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\title{\textcolor{yellow}{Anuv\d{r}tti}}
\author{Amba Kulkarni}
\institute{ Fellow IIAS, Shimla}
\date{1st April 2017}

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\frametitle{Anuv\d{r}tti}
{\dv अनुवृत्ति} : Anuv\d{r}tti: Recurrence\\

\vspace{0.2cm}
The concept is very close to factorisation in Mathematics.\\
\vspace{0.2cm}
a*b + a*c = a* (b+c)\\
\vspace{0.2cm}
Languages also use this phenomenon in the form of `sharing' of arguments.
For example, consider following two sentences.\\
\vspace{0.2cm}
Ram went home.\\
Ram slept.\\
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These two sentences can be combined into a single sentence, sharing the Subject as\\
\vspace{0.2cm}
Ram went home and slept.\\
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\frametitle{Anuv\d{r}tti}
Panini has used Anuv\d{r}tti to the maximum extent possible so as to bring in brevity in the system.\\
\vspace{0.2cm}
The function of `Anuv\d{r}tti' is to relate preceeding rules of a domain to its following rules. That is it allows a controlled reading of a former rule, or part of a former rule, in the interpretation or application of a subsequent rule. It thus helps reconstruct the shared context of a given rule within a domain. (Rama Nath Sharma; The A\d{s}\d{t}{\=a}dhy{\=a}yi of P{\=a}\d{n}ini, Vol I, pp 44-45)
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\frametitle{Anuv\d{r}tti}
Consider the rule\\
\textbf{aca\d{h} karmakarttari 3.1.62}\\
Meaning: after something ending in ac (a vowel), which is followed by a karmakart\d{r}.\\
In order to understand this s{\=u}tra, we need the following borrowings.\\
\begin{itemize}
\item pratyaya\d{h} 3.1.1
\item para\'{s}ca 3.1.2
\item dh{\=a}to\d{h} 3.1.22
\item cli li\.ni 3.1.43
\item cle\d{h} sic 3.1.44
\item ci\d{n} te 3.1.60
\item ... anyatarasy{\=a}m 3.1.62
\end{itemize}
Complete s{\=u}tra now is\\
pratyaya\d{h} para\'{s} ca dh{\=a}to\d{h} lu\.ni ci\d{n} te anyatarasy{\=a}m aca\d{h} karmakarttari\\
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\frametitle{Anuv\d{r}tti ...}
Complete s{\=u}tra now is\\
pratyaya\d{h} para\'{s} ca dh{\=a}to\d{h} lu\.ni ci\d{n} te anyatarasy{\=a}m aca\d{h} karmakarttari\\
\vspace{0.2cm}
which means\\
\vspace{0.2cm}
ajant{\=a}d dh{\=a}to\d{h} parasya cle\d{h} pratyayasya karmakarttari ta\'{s}abde parata\d{h} ci\d{n}{\=a}de\'{s}a\d{h} bhavati anyatarasy{\=a}m\\
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Affix CLI optionally is replaced by CI\d{N} when the former occurs after a verb root ending in AC (a vowel) and when ta, a replacement of LU\d{N} which denotes karmakarattari (object treated as if agent) follows.\\
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\frametitle{Anuv\d{r}tti}
Consider the following s{\=u}tras:\\
\vspace{0.2cm}
\begin{itemize}
\item \textit{\it upade\'{s}e ac anun{\=a}sik it} 1.3.2\\
{\dv उपदेशे अच् अनुनासिक इत्}
\item \textit{\it hal antyam} 1.3.3\\
{\dv हल् अन्त्यम्}
\item \textit{\it na vibhaktau tusm{\=a}\d{h}} 1.3.4\\
{\dv न विभक्तौ तुस्मा}
\item \textit{\it {\=a}di\d{h} \~ni\d{t}u\d{d}av{\=a}\d{h}} 1.3.5\\
{\dv आदिः    ञिटुडवः}
\item \textit{\it \d{s}a\d{h} pratyayasya} 1.3.6\\
{\dv षः प्रत्ययस्य}
\item \textit{\it cu\d{t}{\=u}} 1.3.7\\
{\dv चुटू}
\item \textit{\it la\d{s}aku ataddhite} 1.3.8\\
{\dv लशकु अतद्धिते}
\end{itemize}
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\frametitle{Anuv\d{r}tti}
These s{\=u}tras after borrowing the necessary words from previous s{\=u}tras expand to
\vspace{0.2cm}
\begin{itemize}
\item \textit{\it upade\'{s}e ac anun{\=a}sik it} 1.3.2\\
{\dv उपदेशे अच् अनुनासिक इत्}\\
The nasalised ({\dv अनुनासिक}) vowels( {\dv अच् }) are {\dv इत् }in original enunciation ({\dv उपदेश }).
