Display the values of Christoffel symbols in simplified form in Maxima software
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I have calculated all Christoffels symbols (my metric is symmetric type) by hand and now I am trying a lot to compute all of the non-zero values of Christoffel symbols by maxima just for confirmation only. I know that maxima only shows the UNIQUE values of Christoffel symbols. All looks good to me but the problem is maxima shows the values of Christoffel symbols in general format and it looks really messy. Is there any way so that I can view the outputs (for my case, the values of Christoffel symbols) in simplified form? Expecting experts' suggestion here. Thanks in advance. The metric and output form that I found Looks like:
the metric:
[ - a (2 ψ + 1) - 2 Bx a - 2 By a - 2 Bz a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bx a - 2 Bx a a (hxx - 2 S + 1) a hxy ]
[ ]
[ 2 2 2 2 ]
[ - 2 By a a (hxx - 2 S + 1) a hxz - 2 By a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bz a a hxy - 2 By a a hyx ]
here is one output form:
(%t44) mcs = ((2 a hxy hxy hxz + (4 By a hxx + (4 By - 8 By S) a) hxy
4, 4, 4 z z
+ (4 By a hxx + (4 By - 8 By S) a) hxy - 16 Bx By By a) ψ
z z z z
+ ((2 Bx a hxy + 4 Bx Bz a ) hxz + ((4 By S - 2 By) a - 2 By a hxx) hxy
t t t t
2
+ 2 Bz a hxx + ((- 8 Bz S) + 4 Bz + 4 Bx By) a hxx
t t
2 2
+ (8 Bz S + ((- 8 Bz) - 8 Bx By) S + 2 Bz + 8 Bx By + 4 Bx By) a ) hyx
t
+ ((a hxy + 4 Bx Bz a) hxy + 4 Bx Bz a hxy + 8 Bx Bz Bz a) hxz
z z z
2
+ (4 By a hxy + (2 By - 4 By Bz) a hxx
2
+ ((8 By Bz - 4 By) S - 4 By Bz + 8 Bx By + 2 By) a) hxy
z
+ ((2 By - 4 By Bz ) a hxx + ((8 By Bz - 4 By ) S - 4 By Bz
z z z z z
2
+ (8 Bx By + 2) By ) a) hxy + 4 Bz Bz a hxx
z z
+ ((- 16 Bz Bz S) + (8 Bz + 8 Bx By) Bz + 8 Bx By Bz) a hxx
z z z
2
+ (16 Bz Bz S + (((- 16 Bz) - 16 Bx By) Bz - 16 Bx By Bz) S
z z z
2
+ (4 Bz + 16 Bx By + 8 Bx By) Bz + (16 Bx By + 8 Bx) By Bz
z z
2 2
+ (16 Bx - 8 Bx) By By ) a)/(((4 Bx a hxz + 2 a hxx + (4 - 8 S) a hxx
z
2 2
+ (8 S - 8 S + 2) a) hyx + 2 a hxy hxz
2
+ (8 By a hxx + (8 By - 16 By S) a) hxy - 16 Bx By a) ψ
2 2
+ ((2 Bx - 4 Bx ) a hxz + a hxx + ((- 4 S) + 8 Bx By + 2) a hxx
2 2
+ (4 S + ((- 16 Bx By) - 4) S + 8 Bx By + 8 Bx By + 1) a) hyx
2 2 2 2
+ (a hxy + 8 Bx Bz a hxy + 8 Bx Bz a) hxz + 4 By a hxy
2
+ ((4 By - 8 By Bz) a hxx + ((16 By Bz - 8 By) S - 8 By Bz + 16 Bx By + 4 By)
2 2 2 2
a) hxy + 4 Bz a hxx + ((- 16 Bz S) + 8 Bz + 16 Bx By Bz) a hxx
2 2 2 2
+ (16 Bz S + ((- 16 Bz ) - 32 Bx By Bz) S + 4 Bz
2 2 2
+ (32 Bx By + 16 Bx By) Bz + (16 Bx - 8 Bx) By ) a)
tensors maxima-software maximal-subgroup
asked Jan 10 at 2:37
PhotonPhoton
455
