Symmetrization and antisymmetrization of tensor products











up vote
2
down vote

favorite












How do I achieve something like



enter image description here



or



enter image description here



in LaTeX? The curved lines indicate symmetrization with respect to the indices they join, and the straight lines indicate antisymmetrization.






math-mode tensor







share|improve this question


























    up vote
    2
    down vote

    favorite












    How do I achieve something like



    enter image description here



    or



    enter image description here



    in LaTeX? The curved lines indicate symmetrization with respect to the indices they join, and the straight lines indicate antisymmetrization.






    math-mode tensor







    share|improve this question
























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      How do I achieve something like



      enter image description here



      or



      enter image description here



      in LaTeX? The curved lines indicate symmetrization with respect to the indices they join, and the straight lines indicate antisymmetrization.






      math-mode tensor







      share|improve this question













      How do I achieve something like



      enter image description here



      or



      enter image description here



      in LaTeX? The curved lines indicate symmetrization with respect to the indices they join, and the straight lines indicate antisymmetrization.






      math-mode tensor




      math-mode tensor






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      leastaction

      19311




      19311






















          2 Answers
          2






          active

          oldest

          votes

















          up vote
          2
          down vote



          accepted










          Here is a simpleminded proposal.



          documentclass{article}
          
usepackage{tikz}
          
usetikzlibrary{tikzmark}
          
begin{document}
          
$u^{tikzmarknode{i1}{i}tikzmarknode{j1}{j}}
          
tikzmarknode{v1}{v}^{tikzmarknode{k1}{k}tikzmarknode{l1}{ell}}$
          
begin{tikzpicture}[overlay,remember picture]
          
draw[blue,thick] (i1.north east) to[out=30,in=150] (l1.north west);
          
draw[blue,thick] (j1) -- ++(0,-1.5ex)  -| (k1);
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer





















          • Thanks! In your code, I suppose v1 isn’t being used.
            – leastaction
            2 hours ago










          • Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
            – leastaction
            16 mins ago


















          up vote
          1
          down vote













          Also with pstricks (compile with xelatex):



          documentclass{article}
          
usepackage{pst-node}
          

          
begin{document}
          

          
$u^{rnode{i}{i}rnode{j}{j}} v^{rnode{k}{k}rnode{l}{ell}}$ 
          
ncarc[linecolor=blue,nodesep=1pt,arcangle=60]{i}{l}
          
ncbar[linecolor=blue,nodesep=1pt,arm=3pt,angle=-90]{j}{k}
          

          
end{document}



          enter image description here







          share|improve this answer























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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            2
            down vote



            accepted










            Here is a simpleminded proposal.



            documentclass{article}
            
usepackage{tikz}
            
usetikzlibrary{tikzmark}
            
begin{document}
            
$u^{tikzmarknode{i1}{i}tikzmarknode{j1}{j}}
            
tikzmarknode{v1}{v}^{tikzmarknode{k1}{k}tikzmarknode{l1}{ell}}$
            
begin{tikzpicture}[overlay,remember picture]
            
draw[blue,thick] (i1.north east) to[out=30,in=150] (l1.north west);
            
draw[blue,thick] (j1) -- ++(0,-1.5ex)  -| (k1);
            
end{tikzpicture}
            
end{document}


            enter image description here






            share|improve this answer





















            • Thanks! In your code, I suppose v1 isn’t being used.
              – leastaction
              2 hours ago










            • Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
              – leastaction
              16 mins ago















            up vote
            2
            down vote



            accepted










            Here is a simpleminded proposal.



            documentclass{article}
            
usepackage{tikz}
            
usetikzlibrary{tikzmark}
            
begin{document}
            
$u^{tikzmarknode{i1}{i}tikzmarknode{j1}{j}}
            
tikzmarknode{v1}{v}^{tikzmarknode{k1}{k}tikzmarknode{l1}{ell}}$
            
begin{tikzpicture}[overlay,remember picture]
            
draw[blue,thick] (i1.north east) to[out=30,in=150] (l1.north west);
            
draw[blue,thick] (j1) -- ++(0,-1.5ex)  -| (k1);
            
end{tikzpicture}
            
end{document}


            enter image description here






            share|improve this answer





















            • Thanks! In your code, I suppose v1 isn’t being used.
              – leastaction
              2 hours ago










            • Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
              – leastaction
              16 mins ago













            up vote
            2
            down vote



            accepted







            up vote
            2
            down vote



            accepted






            Here is a simpleminded proposal.