\item \textbf{upade\'{s}e } \textit{\it hal antyam} \textbf{it} 1.3.3\\
{\dv उपदेशे हल् अन्त्यम् इत्}\\
In {\dv उपदेश }, the final consonant ({\dv हल् })  is {\dv इत्}|
\item \textbf{upade\'{s}e } \textit{\it na vibhaktau tusm{\=a}\d{h}} \textbf{it} 1.3.4\\
{\dv उपदेशे न विभक्तौ तुस्माः इत्}\\
The final dental consonants ({\dv तु}) and the final {\dv स् } and {\dv म् } are not {\dv इत् } in affixes called {\dv विभक्ति}
\item \textbf{upade\'{s}e } \textit{\it {\=a}di\d{h} \~ni\d{t}u\d{d}av{\=a}\d{h}} \textbf{it} 1.3.5\\
{\dv उपदेशे आदिः   ञिटुडवः इत्}\\
The initial {\dv ञि}, {\dv टु}, {\dv डु} are {\dv इत्}
\end{itemize}
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\frametitle{Anuv\d{r}tti}
\begin{itemize}
\item \textbf{upade\'{s}e {\=a}di\d{h}} \textit{\it \d{s}a\d{h} pratyayasya} \textbf{it} 1.3.6\\
{\dv उपदेशे आदिः षः प्रत्ययस्य इत्}\\
The initial {\dv ष् }of an affix is {\dv इत्}
\item \textbf{upade\'{s}e {\=a}di\d{h} pratyayasya} \textit{\it cu\d{t}{\=u}} \textbf{it} 1.3.7\\
{\dv उपदेशे आदिः प्रत्ययस्य चुटू इत्}\\
The initial palatals ({\dv चु}) and linguals ({\dv टु}) of an affix are {\dv इत्}
\item \textbf{upade\'{s}e  {\=a}di\d{h} pratyayasya} \textit{\it la\d{s}aku ataddhite} \textbf{it} 1.3.8\\
{\dv उपदेशे आदिः प्रत्ययस्य लशकु अतद्धिते इत्}\\
The initial {\dv ल् } and {\dv श् }and the gutturals  ({\dv कु}) of all affixes, except  {\dv तद्धित} are {\dv इत्}
\end{itemize}
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\frametitle{Anuv\d{r}tti}
Introduce variables for words
\vspace{0.2cm}
\begin{itemize}
\item \textit{\it upade\'{s}e(A) ac(B) anun{\=a}sik(C) it(D)} 1.3.2\\
{\dv उपदेशे अच् अनुनासिक इत्}
\item \textbf{upade\'{s}e(A) } \textit{\it hal antyam (E)} \textbf{it (D)} 1.3.3\\
{\dv उपदेशे हल् अन्त्यम् इत्}
\item \textbf{upade\'{s}e(A) } \textit{\it na vibhaktau tusm{\=a}\d{h}(F)} \textbf{it (D)} 1.3.4\\
{\dv उपदेशे न विभक्तौ तुस्मा इत्}
\item \textbf{upade\'{s}e(A) } \textit{\it {\=a}di\d{h}(G) \~ni\d{t}u\d{d}av{\=a}\d{h}(H)} \textbf{it (D)} 1.3.5\\
{\dv उपदेशे आदिः    ञिटुडवः इत्}
\item \textbf{upade\'{s}e(A) {\=a}di\d{h}(G)} \textit{\it \d{s}a\d{h}(I) pratyayasya(J)} \textbf{it (D)} 1.3.6
{\dv  उपदेशे षः प्रत्ययस्य इत्}
\item \textbf{upade\'{s}e(A) {\=a}di\d{h}(G) pratyayasya(J)} \textit{\it cu\d{t}{\=u}(K)} \textbf{it (D)} 1.3.7\\
{\dv उपदेशे चुटू इत्}
\item \textbf{upade\'{s}e(A)  {\=a}di\d{h}(G) pratyayasya(J)} \textit{\it la\d{s}aku ataddhite(L)} \textbf{it (D)} 1.3.8\\
{\dv उपदेशे लशकु अतद्धिते इत्}
\end{itemize}
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\frametitle{Anuv\d{r}tti}
After removing the text, we have
\vspace{0.2cm}
\begin{itemize}
\item A B C D    (1.3.2)
\item A E D      (1.3.3)
\item A F D      (1.3.4)
\item A G H D    (1.3.5)
\item A G I J D  (1.3.6)
\item A G J K D  (1.3.7)
\item A G J L D  (1.3.8)
\end{itemize}
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\frametitle{Anuv\d{r}tti}
Treating each of the s{\=u}tras as one term in a mathematical expression, and the set of s{\=u}tras as sum of the terms, we can simplify the above expression as follows.\\
\vspace{0.2cm}
A B C D + A E D + A F D + A G H D + A G I J D + A G J K D + A G J L D \\
$\rightarrow$\\
A (B C +  E  +  F  +  G { H  +  J [ I +   K +  L ] }) D \\
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Writing each term again on separate line, we get\\
\begin{itemize}
\item A B C D 
\item E
\item F
\item G H
\item I J
\item K
\item L
\end{itemize}
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\frametitle{Anuv\d{r}tti}
Replacing each variable by the corresponding word, we get the Ashtadhyayi s{\=u}tras.
