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Centralize (long) equations with pgfkeys

pgf add tag

JeT

**My (open) question**

How can I extend the benefits of `pgfkeys` to store and resuse formulae ?

**Context**

So many long formuale I use again and again... I saw many advantages to store my formulae in `pgfkeys`:

- It simplifies typing (e.g. `\RF[delta]`), especially when long formulae got to be in a table.
- it avoids the multiplication of `\def` (I get lost after 100 macros with weirder and longer names to remember).
- One can use numbers (e.g. `\RF[d1]`) 
- One centralizes the format and thus one can check the consistency of notations.
- as a result, one avoid discrepancies in typing of the formulae between different documents.
- Could be useful for index, labelling/cross referencing, nomenclatures
- ... probably many other thing (I've not thought about yet...)

**Where do I stand ?**

So far I have a simple working (storing) solution (see MWE below).
![image.png](/image?hash=e0a3fc9853519bc0fee75730e8e5339df447920f8adae5e0b568babb0f264636)


**Where do I need insight ?** 

If you had to think about the equations you keep using, How would you see a smart way to centralize information you'll need about these equations ? And reuse it efficiently.

I bascally use `/.initial` but there must be other keys to do the job better (list ?).

PS : Probably related to [this great answer](https://topanswers.xyz/tex?q=1557) since I intend to draw or calculate values for these equations at some point.


**Example of applications I have in mind**

```
\documentclass{article}

\usepackage{tikz}
\usepackage{mathtools}

% I used long formulae on purpose
\pgfkeys{
  formula/.is family,
  formula,
  spot/.initial		= { S },
  today/.initial	= { t_0 },
  maturity/.initial	= { T },
  TTM/.initial		= { T-t },
  abm/.initial		= { {S_{t}=S_{0}+\mu t+\sigma W_{t}} },
  gmb/.initial		= { \mu=\mathbb{E}(R_{t})=\mathbb{E}\left[\frac{dS_{t}}{S_{t}}\right] },
  forward/.initial	= { F =\displaystyle Se^{rt}},
  forward div repo/.initial	= { F_T = S_0 e^{(r-\text{div}-\text{repo})\times T} },
  delta/.initial	= { \mathcal{N}\left(\frac{\ln \frac{F}{K} +\frac{1}{2}\sigma^2T}{\sigma \sqrt{T}}\right)  },
  d1/.initial		= { d_1 = \displaystyle \frac{\ln\frac{S}{K} + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}},
  d2/.initial		= { d_2 = \displaystyle \frac{\ln\frac{S}{K} + (r - \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}},
  edp/.initial		= { \Theta + r S \Delta + \frac{1}{2} \sigma^2 S^2 \Gamma = r V},
  call/.initial		= { C(S, T) =  S \mathcal{N}\left(   d_1 \right) - K e^{-rT} \mathcal{N}\left(   d_2\right)},
  put/.initial		= { P(S, T) = -S \mathcal{N}\left( - d_1 \right) + K e^{-rT} \mathcal{N}\left( - d_2\right)},
}

\newcommand\formula[1]{\pgfkeys{formula,#1}}

% ReuseFormula (\RF)
\newcommand\RF[1][]{ \formula{#1} }		

\begin{document}

It's easy to use in text $\RF[call]$.

This is Delta, noted $\Delta$ that is worth $ \RF[delta] $.

Delta  is a rate of variation generally used to know the senisitivity of your option to changes in your underlying. 
  
\[\RF[forward div repo] \]

\[ \RF[edp] \]

Or format table with such long formulae

\begin{table}[tph]
	\centering
	\begin{tabular}{c}
		\hline      
		$\RF[call]$ \\
		$\RF[put]$  \\ 
		$\RF[d1]$   \\
		$\RF[d2]$   \\ 
		\hline      
	\end{tabular} 
	\caption{Much simplier tables}
\end{table}

\end{document}
```

