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Manual equation for ifb incorrect. #4197

Open rtoy opened 1 month ago

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:41:45 Created by richardgobeli on 2021-10-15 00:29:01 Original: https://sourceforge.net/p/maxima/bugs/3877

The equation at the bottom should not have the last term using -ifri times itr. It was shown few lines above from actual output, but having different dummy indices and ifrs are on the end and not the beginning. A sample of the correct text is here:

(%i7) ishow(ifb([a,b,c]))$ %3 %4 (%t7) (ifri - ifri ) ifr ifr a %3,%4 a %4,%3 b c

This is the leading text before the wrong equation so it would be easier to find below. This was copied from the manual.

The frame bracket itself is defined in terms of the frame field and frame metric. Two alternate methods of computation are used depending on the value of frame_bracket_form. If true (the default) or if the itorsion_flag is true:

This is in the gray box. d e f ifb = ifr ifr (ifri - ifri - ifri itr ) abc b c a d,e a e,d a f d e

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rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:41:47 Created by vttoth on 2021-10-15 04:29:04 Original: https://sourceforge.net/p/maxima/bugs/3877/#8a4f

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:41:50 Created by richardgobeli on 2021-10-16 06:25:18 Original: https://sourceforge.net/p/maxima/bugs/3877/#2645

The document is definitely wrong, because the frame bracket does not have torsion in its calculation. The text in the gray box should not have the third term.

the two descriptions of the two versions are not the same. The first document description has three terms with the itr included, which definitely is incorrect.

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rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:41:54 Created by vttoth on 2021-10-18 06:17:41 Original: https://sourceforge.net/p/maxima/bugs/3877/#db50

Diff:


--- old
+++ new
@@ -0,0 +1 @@
+ifb.png (4.0 kB; image/png)
rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:41:58 Created by vttoth on 2021-10-18 06:17:41 Original: https://sourceforge.net/p/maxima/bugs/3877/#cdaa

See attached.

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:42:01 Created by richardgobeli on 2021-10-18 14:38:47 Original: https://sourceforge.net/p/maxima/bugs/3877/#c106

Ok, I get it now. It is good.
I see the ctensor code has only one version of the frame_bracket. Does that make sense?

I have been trying to model teleparallel gravity with torsion and was trying to understand the torsion, frame bracket, curvature, and contorsion.

rtoy commented 1 month ago

Imported from SourceForge on 2024-07-09 19:42:05 Created by vttoth on 2021-10-19 03:46:48 Original: https://sourceforge.net/p/maxima/bugs/3877/#e8f3

Well, it makes sense, but only because ctensor doesn't compute a torsion tensor in the first place. The only function that explicitly uses a torsion tensor is contortion(tr), which in turn expects the user to supply the tensor. I suppose we could add an optional tr parameter to frame_bracket() and then include a term like -sum(tr[m%,e%,f%]*fri[a,m%],m%,1,dim) in frame_bracket...