#4435 When using a frame field the icc2 or msc symbol is incorrect.

[Richard Gobeli]

I was using the attached paper and the example Macsyma program.
I found that using the cframe_flag: true the icc1 or lcs symbol is correct when accounting for the fri tensor difference. Macsyma used the mixed tensor for mfri = lfg . fri so the local index is raised.
Becaue the icc1 is not symmetrical then icc2 can't be symmetrical and ctensor forces icc2 to be symmetric.
This does not match what comes out of my Macsyma program or the attached paper for the icc2 or mcs symbol.
It took me a few days to realize the Macsyma icc2 from the Christof() function was just the last index raise from the icc1 symbol and not forced to be symmetric. icc1 and icc2 in this case are both not symmetrical.
Below is the code where mcs is forced to be symmterical even when cframe_flag is true.
This may also cause issues with the torsion flag and nomet flags.
In this case I think mcs is not used to calculate the riemann tensor, but lcs is used.
So currently the mcs is only a display in this case, but the attached paper uses mcs for more calculations that don't work.
I also needed to do the change for the frame_backet as in the other bug report below to make it match Macsyma by using mfri=lfg . fri in the frame_backet. There was a over all sign difference.
https://sourceforge.net/p/maxima/bugs/4425/

if symmmetric then
(
for i thru dim do
(
for j from i thru dim do
(
if not cframe_flag then for k thru dim do
(
lcs[i,j,k]:(diff(lg[j,k],ct_coords[i])
+diff(lg[k,i],ct_coords[j])-diff(lg[i,j],ct_coords[k]))/2,
lcs[j,i,k]:lcs[i,j,k]
),
for k thru dim do
(
mcs[i,j,k]:ctaylor
(
if diagmetric then ratsimp(_ug()[k,k]lcs[i,j,k])
else sum(_ug()[l%,k]lcs[i,j,l%],l%,1,dim)
),
if ratchristof then mcs[i,j,k]:ratsimp(mcs[i,j,k]),
mcs[j,i,k]:mcs[i,j,k], * this should not happen when cframe_flag is true.*
if ctorsion_flag then
(
mcs[i,j,k]:mcs[i,j,k]-kt[i,j,k],
if j#i then mcs[j,i,k]:mcs[j,i,k]-kt[j,i,k]
),
if cnonmet_flag then
(
mcs[i,j,k]:mcs[i,j,k]-nmc[i,j,k],
if j#i then mcs[j,i,k]:mcs[j,i,k]-nmc[j,i,k]
)
)
)
)
)

[Richard Gobeli]

It dropped the labels ctensor and shared code.

[Richard Gobeli]

The attachment also did not work. Document is title below
Derivation of Einstein–Cartan Theory from General Relativity by Richard James Petti.
paper 1301.1588v30 on arxiv.org

[Richard Gobeli]

This bug report is replaced by :
https://sourceforge.net/p/maxima/bugs/4438/
Please close.

[Jaime E. Villate]

closed by request of the user who created it.