How may I negate long equality signs?

Question

As an answer to How do I make a long identity sign? @egreg offered the solutions:
documentclass{article}
usepackage{amsmath,color}

makeatletter
newlength{longeq@wd}
newcommand{longeq}[1][2]{mathrel{mathpalettelongeq@{#1}}}
newcommand{longeq@}[2]{%
  begingroup
  settowidthlongeq@wd{$m@th#1=$}%
  makebox[#2longeq@wd][s]{%
    $m@th#1mspace{1mu}$%
    ifdim#2pt<2pt
      $m@th#1{=}hss{=}$%
    else
      $m@th#1{=}kern-0.5longeq@wdcleaderslongeqfill@{#1}hfilkern-0.5longeq@wd{=}$%
    fi
    $m@th#1mspace{1mu}$%
  }%
  endgroup
}
newcommand{longeqfill@}[1]{hbox{$m@th#1mspace{-3mu}{=}mspace{-3mu}$}}
makeatother

begin{document}

makeatletter

$a==b$

$alongeq b$

$alongeq[1.25]b$

$alongeq[1.5]b$

$alongeq[1.75]b$

$alongeq[3]b$

end{document}

How may I negate the long identity signs as with $neq$?

egreg · Accepted Answer

Use centernot:
documentclass[draft]{article}
usepackage{amsmath,centernot}

makeatletter
newlength{longeq@wd}
newcommand{nlongeq}[1][2]{centernot{longeq[#1]}}
newcommand{longeq}[1][2]{mathrel{mathpalettelongeq@{#1}}}
newcommand{longeq@}[2]{%
  begingroup
  settowidthlongeq@wd{$m@th#1=$}%
  makebox[#2longeq@wd][s]{%
    $m@th#1mspace{1mu}$%
    ifdim#2pt<2pt
      $m@th#1{=}hss{=}$%
    else
      $m@th#1{=}kern-0.5longeq@wdcleaderslongeqfill@{#1}hfilkern-0.5longeq@wd{=}$%
    fi
    $m@th#1mspace{1mu}$%
  }%
  endgroup
}
newcommand{longeqfill@}[1]{hbox{$m@th#1mspace{-3mu}{=}mspace{-3mu}$}}
makeatother

begin{document}

makeatletter

$a==b$

$alongeq bnlongeq c$

$alongeq[1.25]bnlongeq[1.25] c$

$alongeq[1.5]bnlongeq[1.5] c$

$alongeq[1.75]bnlongeq[1.75] c$

$alongeq[3]bnlongeq[3] c$

end{document}

Steven B. Segletes · Answer

Employing the alternate solution at the cited answer, if you end up using an odd number of = signs for the construction, just apply not to the middle one.
documentclass{article}
newcommandlongeq{mathrel{{=}mkern-4mu{=}mkern-4mu{=}}}
newcommandnlongeq{mathrel{{=}mkern-4mu{not=}mkern-4mu{=}}}
begin{document}
$xlongeq y nlongeq z$
end{document}

Werner, in a comment below, notes a simpler syntax of
newcommandlongeq{=joinrel=joinrel=}
newcommandnlongeq{=joinrelnot=joinrel=}

However, the joinrel (join relation) macro uses a 3mu shift to achieve the overlay, whereas, my original definition chose the shift as 4mu, making the overall length slightly shorter in my original case, by comparison.
If one finds it too wide, jack up the negativity of the mkern.  Here it is, to -10mu (was -4mu above):

How may I negate long equality signs?

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