MathAction SandBoxMaxima3

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Computing Christoffel symbols in Maxima

maxima(%i2) load(ctensor)

(%o2)

$\label{eq1} \mbox{{}/usr/local/share/maxima/5.30.0/share/tensor/ctensor.mac{}}$

(1)

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

(%o3)

$\label{eq2} \left[ a\left(t , r\right) , b\left(t , r\right) \right]$

(2)

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)

(%o5)

$\label{eq3} \pmatrix{1&0&0&0 \cr 0&1&0&0\cr 0&0&1&0\cr 0&0&0&1\cr }$

(3)

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)

(%o7)

$\label{eq4} \mathe^{2list\<em>b}$

(4)

maxima
(%i8) lg[3,3]:r^2

(%o8)

$\label{eq5} r^2$

(5)

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()

(%o10)

$\label{eq6} \mathbf{done}$

(6)

maxima(%i11) ug

(%o11)

$\label{eq7} \pmatrix{-\mathe ^ {- 2list\<em>a }&0&0&0\cr 0&\mathe^ {- 2list\</em>b }&0&0\cr 0&0&{{1 }\over{r^2}}&0\cr 0&0&0&{{1}\over{r^2list\<em>\sin \left(O\right)^2}} \cr }$

(7)

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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