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add a comment |
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I have calculated all Christoffels symbols (my metric is symmetric type) by hand and now I am trying a lot to compute all of the non-zero values of Christoffel symbols by maxima just for confirmation only. I know that maxima only shows the UNIQUE values of Christoffel symbols. All looks good to me but the problem is maxima shows the values of Christoffel symbols in general format and it looks really messy. Is there any way so that I can view the outputs (for my case, the values of Christoffel symbols) in simplified form? Expecting experts' suggestion here. Thanks in advance. The metric and output form that I found Looks like:
the metric:
[ - a (2 ψ + 1) - 2 Bx a - 2 By a - 2 Bz a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bx a - 2 Bx a a (hxx - 2 S + 1) a hxy ]
[ ]
[ 2 2 2 2 ]
[ - 2 By a a (hxx - 2 S + 1) a hxz - 2 By a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bz a a hxy - 2 By a a hyx ]
here is one output form:
(%t44) mcs = ((2 a hxy hxy hxz + (4 By a hxx + (4 By - 8 By S) a) hxy
4, 4, 4 z z
+ (4 By a hxx + (4 By - 8 By S) a) hxy - 16 Bx By By a) ψ
z z z z
+ ((2 Bx a hxy + 4 Bx Bz a ) hxz + ((4 By S - 2 By) a - 2 By a hxx) hxy
t t t t
2
+ 2 Bz a hxx + ((- 8 Bz S) + 4 Bz + 4 Bx By) a hxx
t t
2 2
+ (8 Bz S + ((- 8 Bz) - 8 Bx By) S + 2 Bz + 8 Bx By + 4 Bx By) a ) hyx
t
+ ((a hxy + 4 Bx Bz a) hxy + 4 Bx Bz a hxy + 8 Bx Bz Bz a) hxz
z z z
2
+ (4 By a hxy + (2 By - 4 By Bz) a hxx
2
+ ((8 By Bz - 4 By) S - 4 By Bz + 8 Bx By + 2 By) a) hxy
z
+ ((2 By - 4 By Bz ) a hxx + ((8 By Bz - 4 By ) S - 4 By Bz
z z z z z
2
+ (8 Bx By + 2) By ) a) hxy + 4 Bz Bz a hxx
z z
+ ((- 16 Bz Bz S) + (8 Bz + 8 Bx By) Bz + 8 Bx By Bz) a hxx
z z z
2
+ (16 Bz Bz S + (((- 16 Bz) - 16 Bx By) Bz - 16 Bx By Bz) S
z z z
2
+ (4 Bz + 16 Bx By + 8 Bx By) Bz + (16 Bx By + 8 Bx) By Bz
z z
2 2
+ (16 Bx - 8 Bx) By By ) a)/(((4 Bx a hxz + 2 a hxx + (4 - 8 S) a hxx
z
2 2
+ (8 S - 8 S + 2) a) hyx + 2 a hxy hxz
2
+ (8 By a hxx + (8 By - 16 By S) a) hxy - 16 Bx By a) ψ
2 2
+ ((2 Bx - 4 Bx ) a hxz + a hxx + ((- 4 S) + 8 Bx By + 2) a hxx
2 2
+ (4 S + ((- 16 Bx By) - 4) S + 8 Bx By + 8 Bx By + 1) a) hyx
2 2 2 2
+ (a hxy + 8 Bx Bz a hxy + 8 Bx Bz a) hxz + 4 By a hxy
2
+ ((4 By - 8 By Bz) a hxx + ((16 By Bz - 8 By) S - 8 By Bz + 16 Bx By + 4 By)
2 2 2 2
a) hxy + 4 Bz a hxx + ((- 16 Bz S) + 8 Bz + 16 Bx By Bz) a hxx
2 2 2 2
+ (16 Bz S + ((- 16 Bz ) - 32 Bx By Bz) S + 4 Bz
2 2 2
+ (32 Bx By + 16 Bx By) Bz + (16 Bx - 8 Bx) By ) a)
tensors maxima-software maximal-subgroup
asked Jan 10 at 2:37
PhotonPhoton
455
$endgroup$
add a comment |
