\hpos in math

[Gavin via ntg-context <ntg-context@ntg.nl>]

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Hello List,

I am working on a project which combines graphics with formulas, like this:


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My code for creating this formula is attached. It works well, but I have a couple of questions that could make it work better.

1) Is there a mathematics version of \hpos? The contents of \hpos are set as text, even when \hpos is in mathematics, so I wrote an \mpos macro that uses \hpos but sets the contents as display-style math. This isn’t great for spacing, and it does't adapt to different math styles. \framed has a math version, \mframed, that sets the contents in the appropriate math style. If anyone know a way to accomplish that with \hpos, I’d love to know.

2) Is there a way to limit the scope of the \hpos labels to a single formula. This could turn into a book length project, with several formulas per page and several connections per formula. If every \hpos in the entire book needs a unique identifier, I could go mad. Under no circumstances will I connect one formula to another, so I’d like to be able to use something like \hpos{A}{…}…\hpos{B}{…} in each formula. Any suggestions?

I’ve got to say, LMTX is an absolutely amazing tool for this project, which includes complicated networks of connections above and below many formulas. The integration of TeX, MetaPost, and Lua makes this project tremendous fun.

Thanks!
Gavin

P.S. For the curious, I’m using a method for doing General Relativity based on spinors rather than tensors, following the methods of Penrose and Rindler in their 1985 books “Spinors and Space-time.” In the typesetting example above, the e_\alpha and e_{\dot\beta} are basis spinors (one left-handed, one right-handed). The e^\mu is the Infeld-van der Waerden symbol relating the spin basis to the coordinate basis. The connections are spinor index contractions. The formula above relates the components of the Infeld-van der Waerden symbol to the Pauli sigma matrices. This relationship only works in flat space, so this is an easy example! [Penrose and Rindler, vol 1 p. 125] 


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% Setting up the overlay for \hpos
\defineoverlay [graphics] [\positionoverlay{graphics}]
\setupbackgrounds
  [page]
  [background={foreground,graphics}]

% My own \mpos that sets its contents in math, displaystyle
\define[2]\mpos{\hpos{#1}{$\displaystyle#2$}}

% Two commands for requesting contractions (the connections between spinors).
\define[2]\contract{%
  \startpositionoverlay{graphics}%
    \setMPpositiongraphic{#1}{mypos:contract}{to=#2}%
  \stoppositionoverlay%
}
\define[2]\contractbelow{%
  \startpositionoverlay{graphics}%
    \setMPpositiongraphic{#1}{mypos:contractbelow}{to=#2}%
  \stoppositionoverlay%
}

% The MetaPost code for drawing the contractions.
\startMPpositiongraphic{mypos:contract}
     path pa, pb, pab ; numeric na, nb ; string ta, tb ;
     ta := mpvars("from") ;
     tb := mpvars("to") ;
     na := positionpage(ta) ; % page number of a
     nb := positionpage(tb) ; % page number of b
     pa := positionbox(ta) ;  % box of a
     pb := positionbox(tb) ;  % box of b
     z1 = 0.5[ulcorner pa,urcorner pa] ;
     z2 = 0.5[ulcorner pb,urcorner pb] ;
     y3 = max(y1,y2) + 3pt ; 
     if na = nb : % Check that positions are on the same page
       pab := z1 -- (x1,y3) -- (x2,y3) -- z2{down} ;
       pickup pencircle scaled 0.6pt ;
       draw pab yshifted 1pt ;
       positioninregion ;
     fi ;
\stopMPpositiongraphic

\startMPpositiongraphic{mypos:contractbelow}
     path pa, pb, pab ; numeric na, nb ; string ta, tb ;
     ta := mpvars("from") ;
     tb := mpvars("to") ;
     na := positionpage(ta) ; % page number of a
     nb := positionpage(tb) ; % page number of b
     pa := positionbox(ta) ;  % box of a
     pb := positionbox(tb) ;  % box of b
     z1 = 0.5[llcorner pa,lrcorner pa] ;
     z2 = 0.5[llcorner pb,lrcorner pb] ;
     y3 = min(y1,y2) - 3pt ; 
     if na = nb : % Check that positions are on the same page
       pab := z1 -- (x1,y3) -- (x2,y3) -- z2{down} ;
       pickup pencircle scaled 0.6pt ;
       draw pab yshifted -1pt ;
       positioninregion ;
     fi ;
\stopMPpositiongraphic

% A textstyle fraction to make the normalization factor look nice.
\define[2]\textfrac{{\textstyle\frac{#1}{#2}}}


\starttext

\startformula
  \mpos{X}{e}_\alpha \mpos{Y}{e}^\mu \mpos{Z}{e}_{\dot\beta}
    = \textfrac{1}{\sqrt{2}}\sigma_{\alpha\dot\beta}^\mu
  \contract{X}{Y}
  \contractbelow{Y}{Z}
\stopformula

\stoptext

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