Top Answer

user 3.14159

I'm not sure if any of my suggestions is useful. Yes, you can store elements of equations in pgf keys, and this can make a lot of sense because of name space limitations. You can also "learn" and repeat combinations, but this affords global styles. Unfortunately, I was unable to get satisfactory results in align environments generated by the `/.list` key handler, but if you are willing to use a "refined" list handler this works, too.
```
\documentclass{article}
\usepackage{pgffor}
\usepackage{mathtools}
\makeatletter% stolen from forest
\pgfkeys{/handlers/.global style/.code=\pgfkeys{\pgfkeyscurrentpath/.global code=\pgfkeysalso{#1}}}
\pgfkeysdef{/handlers/.global code}{\pgfkeysglobaldef{\pgfkeyscurrentpath}{#1}}
\long\def\pgfkeysglobaldef#1#2{%
  \long\def\pgfkeys@temp##1\pgfeov{#2}%
  \pgfkeysgloballet{#1/.@cmd}{\pgfkeys@temp}%
  \pgfkeysglobalsetvalue{#1/.@body}{#2}%
}
\def\pgfkeysgloballet#1#2{%
  \expandafter\global\expandafter\let\csname pgfk@#1\endcsname#2%
}
\long\def\pgfkeysglobalsetvalue#1#2{%
  \pgfkeys@temptoks{#2}\expandafter\xdef\csname pgfk@#1\endcsname{\the\pgfkeys@temptoks}%
}
\makeatother
\newcommand{\diff}{\mathop{}\!\text{d}}
\DeclareMathOperator{\Euler}{e}
% I used long formulae on purpose
\pgfkeys{
  formula/.is family,
  formula/.unknown/.code={#1},
  formula/.cd,
  plain/.code={#1},
  edp/.code		= { \Theta + r S \Delta + \frac{1}{2} \sigma^2 S^2 \Gamma = r V},
  spot/.code		= { S },
  today/.code		= { t_0 },
  maturity/.code	= { T },
  TTM/.code			= { T-t },
  delta/.initial	= { \mathcal{N}\left(\frac{\ln \frac{F}{K} +\frac{1}{2}\sigma^2T}{\sigma \sqrt{T}}\right)  },
  d_1/.code		= { \frac{\ln\frac{S}{K} + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}},
  d_2/.code		= { \frac{\ln\frac{S}{K} + (r - \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}},
  do align/.code={\pgfkeys{formula/list/unless first=\\}%
 	#1&=\formula{#1}},
}
\makeatletter
\newif\if@pgf@rlist@first
\pgfkeys{
  formula/.cd,
  list/only first/.code={\if@pgf@rlist@first#1\fi},
  list/unless first/.code={\if@pgf@rlist@first\global\@pgf@rlist@firstfalse\else#1\fi},
  }
\pgfkeys{/handlers/.rlist/.code=%
  {%
    \ifx\foreach\@undefined%
      \pgfkeys@error{You need to load the pgffor package to use the .list key syntax.}%
    \fi%
	\global\@pgf@rlist@firsttrue
    % Use foreach to unfold the list
    \def\pgf@keys@temp{}%
    \foreach \pgf@keys@key in{#1}%
    {\expandafter\expandafter\expandafter\gdef%
      \expandafter\expandafter\expandafter\pgf@keys@temp%
      \expandafter\expandafter\expandafter{\expandafter\pgf@keys@temp\expandafter{\pgf@keys@key}}}%
    \edef\pgf@keys@list@path{\pgfkeyscurrentpath}%
    \expandafter\expandafter\expandafter\pgf@keys@do@list%
    \expandafter\expandafter\expandafter{\expandafter\pgf@keys@list@path\expandafter}\pgf@keys@temp\pgf@stop%
  }%
}
\makeatother

\newcommand\formula[2][]{%
\ifx#1\relax\relax
\else
\pgfkeys{formula/.cd,@#1/.global style={#2}}%
\fi
\pgfkeys{formula/.cd,#2}}

\newcommand\RF[2][]{\formula{@#2}}		

\begin{document}
You can use formulas from your repository:
$\formula{edp}$.\bigskip

The optional argument can be used to store the keys in a global (!) style:
$\formula[f1]{spot,plain={=},today}$. As you can see, plain can be used to add
some arbitrary elements.\bigskip

You can repeat the style, $\RF{f1}$.\bigskip

Align can be used, too,
\begin{align}
\pgfkeys{formula/do align/.rlist={d_1,d_2}}
\end{align}
but at the expense of defining a ``refined'' list handler \texttt{/.rlist}. This
list handler allows us to distinguish the first item from the rest. Notice that
the \texttt{/.list} key handler is based on \verb|\foreach|, for which some
folklore says that it always puts things in groups and cannot deal with ampersands
($\&$) and the like. As one can see, the \texttt{/.list} key handler does not
have any of those limitations, nor does \verb|\foreach|, one only has to
``train'' it a little bit, which is precisely what the \texttt{/.list} key
handler does. The above-mentioned ficiticous limitations are those which are
often said to prevent us from using \verb|\foreach| to create tabulars,
matrices, and/or aligned equations. 
\end{document}
```
![Screen Shot 2021-05-19 at 2.55.34 PM.png](/image?hash=7848a262d22a64beb19a1ecb0830363aa9781f9d8c319783e86267b013778aab)

