
+
+;(define R2 (make-manifold R^n-type 2)) ; doesn't work, so...
+(define R2 (rectangular 2))
+;(define U (patch 'origin R2)) ; also undefined so going to AIM-2005-003.pdf
+
+(define R2 (rectangular 2))
+(define P2 (polar/cylindrical 2))
+
+(define R2-chi-inverse (R2 '->point))
+(define R2-chi-inverse (R2 '->coords))
+(define P2-chi (P2 '->coords))
+(define P2-chi-inverse (P2 '->point))
 
+#|
+(define cartesian-plane-basis
+    (coordinate-system->basis cartesian-plane))
+(define d/dx (coordinate-basis-vector-field cartesian-plane 'd/dx 0))
+(define d/dy (coordinate-basis-vector-field cartesian-plane 'd/dy 1))
+(define dx (coordinate-basis-1form cartesian-plane 'dx 0))
+(define dy (coordinate-basis-1form cartesian-plane 'dy 0))
+
+
+(define polar-basis (coordinate-system->basis polar))
+(define r (compose (component 0) (polar '->coords)))
+(define theta (compose (component 1) (polar '->coords)))
+(define d/dr (coordinate-basis-vector-field polar 'd/dr 0))
+(define d/dtheta (coordinate-basis-vector-field polar 'd/dtheta 1))
+(define dr (coordinate-basis-1form polar 'dr 0))
+(define dtheta (coordinate-basis-1form polar 'dtheta 1))
+
+(define X
+    (components->vector-field
+         (up (literal-function 'X^0 (-> (UP Real Real) Real))
+                    (literal-function 'X^1 (-> (UP Real Real) Real)))
+            cartesian-plane
+               'X))
+
+(define V
+    (components->vector-field
+         (up (literal-function 'V^0 (-> (UP Real Real) Real))
+                    (literal-function 'V^1 (-> (UP Real Real) Real)))
+            cartesian-plane
+               'V))
+|#
+
+;;; the following doesn't work at all...
+;;; Jan 26th
+#|
 (declare (usual-integrations))
 (load "~/thesis/scmutils/src/calculus/load.scm")
 
@@ -14,4 +64,5 @@
 
 (define J (- (* x d/dy) (* y (d/dx))))
 
-(define omega (literal-1form-field 'a R2-rect))
\ No newline at end of file
+(define omega (literal-1form-field 'a R2-rect))
+|#