$begingroup$
I have calculated all Christoffels symbols (my metric is symmetric type) by hand and now I am trying a lot to compute all of the non-zero values of Christoffel symbols by maxima just for confirmation only. I know that maxima only shows the UNIQUE values of Christoffel symbols. All looks good to me but the problem is maxima shows the values of Christoffel symbols in general format and it looks really messy. Is there any way so that I can view the outputs (for my case, the values of Christoffel symbols) in simplified form? Expecting experts' suggestion here. Thanks in advance. The metric and output form that I found Looks like:
the metric:
[ - a (2 ψ + 1) - 2 Bx a - 2 By a - 2 Bz a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bx a - 2 Bx a a (hxx - 2 S + 1) a hxy ]
[ ]
[ 2 2 2 2 ]
[ - 2 By a a (hxx - 2 S + 1) a hxz - 2 By a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bz a a hxy - 2 By a a hyx ]
here is one output form:
(%t44) mcs = ((2 a hxy hxy hxz + (4 By a hxx + (4 By - 8 By S) a) hxy
4, 4, 4 z z
+ (4 By a hxx + (4 By - 8 By S) a) hxy - 16 Bx By By a) ψ
z z z z
+ ((2 Bx a hxy + 4 Bx Bz a ) hxz + ((4 By S - 2 By) a - 2 By a hxx) hxy
t t t t
2
+ 2 Bz a hxx + ((- 8 Bz S) + 4 Bz + 4 Bx By) a hxx
t t
2 2
+ (8 Bz S + ((- 8 Bz) - 8 Bx By) S + 2 Bz + 8 Bx By + 4 Bx By) a ) hyx
t
+ ((a hxy + 4 Bx Bz a) hxy + 4 Bx Bz a hxy + 8 Bx Bz Bz a) hxz
z z z
2
+ (4 By a hxy + (2 By - 4 By Bz) a hxx
2
+ ((8 By Bz - 4 By) S - 4 By Bz + 8 Bx By + 2 By) a) hxy
z
+ ((2 By - 4 By Bz ) a hxx + ((8 By Bz - 4 By ) S - 4 By Bz
z z z z z
2
+ (8 Bx By + 2) By ) a) hxy + 4 Bz Bz a hxx
z z
+ ((- 16 Bz Bz S) + (8 Bz + 8 Bx By) Bz + 8 Bx By Bz) a hxx
z z z
2
+ (16 Bz Bz S + (((- 16 Bz) - 16 Bx By) Bz - 16 Bx By Bz) S
z z z
2
+ (4 Bz + 16 Bx By + 8 Bx By) Bz + (16 Bx By + 8 Bx) By Bz
z z
2 2
+ (16 Bx - 8 Bx) By By ) a)/(((4 Bx a hxz + 2 a hxx + (4 - 8 S) a hxx
z
2 2
+ (8 S - 8 S + 2) a) hyx + 2 a hxy hxz
2
+ (8 By a hxx + (8 By - 16 By S) a) hxy - 16 Bx By a) ψ
2 2
+ ((2 Bx - 4 Bx ) a hxz + a hxx + ((- 4 S) + 8 Bx By + 2) a hxx
2 2
+ (4 S + ((- 16 Bx By) - 4) S + 8 Bx By + 8 Bx By + 1) a) hyx
2 2 2 2
+ (a hxy + 8 Bx Bz a hxy + 8 Bx Bz a) hxz + 4 By a hxy
2
+ ((4 By - 8 By Bz) a hxx + ((16 By Bz - 8 By) S - 8 By Bz + 16 Bx By + 4 By)
2 2 2 2
a) hxy + 4 Bz a hxx + ((- 16 Bz S) + 8 Bz + 16 Bx By Bz) a hxx
2 2 2 2
+ (16 Bz S + ((- 16 Bz ) - 32 Bx By Bz) S + 4 Bz
2 2 2
+ (32 Bx By + 16 Bx By) Bz + (16 Bx - 8 Bx) By ) a)
tensors maxima-software maximal-subgroup
asked Jan 10 at 2:37
PhotonPhoton
455
$endgroup$
