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The following works with free indices but not with fixed indices. Don't understand why

gup:=gup^{b c} = g^{b c} - h^{b c}+  h^{b d} h^{c}_{d} - h^{b d} h_{d e} h^{e c};
Gamma:=\Gamma^{f}_{b c} =1/2 gup^{f d} ( \partial_{b}{h_{d c}} + \partial_{c}{h_{d b}} - \partial_{d}{h_{b c}});
substitute(Gamma, gup);

With substitute command get error -- Consistency Exception: Fixed index pair with two upper or two lower indices found

in General questions by (520 points)

1 Answer

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Mmm, that's a funny one. Not sure how that slipped the net, hang on while I try to get this sorted.

by (66.3k points)