Maxima Function
covdiff (expr, v_1, v_2, ...)
Yields the covariant derivative of expr with
respect to the variables v_i in terms of the Christoffel symbols of the
second kind (ichr2
). In order to evaluate these, one should use
ev(expr,ichr2)
.
(%i1) load(itensor); (%o1) /share/tensor/itensor.lisp (%i2) entertensor()$ Enter tensor name: a; Enter a list of the covariant indices: [i,j]; Enter a list of the contravariant indices: [k]; Enter a list of the derivative indices: []; k (%t2) a i j (%i3) ishow(covdiff(%,s))$ k %1 k %1 k (%t3) - a ichr2 - a ichr2 + a i %1 j s %1 j i s i j,s k %1 + ichr2 a %1 s i j (%i4) imetric:g; (%o4) g (%i5) ishow(ev(%th(2),ichr2))$ %1 %4 k g a (g - g + g ) i %1 s %4,j j s,%4 j %4,s (%t5) - ------------------------------------------ 2 %1 %3 k g a (g - g + g ) %1 j s %3,i i s,%3 i %3,s - ------------------------------------------ 2 k %2 %1 g a (g - g + g ) i j s %2,%1 %1 s,%2 %1 %2,s k + ------------------------------------------- + a 2 i j,s (%i6)