I have calculated all Christoffels symbols (my metric is symmetric type) by hand and now I am trying a lot to compute all of the non-zero values of Christoffel symbols by maxima just for confirmation only. I know that maxima only shows the UNIQUE values of Christoffel symbols. All looks good to me but the problem is maxima shows the values of Christoffel symbols in general format and it looks really messy. Is there any way so that I can view the outputs (for my case, the values of Christoffel symbols) in simplified form? Expecting experts' suggestion here. Thanks in advance. The metric and output form that I found Looks like:
the metric:
[ - a (2 ψ + 1) - 2 Bx a - 2 By a - 2 Bz a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bx a - 2 Bx a a (hxx - 2 S + 1) a hxy ]
[ ]
[ 2 2 2 2 ]
[ - 2 By a a (hxx - 2 S + 1) a hxz - 2 By a ]
[ ]
[ 2 2 2 2 ]
[ - 2 Bz a a hxy - 2 By a a hyx ]
here is one output form:
(%t44) mcs = ((2 a hxy hxy hxz + (4 By a hxx + (4 By - 8 By S) a) hxy
4, 4, 4 z z
+ (4 By a hxx + (4 By - 8 By S) a) hxy - 16 Bx By By a) ψ
z z z z
+ ((2 Bx a hxy + 4 Bx Bz a ) hxz + ((4 By S - 2 By) a - 2 By a hxx) hxy
t t t t
2
+ 2 Bz a hxx + ((- 8 Bz S) + 4 Bz + 4 Bx By) a hxx
t t
2 2
+ (8 Bz S + ((- 8 Bz) - 8 Bx By) S + 2 Bz + 8 Bx By + 4 Bx By) a ) hyx
t
+ ((a hxy + 4 Bx Bz a) hxy + 4 Bx Bz a hxy + 8 Bx Bz Bz a) hxz
z z z
2
+ (4 By a hxy + (2 By - 4 By Bz) a hxx
2
+ ((8 By Bz - 4 By) S - 4 By Bz + 8 Bx By + 2 By) a) hxy
z
+ ((2 By - 4 By Bz ) a hxx + ((8 By Bz - 4 By ) S - 4 By Bz
z z z z z
2
+ (8 Bx By + 2) By ) a) hxy + 4 Bz Bz a hxx
z z
+ ((- 16 Bz Bz S) + (8 Bz + 8 Bx By) Bz + 8 Bx By Bz) a hxx
z z z
2
+ (16 Bz Bz S + (((- 16 Bz) - 16 Bx By) Bz - 16 Bx By Bz) S
z z z
2
+ (4 Bz + 16 Bx By + 8 Bx By) Bz + (16 Bx By + 8 Bx) By Bz
z z
2 2
+ (16 Bx - 8 Bx) By By ) a)/(((4 Bx a hxz + 2 a hxx + (4 - 8 S) a hxx
z
2 2
+ (8 S - 8 S + 2) a) hyx + 2 a hxy hxz
2
+ (8 By a hxx + (8 By - 16 By S) a) hxy - 16 Bx By a) ψ
2 2
+ ((2 Bx - 4 Bx ) a hxz + a hxx + ((- 4 S) + 8 Bx By + 2) a hxx
2 2
+ (4 S + ((- 16 Bx By) - 4) S + 8 Bx By + 8 Bx By + 1) a) hyx
2 2 2 2
+ (a hxy + 8 Bx Bz a hxy + 8 Bx Bz a) hxz + 4 By a hxy
2
+ ((4 By - 8 By Bz) a hxx + ((16 By Bz - 8 By) S - 8 By Bz + 16 Bx By + 4 By)
2 2 2 2
a) hxy + 4 Bz a hxx + ((- 16 Bz S) + 8 Bz + 16 Bx By Bz) a hxx
2 2 2 2
+ (16 Bz S + ((- 16 Bz ) - 32 Bx By Bz) S + 4 Bz
2 2 2
+ (32 Bx By + 16 Bx By) Bz + (16 Bx - 8 Bx) By ) a)
tensors maxima-software maximal-subgroup
tensors maxima-software maximal-subgroup
asked Jan 10 at 2:37
PhotonPhoton
455
asked Jan 10 at 2:37
PhotonPhoton
455
asked Jan 10 at 2:37
PhotonPhoton
455
asked Jan 10 at 2:37
PhotonPhoton
455
asked Jan 10 at 2:37
PhotonPhoton
455
455
add a comment |
add a comment |
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