I was encouraged by Karl Berry to make a report here as well.
The LaTeX syntax \sqrt[...] is essentially a wrap of the plain TeX syntax \root...\of, so it inherits the good and the bad of plain TeX. The following code and description are adapted from my original report.
\documentclass{article}
\setlength{\parindent}{0pt}
\begin{document}
$a+\sqrt[np]2$ has large unwanted space.
$a+\sqrt[]2$ almost has collision versus $a+\sqrt2$.
$\sqrt[3]2$ in the first line%
\cleaders\hbox{.}\hskip\glueexpr\hsize-99.88329pt\relax
$a+\sqrt[3]2+\sqrt[3]4$ in the second line.
\[x=\sqrt[np]{-\frac{q}{2}+\sqrt[]{\frac{q^2}{4}+\frac{p^3}{27}}}%
=\sqrt[np]{2+\sqrt[]{-121}}\]
\end{document}reveals several problems:
- collision between the p and the surd;
- too much space in front of the wide radical index;
- not enough space in front of the narrow radical index (in the extreme, the empty radical index does not match the behavior of
\sqrt);
- and even worse,
\mkern5mu will disappear at line-breaks, so the surd will protrude the left edge of the text block. It’s impossible to align \sqrt[3]2 to the left.
The faulty code is:
|
\def\r@@t#1#2{% |
|
\setbox\z@\hbox{$\m@th#1\sqrtsign{#2}$}% |
|
\dimen@\ht\z@ \advance\dimen@-\dp\z@ |
|
\mkern5mu\raise.6\dimen@\copy\rootbox |
|
\mkern-10mu\box\z@} |
This was discovered during my on-going investigation into OpenType MATH. OpenType MATH inherited this faulty design by
- correcting the index raise amount from
.6(\ht0-\dp0) to (\ht0+\dp0-padding)*radicalDegreeBottomRaisePercent/100-\dp0+\dp\rootbox;
- mapping
\mkern5mu to radicalKernBeforeDegree;
- mapping
\mkern-10mu to radicalKernAfterDegree.
In turn, the issue slips into MathML Requirements, which affects all math rendering on the web. :(
In my follow-up, I propose abandoning BeforeKern altogether, and making AfterKern proportional to the width of surd instead of constant. This works (surprisingly well):
\documentclass{article}
\setlength{\parindent}{0pt}
\begin{document}
$a+\sqrt[np]2$ has large unwanted space.
$a+\sqrt[]2$ almost has collision versus $a+\sqrt2$.
$\sqrt[3]2$ in the first line%
\cleaders\hbox{.}\hskip\glueexpr\hsize-99.88329pt\relax
$a+\sqrt[3]2+\sqrt[3]4$ in the second line.
\[x=\sqrt[np]{-\frac{q}{2}+\sqrt[]{\frac{q^2}{4}+\frac{p^3}{27}}}%
=\sqrt[np]{2+\sqrt[]{-121}}\]
\makeatletter
\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1{#2}$}\dimen@ii\wd\z@
\setbox\z@\hbox{$\m@th#1\sqrtsign{#2}$}\advance\dimen@ii-\wd\z@
\dimen@ii.66666\dimen@ii % 10mu is about 2/3 of the width of surd
\dimen@.6\ht\z@
\advance\dimen@-.4\dp\z@ \advance\dimen@\dp\rootbox
\advance\dimen@-.6\fontdimen8
\ifx#1\scriptscriptstyle\scriptscriptfont\else
\ifx#1\scriptstyle\scriptfont\else\textfont\fi\fi\thr@@
\raise\dimen@
\ifdim-\dimen@ii<\wd\rootbox\copy\rootbox
\else\hbox to-\dimen@ii{\hfil\copy\rootbox}\fi
\kern\dimen@ii\box\z@}
\makeatother
$a+\sqrt[np]2$ has no large unwanted space.
$a+\sqrt[]2$ has no collision; identical to $a+\sqrt2$.
$\sqrt[3]2$ in the first line%
\cleaders\hbox{.}\hskip\glueexpr\hsize-99.88329pt\relax
$a+\sqrt[3]2+\sqrt[3]4$ in the second line.
\[x=\sqrt[np]{-\frac{q}{2}+\sqrt[]{\frac{q^2}{4}+\frac{p^3}{27}}}%
=\sqrt[np]{2+\sqrt[]{-121}}\]
\end{document}Edits:
\sqrtsign instead of \sqrt;\dimen@ii.66666\dimen@ii (-364084sp) instead of \dimen@ii.66667\dimen@ii (-364092sp), 8sp closer to -10mu (-364080sp).
I was encouraged by Karl Berry to make a report here as well.
The LaTeX syntax
\sqrt[...]is essentially a wrap of the plain TeX syntax\root...\of, so it inherits the good and the bad of plain TeX. The following code and description are adapted from my original report.reveals several problems:
\sqrt);\mkern5muwill disappear at line-breaks, so the surd will protrude the left edge of the text block. It’s impossible to align\sqrt[3]2to the left.The faulty code is:
latex2e/base/ltmath.dtx
Lines 241 to 245 in 7b35c82
This was discovered during my on-going investigation into OpenType MATH. OpenType MATH inherited this faulty design by
.6(\ht0-\dp0)to(\ht0+\dp0-padding)*radicalDegreeBottomRaisePercent/100-\dp0+\dp\rootbox;\mkern5mutoradicalKernBeforeDegree;\mkern-10mutoradicalKernAfterDegree.In turn, the issue slips into MathML Requirements, which affects all math rendering on the web. :(
In my follow-up, I propose abandoning BeforeKern altogether, and making AfterKern proportional to the width of surd instead of constant. This works (surprisingly well):
Edits:
\sqrtsigninstead of\sqrt;\dimen@ii.66666\dimen@ii(-364084sp) instead of\dimen@ii.66667\dimen@ii(-364092sp), 8sp closer to-10mu(-364080sp).