Continuous fractions - YAF (Yet Another Formatting)

Question

This post in this website proposes the following code.

\documentclass{article}
\usepackage{amsmath,array}
\begin{document}
[
\setlength{\arraycolsep}{0pt}
\newcommand{\md}[2][1.45]{\mathbin{\raisebox{-#1ex}[0pt][0pt]{$\displaystyle#2$}}}
\md{A + B ={}}
\begin{array}[t]{ *{13}{>{\displaystyle{\mathstrut}}c<{{}}} }
1 \
\cline{1-1}
\md{7} & \md{+} & 1 \
\cline{3-3}
&& \md{15} & \md{+} & 1 \
\cline{5-5}
&&&& 7 & + & \cfrac{1}{4}
\end{array}
]
\end{document}

Could it be possible to obtain a similar output but with a better vertical alignment as if standard fractions have been used? See the red arrow in the picture below.

\cline{3-3}\noalign{\vspace{-2pt}} ? – David Carlisle Nov 08 '22 at 17:54 — David Carlisle, Nov 08 '22 at 17:54

score 6 · Answer 1 · answered Nov 08 '22 at 19:12

6

I suggest to use fractions-in-fractions concept. I used \smash in the nominators in order to avoid the mentioned spaces.

$$
  \everymath={\displaystyle}
  A + B = {1\over 7 \rlap{${}+ {\smash 1\over 15
                    \rlap{${}+ {\smash 1\over 7 
                    \rlap{${}+ {\smash 1\over 5}$}}$}}$}} 
$$

answered Nov 08 '22 at 19:12

wipet

74,238

Good proposition, but the first fraction is not in displaystyle. – projetmbc Nov 08 '22 at 19:33
2

@projetmbc First fraction is in displaystyle because it is between $$ .. $$. – wipet Nov 08 '22 at 20:45

score 4 · Accepted Answer · answered Nov 08 '22 at 22:52

Simple user level syntax and correct spacing.

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum}
\ExplSyntaxOn
\NewDocumentCommand{\altcfrac}{m}
 {
  \projetmbc_altcfrac:n { #1 }
 }
\tl_new:N \l__projetmbc_altcfrac_tl
\tl_new:N \l__projetmbc_altcfrac_last_tl
\seq_new:N \l__projetmbc_altcfrac_seq
\cs_new_protected:Nn __projetmbc_frac:nn { \dfrac{#1}{#2} }
\cs_new_protected:Nn __projetmbc_smash:n { \mathrlap{\smash[t]{#1}} }
\cs_new:Nn __projetmbc_lbrace: { \if_true: { \else: } \fi: }
\cs_new:Nn __projetmbc_rbrace: { \if_false: { \else: } \fi: }
\cs_new_protected:Nn \projetmbc_altcfrac:n
 {
  \tl_clear:N \l__projetmbc_altcfrac_tl
  \seq_set_from_clist:Nn \l__projetmbc_altcfrac_seq { #1 }
  \seq_pop_right:NN \l__projetmbc_altcfrac_seq \l__projetmbc_altcfrac_last_tl
  \seq_map_inline:Nn \l__projetmbc_altcfrac_seq
   {
    \tl_put_right:Nn \l__projetmbc_altcfrac_tl
     {
      __projetmbc_frac:nn { 1 } __projetmbc_lbrace: ##1
      __projetmbc_smash:n __projetmbc_lbrace: {} +
     }
   }
  \tl_put_right:Nn \l__projetmbc_altcfrac_tl { __projetmbc_frac:nn { 1 } __projetmbc_lbrace: }
  \tl_put_right:NV \l__projetmbc_altcfrac_tl \l__projetmbc_altcfrac_last_tl
  \prg_replicate:nn { (\seq_count:N \l__projetmbc_altcfrac_seq + 1) * 2 - 1 }
   {
    \tl_put_right:Nn \l__projetmbc_altcfrac_tl { __projetmbc_rbrace: }
   }
  \tl_set:Nx \l__projetmbc_altcfrac_tl { \l__projetmbc_altcfrac_tl }
  \tl_use:N \l__projetmbc_altcfrac_tl
  \hphantom{\seq_use:Nn \l__projetmbc_altcfrac_seq { + } + \l__projetmbc_altcfrac_last_tl }
 }
\ExplSyntaxOff
\begin{document}
\lipsum[1][1-4]
[
A=3+\altcfrac{7,15,7,4}
]
\lipsum[1][1-4]
\end{document}

The idea is to build the whole series of

\dfrac{1}{7\mathrlap{\smash[t]{{}+\dfrac{1}{15...

step by step. The braces are hidden in macros that expand to them, but we expand only after the whole structure has been built.

Next we add a phantoms to take care of the width and it's sufficient to sum the denominators.

Thanks for the API. It was on my to-do list. I can cross out the corresponding line. :-) — projetmbc, Nov 09 '22 at 09:05

score 2 · Answer 3 · answered Nov 08 '22 at 18:06

2

adding some negative space...

\documentclass{article}
\usepackage{amsmath,array}
\begin{document}
[
\setlength{\arraycolsep}{0pt}
\newcommand{\md}[2][1.45]{\mathbin{\raisebox{-#1ex}[0pt][0pt]{$\displaystyle#2$}}}
\md{A + B ={}}
\begin{array}[t]{ *{13}{>{\displaystyle{\mathstrut}}c<{{}}} }
1 \
\cline{1-1}\noalign{\vspace{-.7ex}}
\md{7} & \md{+} & 1 \
\cline{3-3}\noalign{\vspace{-.7ex}}
&& \md{15} & \md{+} & 1 \
\cline{5-5}\noalign{\vspace{-.7ex}}
&&&& 7 & + & \cfrac{1}{4}
\end{array}
]
\end{document}

answered Nov 08 '22 at 18:06

David Carlisle

757,742

wipet seems to have found a better solution. – projetmbc Nov 08 '22 at 19:33
3

@projetmbc well yes (but \frac not \over) but I thought the spirit of the question was to adjust the provided tabular based approach rather than simply setting nested fractions by nesting a fraction construct. But I can survive if you give wipet the tick:-) – David Carlisle Nov 08 '22 at 19:39
Sorry! :-) You are a kind of wizard to me, so I totally respect you. :-) – projetmbc Nov 08 '22 at 20:30

Continuous fractions - YAF (Yet Another Formatting)

3 Answers3