BTW, the `\expandafter`s are not mine, I literally copied the `/.list` key handler and added a separator. If you look e.g. at the examples from pgfmanual 3.1.9 on p. 1002, ![Screen Shot 2021-05-20 at 1.48.22 PM.png](/image?hash=008fcf84bd37b6cba5b89bf91c7d239893885e4033cd6c9e9603071c3c0e02a5) then you may agree that there comma at the very end is a bit unfortunate, so `/.rlist` is an attempt to improve this. Otherwise it is just the `/.list` handler., which certainly deals with ampersands and does *not* do grouping. You will find on the other site but also here statements of the sort that `\foreach` is not able to deal with those, but this is clearly wrong because `/.list` is based on `\foreach`. Sometimes these statements are paired with the conclusion that one has to use `expl3`, and I happen to disagree with those sentiments. (`expl3` also uses tons of `\expandafter`s or equivalent macros under the hood, but does not understand instructions like `{1,3,...,7}` which make `\foreach` so powerful.)

One can make `delta` work, but it might be dangerous. I added a key, `typeset`, which tries to make sense of `delta` and the like. It checks if a macro `\delta` exists, and if so, it prints `\delta`, otherwise `delta`. This can have the intended effect for variables like `\delta`, `\mu` etc. but fails for `delta_1` and similar, and may have unwanted consequences if you call a variable, say, `sum`. ``` \documentclass{article} \usepackage{pgffor} \usepackage{mathtools} \makeatletter% stolen from forest \pgfkeys{/handlers/.global style/.code=\pgfkeys{\pgfkeyscurrentpath/.global code=\pgfkeysalso{#1}}} \pgfkeysdef{/handlers/.global code}{\pgfkeysglobaldef{\pgfkeyscurrentpath}{#1}} \long\def\pgfkeysglobaldef#1#2{% \long\def\pgfkeys@temp##1\pgfeov{#2}% \pgfkeysgloballet{#1/.@cmd}{\pgfkeys@temp}% \pgfkeysglobalsetvalue{#1/.@body}{#2}% } \def\pgfkeysgloballet#1#2{% \expandafter\global\expandafter\let\csname pgfk@#1\endcsname#2% } \long\def\pgfkeysglobalsetvalue#1#2{% \pgfkeys@temptoks{#2}\expandafter\xdef\csname pgfk@#1\endcsname{\the\pgfkeys@temptoks}% } \makeatother \newcommand{\diff}{\mathop{}\!\text{d}} \DeclareMathOperator{\Euler}{e} % I used long formulae on purpose \pgfkeys{ formula/.is family, formula/.unknown/.code={#1}, formula/.cd, typeset/.code={\ifcsname#1\endcsname\csname#1\endcsname\else#1\fi}, plain/.code={#1}, delta/.initial = { \mathcal{N}\left(\frac{\ln \frac{F}{K} +\frac{1}{2}\sigma^2T}{\sigma \sqrt{T}}\right) }, d_1/.code = { \frac{\ln\frac{S}{K} + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}}, d_2/.code = { \frac{\ln\frac{S}{K} + (r - \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}}, normal/.initial = { {\frac {1}{\sigma {\sqrt {2\pi }}}} \int _{-\infty }^{x} \Euler ^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}\,\diff t }, normal standard/.initial = { {\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{x}\Euler ^{-{\frac {1}{2}}t^{2}}\,\diff t }, do align/.code={\pgfkeys{formula/list/unless first=\\}% \pgfkeys{formula/typeset={#1}}&=\formula{#1}}, } \makeatletter \newif\if@pgf@rlist@first \pgfkeys{ formula/.cd, list/only first/.code={\if@pgf@rlist@first#1\fi}, list/unless first/.code={\if@pgf@rlist@first\global\@pgf@rlist@firstfalse\else#1\fi}, } \pgfkeys{/handlers/.rlist/.code=% {% \ifx\foreach\@undefined% \pgfkeys@error{You need to load the pgffor package to use the .list key syntax.}% \fi% \global\@pgf@rlist@firsttrue % Use foreach to unfold the list \def\pgf@keys@temp{}% \foreach \pgf@keys@key in{#1}% {\expandafter\expandafter\expandafter\gdef% \expandafter\expandafter\expandafter\pgf@keys@temp% \expandafter\expandafter\expandafter{\expandafter\pgf@keys@temp\expandafter{\pgf@keys@key}}}% \edef\pgf@keys@list@path{\pgfkeyscurrentpath}% \expandafter\expandafter\expandafter\pgf@keys@do@list% \expandafter\expandafter\expandafter{\expandafter\pgf@keys@list@path\expandafter}\pgf@keys@temp\pgf@stop% }% } \makeatother \newcommand\formula[2][]{% \ifx#1\relax\relax \else \pgfkeys{formula/.cd,@#1/.global style={#2}}% \fi \pgfkeys{formula/.cd,#2}} \newcommand\RF[2][]{\formula{@#2}} \begin{document} You can use formulas from your repository \[ \formula{delta} \] It works perfectly and simplifies typing. The optional argument can be used to store the keys in a global (!) style. You can give some context indeed (great feature !) Add $\Delta=$ on the left hand side \[ \formula{plain={\Delta=},delta} \]. Easy to include limits \[ \formula{plain={L=\lim_{\sigma\to\infty}},delta} \] For integrals, I would miss the d-measure \[ \formula{plain={I=\int _{-\infty }^{T}},delta,plain={\diff t}} \] Easy to include sums \[ \formula[Delta sum]{plain={S= \sum _{K=1}^{\infty}},delta} \] and use a "natural" language like \texttt{Delta sum} to recall the style later You can then repeat the style easily in text $\RF{Delta sum}$. Align can be used, too, but tell me if I'm mis-using it or if there are limitations. For instance: \begin{align} \pgfkeys{formula/do align/.rlist={d_1,d_2}} \end{align} works perfectly but (legimately) if one want to use natural language like \begin{align} \pgfkeys{formula/do align/.rlist={delta,d_2}} \end{align} \end{document} ````