            documentclass{article}
            
usepackage{tikz}
            
usetikzlibrary{tikzmark}
            
begin{document}
            
$u^{tikzmarknode{i1}{i}tikzmarknode{j1}{j}}
            
tikzmarknode{v1}{v}^{tikzmarknode{k1}{k}tikzmarknode{l1}{ell}}$
            
begin{tikzpicture}[overlay,remember picture]
            
draw[blue,thick] (i1.north east) to[out=30,in=150] (l1.north west);
            
draw[blue,thick] (j1) -- ++(0,-1.5ex)  -| (k1);
            
end{tikzpicture}
            
end{document}


            enter image description here






            share|improve this answer












            Here is a simpleminded proposal.



            documentclass{article}
            
usepackage{tikz}
            
usetikzlibrary{tikzmark}
            
begin{document}
            
$u^{tikzmarknode{i1}{i}tikzmarknode{j1}{j}}
            
tikzmarknode{v1}{v}^{tikzmarknode{k1}{k}tikzmarknode{l1}{ell}}$
            
begin{tikzpicture}[overlay,remember picture]
            
draw[blue,thick] (i1.north east) to[out=30,in=150] (l1.north west);
            
draw[blue,thick] (j1) -- ++(0,-1.5ex)  -| (k1);
            
end{tikzpicture}
            
end{document}


            enter image description here







            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 2 hours ago









            marmot

            81.7k491174




            81.7k491174












            • Thanks! In your code, I suppose v1 isn’t being used.
              – leastaction
              2 hours ago










            • Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
              – leastaction
              16 mins ago


















            • Thanks! In your code, I suppose v1 isn’t being used.
              – leastaction
              2 hours ago










            • Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
              – leastaction
              16 mins ago
















            Thanks! In your code, I suppose v1 isn’t being used.
            – leastaction
            2 hours ago




            Thanks! In your code, I suppose v1 isn’t being used.
            – leastaction
            2 hours ago












            Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
            – leastaction
            16 mins ago




            Can you perhaps edit your answer to include the symmetrization below and antisymmetrization above as well? I couldn't get them to work in spite of using something like "draw[red,thick] (j1.south west) to [out=300,in=225] (k1.south west);"
            – leastaction
            16 mins ago










            up vote
            1
            down vote













            Also with pstricks (compile with xelatex):



            documentclass{article}
            
usepackage{pst-node}
            

            
begin{document}
            

            
$u^{rnode{i}{i}rnode{j}{j}} v^{rnode{k}{k}rnode{l}{ell}}$ 
            
ncarc[linecolor=blue,nodesep=1pt,arcangle=60]{i}{l}
            
ncbar[linecolor=blue,nodesep=1pt,arm=3pt,angle=-90]{j}{k}
            

            
end{document}



            enter image description here







            share|improve this answer



























              up vote
              1
              down vote













              Also with pstricks (compile with xelatex):



              documentclass{article}
              
usepackage{pst-node}
              

              
begin{document}
              

              
$u^{rnode{i}{i}rnode{j}{j}} v^{rnode{k}{k}rnode{l}{ell}}$ 
              
ncarc[linecolor=blue,nodesep=1pt,arcangle=60]{i}{l}
              
ncbar[linecolor=blue,nodesep=1pt,arm=3pt,angle=-90]{j}{k}
              

              
end{document}



              enter image description here







              share|improve this answer

























                up vote
                1
                down vote










                up vote
                1
                down vote









                Also with pstricks (compile with xelatex):



                documentclass{article}
                
usepackage{pst-node}
                

                
begin{document}
                

                
$u^{rnode{i}{i}rnode{j}{j}} v^{rnode{k}{k}rnode{l}{ell}}$ 
                
ncarc[linecolor=blue,nodesep=1pt,arcangle=60]{i}{l}
                
ncbar[linecolor=blue,nodesep=1pt,arm=3pt,angle=-90]{j}{k}
                

                
end{document}



                enter image description here







                share|improve this answer














                Also with pstricks (compile with xelatex):



                documentclass{article}
                
usepackage{pst-node}
                

                
begin{document}
                

                
$u^{rnode{i}{i}rnode{j}{j}} v^{rnode{k}{k}rnode{l}{ell}}$ 
                
ncarc[linecolor=blue,nodesep=1pt,arcangle=60]{i}{l}
                
ncbar[linecolor=blue,nodesep=1pt,arm=3pt,angle=-90]{j}{k}
                

                
end{document}



                enter image description here








                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 1 hour ago

























                answered 1 hour ago









                AboAmmar

                31.8k22781




                31.8k22781






























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