Horizontal curly braces inside matrix

Question

I'm trying to make this determinant:

But I don't know how to put the curly braces. I've tried with underbrace but I get the brace only under a_m, not the entire space.
My try:

documentclass{article}
usepackage{amsmath}

begin{document}

begin{equation}
R(f,g)=begin{vmatrix}
    a_0 & & & & b_0 &  &  &  
    a_1 & a_0 & & & b_1 & b_0 &  &  
    a_2 & a_1 & a_0 & & b_2 & b_1 & b_0 &  
     & cdots & & &  & cdots &  &  
     & & & a_m &  &  &  & b_n 
end{vmatrix}   
end{equation}

end{document}

Sebastiano · Accepted Answer

Here there is my idea: to have the curly braces inside the matrix of your determinant I have used always underbrace command.
documentclass[a4paper,12pt]{article}
usepackage{amsmath,amssymb}
begin{document}
begin{equation}
R(f,g)=
begin{vmatrix}
underbrace{begin{matrix}
a_0 &   &   &   
a_1 & a_0 &  &  
a_2 & a_1 & a_0 & 
 & ldots &  &  
 &   &   & a_m 
end{matrix}}_{n text{ columns}} & underbrace{begin{matrix}
b_0 &   &   &   
b_1 & b_0 &  &  
b_2 & b_1 & b_0 & 
 & ldots &  &  
 &   &   & b_m 
end{matrix}}_{m text{ columns}}
end{vmatrix}
end{equation}
end{document}

This MWE have the curly brackets more inside:
documentclass[a4paper,12pt]{article}
usepackage{amsmath,amssymb}
begin{document}
begin{equation}
R(f,g)=begin{array}{c}
begin{vmatrix}
underbrace{begin{matrix}
a_0 &   &   &   
a_1 & a_0 &  &  
a_2 & a_1 & a_0 & 
 & ldots &  &  
 &   &   & a_m 
end{matrix}}_{n text{ columns}} & underbrace{begin{matrix}
b_0 &   &   &   
b_1 & b_0 &  &  
b_2 & b_1 & b_0 & 
 & ldots &  &  
 &   &   & b_m 
end{matrix}}_{m text{ columns}}
 & 
end{vmatrix}
end{array}
end{equation}
end{document}

Mico · Answer

I would place the two underbraced explanatory expressions outside the vertical bars. This may be done by with the help of 2 "smashed" matrix environments and two judiciously chosen typographic struts -- one inside the leftvert ... rightvert group, containing a matrix with 5 columns, and one outside that group, containing a matrix with 7 columns (and a smash[t] directive).

documentclass{article}
usepackage{amsmath}
begin{document}
begin{equation}
R(f,g)=
leftvert 
  smash{underbrace{begin{matrix}
    a_0 &     &     &    
    a_1 & a_0 &     &   
    a_2 & a_1 & a_0 &   
        & cdots   
     & & & a_m  
     end{matrix}}_{text{$n$ columns}}};
  smash{underbrace{begin{matrix}
    b_0 &     &     &    
    b_1 & b_0 &     &   
    b_2 & b_1 & b_0 &   
        & cdots   
     & & & b_n  
     end{matrix}}_{text{$m$ columns}}}
  %% insert a first typographic strut:
  vphantom{begin{matrix} 12345 end{matrix}}
rightvert
%% insert a second typographic strut:
smash[t]{vphantom{begin{matrix} 1234567 end{matrix}}}
end{equation}
end{document}

egreg · Answer

You can use nicematrix. Some work is needed to pull the braces nearer the matrix, but not so much: the idea is to use a phantom matrix to set the width for the underbrace; then it is raised up.
documentclass{article}
usepackage{amsmath}
usepackage{nicematrix}

usepackage{lipsum} % mock text to show spacing around the display

begin{document}

lipsum[1]
begin{equation}
R(f,g)=
begin{vNiceMatrix}[last-row]
  a_0 & & & & b_0 &  &  &  
  a_1 & a_0 & & & b_1 & b_0 &  &  
  a_2 & a_1 & a_0 & & b_2 & b_1 & b_0 &  
  multicolumn{3}{c}{cdots} & &  multicolumn{3}{c}{cdots}  &  
  & & & a_m &  &  &  & b_n 
  multicolumn{4}{c}{%
    raisebox{1ex}{$
      underbrace{%
        hphantom{begin{matrix} a_0 & a_1 & a_2 & a_mend{matrix}}
      }_{text{$n$ columns}}
    $}%
  }
  &
  multicolumn{4}{c}{%
    raisebox{1ex}{$
      underbrace{%
        hphantom{begin{matrix} b_0 & b_1 & b_2 & b_nend{matrix}}
      }_{text{$m$ columns}}
    $}%
  }
end{vNiceMatrix}
end{equation}
lipsum[2]

end{document}

Note the multicolumn instructions in the body to avoid misalignments.

Horizontal curly braces inside matrix

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