\vspace{0.2cm}
\begin{itemize}
\item \textit{\it upade\'{s}e(A) ac(B) anun{\=a}sik(C) it(D)} 1.3.2\\
{\dv उपदेशे अच् अनुनासिक इत्}
\item \textit{\it hal antyam(E)} 1.3.3\\
{\dv हल् अन्त्यम्}
\item \textit{\it na vibhaktau tusm{\=a}\d{h}(F)} 1.3.4\\
{\dv न विभक्तौ तुस्माः }
\item \textit{\it {\=a}di\d{h}(G) \~ni\d{t}u\d{d}av{\=a}\d{h}(H)} 1.3.5\\
{\dv आदिः    ञिटुडवः}
\item \textit{\it \d{s}a\d{h}(I) pratyayasya(J)} 1.3.6\\
{\dv षः प्रत्ययस्य}
\item \textit{\it cu\d{t}{\=u}(K)} 1.3.7\\
{\dv चुटू}
\item \textit{\it la\d{s}aku ataddhite(L)} 1.3.8\\
{\dv लशकु अतद्धिते}
\end{itemize}
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\frametitle{Anuv\d{r}tti: Another example}
Here the words borrowed from previous s{\=u}tras are in parenthesis.\\
\vspace{0.2cm}
\begin{itemize}
\item 6-1-87 \={a}d gu\d{n}a\d{h} (sa\d{m}hit\={a}y\={a}m aci eka\d{h} p\={u}rvaparayo\d{h})
\item 6-1-88 v\d{r}ddhi\d{h} eci (sa\d{m}hit\={a}y\={a}m  eka\d{h} p\={u}rvaparayo\d{h} \={a}d)
\item 6-1-89 etyedhaty\={u}\d{t}hsu (sa\d{m}hit\={a}y\={a}m eka\d{h} p\={u}rvaparayo\d{h} \={a}d v\d{r}ddhi\d{h} eci)
\item 6-1-90 \={a}\d{t}a\d{h} ca (sa\d{m}hit\={a}y\={a}m aci eka\d{h} p\={u}rvaparayo\d{h}  v\d{r}ddhi\d{h})
\item 6-1-91 upasarg\={a}t \d{r}ti dh\={a}tau (sa\d{m}hit\={a}y\={a}m  eka\d{h} p\={u}rvaparayo\d{h} \={a}d v\d{r}ddhi\d{h})
\item 6-1-92 v\={a} supi \={a}pi\'{s}ale\d{h} (sa\d{m}hit\={a}y\={a}m eka\d{h} p\={u}rvaparayo\d{h} \={a}d v\d{r}ddhi\d{h} upasarg\={a}t \d{r}ti dh\={a}tau)
\item 6-1-93 \={a} ot am\'{s}aso\d{h} (sa\d{m}hit\={a}y\={a}m aci eka\d{h} p\={u}rvaparayo\d{h})
\item 6-1-94 e\.{n}i parar\={u}pam (sa\d{m}hit\={a}y\={a}m  eka\d{h} p\={u}rvaparayo\d{h} \={a}d  upasarg\={a}t dh\={a}tau)
\end{itemize}
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\frametitle{Anuv\d{r}tti: Another example}
Assigning variables to various words:
\begin{itemize}
\item 6-1-87 \={a}d(d) gu\d{n}a\d{h}(e) sa\d{m}hit\={a}y\={a}m(a) aci(b) eka\d{h} p\={u}rvaparayo\d{h}(c)\\
{\dv आद्(d) गुणः(e) संहितायाम्(a) अचि(b) एकः पूर्वपरयोः(c)}
\item 6-1-88 v\d{r}ddhi\d{h}(\.{n}) eci(g) sa\d{m}hit\={a}y\={a}m(a)  eka\d{h} p\={u}rvaparayo\d{h}(c) \={a}d(d)\\
{\dv वृद्धिः(f) एचि(g) संहितायाम्(a)  एकः पूर्वपरयोः (c) आद् (d)}
\item 6-1-89 etyedhaty\={u}\d{t}hsu(h) sa\d{m}hit\={a}y\={a}m(a) eka\d{h} p\={u}rvaparayo\d{h}(c) \={a}d(d) v\d{r}ddhi\d{h}(\.{n}) eci(g)\\
{\dv एत्येधत्यूठ्सु(h) संहितायाम्(a) एकः पूर्वपरयोः(c) आद्(d) वृद्धिः(f) एचि(g)}
\item 6-1-90 \={a}\d{t}a\d{h} ca(i) sa\d{m}hit\={a}y\={a}m(a) aci(b) eka\d{h} p\={u}rvaparayo\d{h}(c)  v\d{r}ddhi\d{h}(\.{n})\\
{\dv आटः च(i) संहितायाम्(a) अचि(b) एकः पूर्वपरयोः(c)  वृद्धिः(f)}
\end{itemize}
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\begin{frame}
\frametitle{Anuv\d{r}tti: Another example}
Contd ...\\
\vspace{0.2cm}
\begin{itemize}
\item 6-1-91 upasarg\={a}t(j) \d{r}ti(k) dh\={a}tau(l) sa\d{m}hit\={a}y\={a}m(a)  eka\d{h} p\={u}rvaparayo\d{h}(c) \={a}d(d) v\d{r}ddhi\d{h}(\.{n})\\