@marmot, re: [your answer](#a2026), Dear Marmot, your suggestions were more than usefull ! Merci ! As usual, I spent some time working on your (already dense) V1 yesterday. Smooth and easy. The " training" process enables to adapt your flow instantly. Brilliant. Then today... I saw your V2 that was a big upgrade on what was already great... My comments and testing below : ``` \documentclass{article} \usepackage{pgffor} \usepackage{mathtools} \makeatletter% stolen from forest \pgfkeys{/handlers/.global style/.code=\pgfkeys{\pgfkeyscurrentpath/.global code=\pgfkeysalso{#1}}} \pgfkeysdef{/handlers/.global code}{\pgfkeysglobaldef{\pgfkeyscurrentpath}{#1}} \long\def\pgfkeysglobaldef#1#2{% \long\def\pgfkeys@temp##1\pgfeov{#2}% \pgfkeysgloballet{#1/.@cmd}{\pgfkeys@temp}% \pgfkeysglobalsetvalue{#1/.@body}{#2}% } \def\pgfkeysgloballet#1#2{% \expandafter\global\expandafter\let\csname pgfk@#1\endcsname#2% } \long\def\pgfkeysglobalsetvalue#1#2{% \pgfkeys@temptoks{#2}\expandafter\xdef\csname pgfk@#1\endcsname{\the\pgfkeys@temptoks}% } \makeatother \newcommand{\diff}{\mathop{}\!\mathnormal{d}} \DeclareMathOperator{\Euler}{e} % I used long formulae on purpose \pgfkeys{ formula/.is family, formula/.unknown/.code={#1}, formula/.cd, plain/.code={#1}, delta/.initial = { \mathcal{N}\left(\frac{\ln \frac{F}{K} +\frac{1}{2}\sigma^2T}{\sigma \sqrt{T}}\right) }, d_1/.code = { \frac{\ln\frac{S}{K} + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}}, d_2/.code = { \frac{\ln\frac{S}{K} + (r - \frac{\sigma^2}{2})T}{\sigma \sqrt{T}}}, normal/.initial = { {\frac {1}{\sigma {\sqrt {2\pi }}}} \int _{-\infty }^{x} \Euler ^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}\,\diff t }, normal standard/.initial = { {\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{x}\Euler ^{-{\frac {1}{2}}t^{2}}\,\diff t }, do align/.code={\pgfkeys{formula/list/unless first=\\}% #1&=\formula{#1}}, } \makeatletter \newif\if@pgf@rlist@first \pgfkeys{ formula/.cd, list/only first/.code={\if@pgf@rlist@first#1\fi}, list/unless first/.code={\if@pgf@rlist@first\global\@pgf@rlist@firstfalse\else#1\fi}, } \pgfkeys{/handlers/.rlist/.code=% {% \ifx\foreach\@undefined% \pgfkeys@error{You need to load the pgffor package to use the .list key syntax.}% \fi% \global\@pgf@rlist@firsttrue % Use foreach to unfold the list \def\pgf@keys@temp{}% \foreach \pgf@keys@key in{#1}% {\expandafter\expandafter\expandafter\gdef% \expandafter\expandafter\expandafter\pgf@keys@temp% \expandafter\expandafter\expandafter{\expandafter\pgf@keys@temp\expandafter{\pgf@keys@key}}}% \edef\pgf@keys@list@path{\pgfkeyscurrentpath}% \expandafter\expandafter\expandafter\pgf@keys@do@list% \expandafter\expandafter\expandafter{\expandafter\pgf@keys@list@path\expandafter}\pgf@keys@temp\pgf@stop% }% } \makeatother \newcommand\formula[2][]{% \ifx#1\relax\relax \else \pgfkeys{formula/.cd,@#1/.global style={#2}}% \fi \pgfkeys{formula/.cd,#2}} \newcommand\RF[2][]{\formula{@#2}} \begin{document} You can use formulas from your repository \[ \formula{delta} \] It works perfectly and simplifies typing. The optional argument can be used to store the keys in a global (!) style. You can give some context indeed (great feature !) Add $\Delta=$ on the left hand side \[ \formula{plain={\Delta=},delta} \]. Easy to include limits \[ \formula{plain={L=\lim_{\sigma\to\infty}},delta} \] For integrals, I would miss the d-measure \[ \formula{plain={I=\int _{-\infty }^{T}},delta} \] Easy to include sums \[ \formula[Delta sum]{plain={S= \sum _{K=1}^{\infty}},delta} \] and use a "natural" language like \texttt{Delta sum} to recall the style later You can then repeat the style easily in text $\RF{Delta sum}$. Align can be used, too, but tell me if I'm mis-using it or if there are limitations. For instance: \begin{align} \pgfkeys{formula/do align/.rlist={d_1,d_2}} \end{align} works perfectly but (legimately) if one want to use natural language like \begin{align} \pgfkeys{formula/do align/.rlist={delta,d_2}} \end{align} \end{document} ``` Crossing your answer with the nomenclature package will be a cool feature I'll investigate. PS : Lol for the `\expandafter\expandafter\expandafter` :) ![blob](/image?hash=616c2dc825f82af35390eea95359a96b7629c9296ebf7336e3913ab57f81f2b6)

1 Answer