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Computing Christoffel symbols in Maxima

maxima(%i2) load(ctensor)

maxima(%i3) depends([a,b],[t,r])

maxima(%i4) ct_coords:[t,r,O,P]

maxima<latex>
\mbox{\tt\red(\mathrm{\%o4}) \black}\left[ t , r , O , P \right]
</latex>
(%i5) lg:ident(4)

maxima(%i6) lg[1,1]:-exp(2*a)

maxima<latex>
\mbox{\tt\red(\mathrm{\%o6}) \black}-\mathe^{2list\*a}</latex>
(%i7) lg[2,2]:exp(2*b) 
maxima(%i8) lg[3,3]:r^2

maxima(%i9) lg[4,4]:r^2*sin(O)^2

maxima<latex>
\mbox{\tt\red(\mathrm{\%o9}) \black}r^2list\*\sin \left(O\right)^2
</latex>
(%i10) cmetric()

maxima(%i11) ug

maxima(%i12) christof(mcs)

maxima<latex>\mbox{\tt\red(\mathrm{\%t12}) \black}
\mathrm{mcs}_{1,1,1}={{d}\over{dlist\*t}}list\*a</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t13}) \black}\mathrm{mcs}_{1,1,2}={{d}\over{
dlist\*r}}list\*alist\*\mathe^{2list\*a-2list\*b}</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t14}) \black}\mathrm{mcs}_{1,2,1}={{d}\over{
dlist\*r}}list\*a</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t15}) \black}\mathrm{mcs}_{1,2,2}={{d}\over{
dlist\*t}}list\*b</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t16}) \black}\mathrm{mcs}_{2,2,1}=\mathe^{2list
\*b-2list\*a}list\*\left({{d}\over{dlist\*t}}list\*b\right)</latex>

maxima<latex>\mbox{\tt\red(\mathrm{\%t17}) \black}\mathrm{mcs}_{2,2,2}={{d
}\over{dlist\*r}}list\*b</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t18}) \black}\mathrm{mcs}_{2,3,3}={{1}\over{
r}}</latex>

maxima<latex>\mbox{\tt\red(\mathrm{\%t19}) \black}\mathrm{mcs}
_{2,4,4}={{1}\over{r}}</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t20}) \black}\mathrm{mcs}_{3,3,2}=-\mathe
^ {- 2list\*b }list\*r</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t21}) \black}\mathrm{mcs}_{3,4,4}={{\cos
\left(O\right)}\over{\sin \left(O\right)}}</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t22}) \black}\mathrm{mcs}_{4,4,2}=-\mathe
^ {- 2list\*b }list\*rlist\*\sin \left(O\right)^2</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%t23}) \black}\mathrm{mcs}_{4,4,3}=-\cos
\left(O\right)list\*\sin \left(O\right)</latex>

maxima<latex>
\mbox{\tt\red(\mathrm{\%o23}) \black}\mathbf{done}</latex>
maxima<latex>
\mbox{\tt\red(\mathrm{\%o23}) \black}
\mbox{{}/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/10100654103339040-25px.001.max{}}
</latex>


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