Underbrace under square root sign plain TeX

Question

$$
rlap{$sqrt{phantom{displaystylepmatrix{A^{-1} b(x)cr -1}^T 
        pmatrix{A & b(x) cr b(x)^T & Phi(x,x)}
        pmatrix{A^{-1} b(x) cr -1}}}$}
        mskip14mu
        displaystylepmatrix{A^{-1} b(x)cr -1}^T 
        underbrace{displaystyle
        pmatrix{A & b(x) cr b(x)^T & Phi(x,x)}}%
             _{displaystyle A_{Phi, Xcup{x}}}
        pmatrix{A^{-1} b(x) cr -1}
$$

bye

Is there a better way to obtain the same effect, without having to repeat the formula and manually adding a space (mskip14mu)?

Mico · Accepted Answer

You could (a) apply a smash instruction to the underbrace{...}_{...} part and (b) insert a vphantom directive after the sqrt{...} part.

$$
      sqrt{
         pmatrix{A^{-1} cr -1}^{!T} 
         smash{underbrace{pmatrix{A & b(x) cr b(x)^T & Phi(x,x)}}%
                _{textstyle A_{Phi, Xcup{x}}}}
         pmatrix{A^{-1} b(x) cr -1}
      }
      vphantom{underbrace{pmatrix{.cr .}}_{textstyle A_{Phi}}}
$$
bye

Observe that I've also dropped some displaystyle directives and have converted others to textstyle.

egreg · Answer

TeX can measure the object:
$$
defcontentsA{pmatrix{A^{-1} b(x) cr -1}}
defcontentsB{pmatrix{A & b(x) cr b(x)^T & Phi(x,x)}}
setbox0=hbox{$displaystyle
  contentsA^{!T}
  {underbrace{!contentsB!}_{displaystyle A_{Phi, Xcup{x}}}}
  contentsA
$}
sqrt{vphantom{contentsA^T}hphantom{copy0}}
kern-wd0
box0
$$

bye

I made a couple of changes: braces like {underbrace{...}_{...}} in order to avoid it being considered a math operator with an excess of spacing; for the same reason I introduced a couple of ! tokens. And also one for the exponent in order to place it nearer the top of the parenthesis.

Underbrace under square root sign plain TeX

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