{ "cells" : [ { "cell_origin" : "client", "cell_type" : "latex", "cells" : [ { "cell_origin" : "client", "cell_type" : "latex_view", "source" : "\\algorithm{asym}{Anti-symmetrise or symmetrise an expression in indicated indices or arguments}\n\nAnti-symmetrise or symmetrise (depending on the \\verb|antisymmetric| flag) a product or tensor in the indicated objects.\nThis works both with normal objects and with indices. An example of the former:" } ], "hidden" : true, "source" : "\\algorithm{asym}{Anti-symmetrise or symmetrise an expression in indicated indices or arguments}\n\nAnti-symmetrise or symmetrise (depending on the \\verb|antisymmetric| flag) a product or tensor in the indicated objects.\nThis works both with normal objects and with indices. An example of the former:" }, { "cell_origin" : "client", "cell_type" : "input", "cells" : [ { "cell_origin" : "server", "cell_type" : "latex_view", "source" : "\\begin{dmath*}{}A B C\\end{dmath*}" } ], "source" : "ex:=A B C;" }, { "cell_origin" : "client", "cell_type" : "input", "cells" : [ { "cell_origin" : "server", "cell_type" : "latex_view", "source" : "\\begin{dmath*}{}\\frac{1}{6}A B C - \\frac{1}{6}A C B - \\frac{1}{6}B A C+\\frac{1}{6}B C A+\\frac{1}{6}C A B - \\frac{1}{6}C B A\\end{dmath*}" } ], "source" : "asym(_, $A,B,C$);" }, { "cell_origin" : "client", "cell_type" : "latex", "cells" : [ { "cell_origin" : "client", "cell_type" : "latex_view", "source" : "When used with indices, remember to also\nindicate whether you want to symmetrise upper or lower indices, as in\nthe example below." } ], "hidden" : true, "source" : "When used with indices, remember to also\nindicate whether you want to symmetrise upper or lower indices, as in\nthe example below." }, { "cell_origin" : "client", "cell_type" : "input", "cells" : [ { "cell_origin" : "server", "cell_type" : "latex_view", "source" : "\\begin{dmath*}{}A_{m n} B_{p}\\end{dmath*}" } ], "source" : "ex:=A_{m n} B_{p};" }, { "cell_origin" : "client", "cell_type" : "input", "cells" : [ { "cell_origin" : "server", "cell_type" : "latex_view", "source" : "\\begin{dmath*}{}\\frac{1}{6}A_{m n} B_{p} - \\frac{1}{6}A_{m p} B_{n} - \\frac{1}{6}A_{n m} B_{p}+\\frac{1}{6}A_{n p} B_{m}+\\frac{1}{6}A_{p m} B_{n} - \\frac{1}{6}A_{p n} B_{m}\\end{dmath*}" } ], "source" : "asym(_, $_{m}, _{n}, _{p}$);" }, { "cell_origin" : "client", "cell_type" : "latex", "cells" : [ { "cell_origin" : "client", "cell_type" : "latex_view", "source" : "If you want to \\emph{symmetrise} in the indicated objects instead, use the \\verb|antisymmetric=False| flag:" } ], "hidden" : true, "source" : "If you want to \\emph{symmetrise} in the indicated objects instead, use the \\verb|antisymmetric=False| flag:" }, { "cell_origin" : "client", "cell_type" : "input", "cells" : [ { "cell_origin" : "server", "cell_type" : "latex_view", "source" : "\\begin{dmath*}{}A_{m n} B_{p}\\end{dmath*}" }, { "cell_origin" : "server", "cell_type" : "latex_view", "source" : "\\begin{dmath*}{}\\frac{1}{6}A_{m n} B_{p}+\\frac{1}{6}A_{m p} B_{n}+\\frac{1}{6}A_{n m} B_{p}+\\frac{1}{6}A_{n p} B_{m}+\\frac{1}{6}A_{p m} B_{n}+\\frac{1}{6}A_{p n} B_{m}\\end{dmath*}" } ], "source" : "ex:=A_{m n} B_{p};\nasym(_, $_{m}, _{n}, _{p}$, antisymmetric=False);" }, { "cell_origin" : "client", "cell_type" : "input", "source" : "" } ], "description" : "Cadabra JSON notebook format", "version" : 1 }