diff --git a/Z4co/wolfram/README.md b/Z4co/wolfram/README.md new file mode 100644 index 00000000..6359900b --- /dev/null +++ b/Z4co/wolfram/README.md @@ -0,0 +1,24 @@ +# Z4c + +$$ +\begin{align} +\Gamma^{k}{}_{ij} +&=\frac{1}{2}\gamma^{kl}(\partial_i\gamma_{jl}+\partial_j\gamma_{li}-\partial_l\gamma_{ij}) +\\ +&=\frac{1}{2}\tilde\gamma^{kl} +\left[ + (\partial_i\tilde\gamma_{jl}-\partial_i\ln\chi\tilde\gamma_{jl})+ + (\partial_j\tilde\gamma_{li}-\partial_j\ln\chi\tilde\gamma_{li})- + (\partial_l\tilde\gamma_{ij}-\partial_l\ln\chi\tilde\gamma_{ij}) +\right] +\\ +&=\tilde\Gamma^k{}_{ij} +-\frac{1}{2} +(\partial_i\ln\chi\delta^k{}_j+\partial_j\ln\chi\delta^k{}_i +-\tilde\gamma_{ij}\tilde\gamma^{kl}\partial_l\ln\chi) +\end{align} +$$ +where +$\partial_l\gamma_{ij}=\partial_l(\chi^{-1}\tilde\gamma_{ij}) +=\chi^{-1}(\partial_l\tilde{\gamma}_{ij}-\chi^{-1}\partial_l\chi\tilde\gamma_{ij}) +=\chi^{-1}(\partial_l\tilde{\gamma}_{ij}-\partial_l\ln\chi\tilde\gamma_{ij})$. diff --git a/Z4co/wolfram/check_rhs.nb b/Z4co/wolfram/check_rhs.nb index 7280f688..d47d70c2 100644 --- a/Z4co/wolfram/check_rhs.nb +++ b/Z4co/wolfram/check_rhs.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 59106, 1551] -NotebookOptionsPosition[ 53377, 1458] -NotebookOutlinePosition[ 53773, 1474] -CellTagsIndexPosition[ 53730, 1471] +NotebookDataLength[ 85006, 2252] +NotebookOptionsPosition[ 78358, 2144] +NotebookOutlinePosition[ 78754, 2160] +CellTagsIndexPosition[ 78711, 2157] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -42,11 +42,12 @@ Cell[BoxData["\<\"------------------------------------------------------------\ 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, - 3.9287928720965443`*^9, 3.928792972522664*^9, 3.9287947721188393`*^9, - 3.9287963082892637`*^9}, + 3.9287928720965447`*^9, 3.928792972522664*^9, 3.9287947721188397`*^9, + 3.928796308289264*^9, 3.9288192642614517`*^9, 3.928819829538828*^9, + 3.928821943000177*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"e70cff98-bee7-4fec-b87b-b1c008fd79a0"], +In[1]:=",ExpressionUUID->"b6eb6c4c-6d5c-477b-9525-99ad9cf8dc20"], Cell[BoxData[ InterpretationBox[ @@ -62,11 +63,12 @@ Cell[BoxData[ 3.928786533173875*^9, 3.928786935120081*^9, 3.928787121237308*^9, 3.928787381239373*^9, 3.928791502068035*^9, 3.9287915491944*^9, 3.928791837145893*^9, 3.928792362648822*^9, 3.928792783869076*^9, - 3.9287928720965443`*^9, 3.928792972522664*^9, 3.9287947721188393`*^9, - 3.9287963082903843`*^9}, + 3.9287928720965447`*^9, 3.928792972522664*^9, 3.9287947721188397`*^9, + 3.928796308289264*^9, 3.9288192642614517`*^9, 3.928819829538828*^9, + 3.9288219430012827`*^9}, CellLabel-> "During evaluation of \ -In[1]:=",ExpressionUUID->"c66967f1-33cd-4adb-9b86-91b4e9a04b0b"], +In[1]:=",ExpressionUUID->"43bb992e-79f4-4155-9298-b873f30b2a24"], Cell[BoxData["\<\"CopyRight (C) 2003-2020, Jose M. 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