{\dv उपसर्गात्(j) ऋति(k) धातौ(l) संहितायाम्(a)  एकः पूर्वपरयोः(c) आद्(d) वृद्धिः(f)}
\item 6-1-92 v\={a} supi \={a}pi\'{s}ale\d{h}(m) sa\d{m}hit\={a}y\={a}m(a) eka\d{h} p\={u}rvaparayo\d{h}(c) \={a}d(d) v\d{r}ddhi\d{h}(\.{n}) upasarg\={a}t(j) \d{r}ti(k) dh\={a}tau(l)\\
{\dv वा सुपि आपिशलेः(m) संहितायाम्(a) एकः पूर्वपरयोः(c) आद्(d) वृद्धिः(f) उपसर्गात्(j) ऋति(k) धातौ(l)}
\item 6-1-93 \={a} ot am\'{s}aso\d{h}(n) sa\d{m}hit\={a}y\={a}m(a) aci(b) eka\d{h} p\={u}rvaparayo\d{h} (c)\\
{\dv आ ओत् अम्शसोः(n) संहितायाम्(a) अचि(b) एकः पूर्वपरयोः (c)}
\item 6-1-94 e\.{n}i parar\={u}pam(o) sa\d{m}hit\={a}y\={a}m (a) eka\d{h} p\={u}rvaparayo\d{h} (c) \={a}d (d) upasarg\={a}t(j) dh\={a}tau (l)\\
{\dv एङि पररूपम्(o) संहितायाम् (a) एकः पूर्वपरयोः (c) आद् (d) उपसर्गात्(j) धातौ(l)}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Anuvrtti}
\begin{itemize}
\item a b c d e
\item a c d f g
\item a c d f g h
\item a b c f i
\item a c d f j k l
\item a c d f j k l m
\item a b c n
\item a c d j l o 
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Anuvrtti}
\begin{tabular}{lllllllll}
a&b&  c&d&e&&&&\\
a&(b)&c&d&f&g&&&\\
a&(b)&c&d&f&g&h&&\\
a&b & c&(d)&f&i&&&\\
a&(b)&c&d&  f&j&k&l&\\
a&(b)&c&d&  f&j&k&l& m\\
a&b & c&&   & (j)& &(l)&      n\\
a&(b)&c&d&  &  j& & l& o \\
\end{tabular}
\end{frame}
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\begin{frame}
\frametitle{Anuvrtti}
a b c [ d (e + f\color{red}\{g \color{black}(1 + h) + i + jl\color{blue}( \color{black}k (1 + m)\color{red}\}  \color{black}+ n + o)]
\end{frame}
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\begin{frame}
\frametitle{Anuv\d{r}tti}
Anuv\d{r}tti is different from the mathematical factorisation in following respects.
\begin{itemize}
\item Not necessarily properly nested
\item The beginning of the parenthesis is explicit, but the end is not marked explicitly.
\item There are some cases where the anuv\d{r}tti is in the backward direction. That is words from the following s{\=u}tras are to be considered for proper understanding of the s{\=u}tras.
\item In some cases the recurrence of words are not required for one s{\=u}tra but are required for the following s{\=u}tra. So the words recurr skipping some  s{\=u}tras in between. Hence is also called Ma\d{n}d{\=u}kapluti (leaping of a frog).
\item Sometimes words reccur with different vibhakti (form).
\end{itemize}
\end{frame}
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\begin{frame}
\begin{tabular}{ll}
Total S{\=u}tras &      (3,984)  4,000 \\
Total Words & (7,007) 7,000    \\
Total Words after repeating &\\
the words with anuv\d{r}tti& 40,000 \\
Compression due to anuv\d{r}tti&   (40,000/7,000 $\approx$) 1/6 \\
In terms of byte size, compression&      1/3 \\
\end{tabular}
\end{frame}
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