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\title{\textcolor{yellow}{Algorithms in Ancient India}}
\author{Amba Kulkarni}
\institute{ Department of Sanskrit Studies, \\University of Hyderabad}
\date{8th February 2018}

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\titlepage

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Various recitation styles to allow complete and perfect memorization
\begin{itemize}
\item Prak\d{r}ti p{\=a}\d{t}ha
\item Vik\d{r}ti p{\=a}\d{t}ha
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\frametitle{Preservation of Vedas: Oral Tradition}
Prak\d{r}ti p{\=a}\d{t}ha
\begin{itemize}
\item Sa\.mhit{\=a}: Continuous recitation
\item Pada: Pause after every word
\item Krama: consecutive words are paired and recited\\
1 2; 2 3; 3 4; 4 5; ..
\end{itemize}
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Which one is given / Basic ? -- Sa\.mhit{\=a}p{\=a}\d{t}ha or Padap{\=a}\d{t}ha ?\\
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Padap{\=a}\d{t}ha involves undoing Sandhi operation, while Sa\.mhit{\=a} involves doing a sandhi operation.\\
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Sandhi: V * V $\rightarrow$ V\\
where V: one or two var\d{n}as\\
This relation is Many-Many\\
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Hence both Sa\.mhit{\=a} as well as Pada p{\=a}\d{t}ha should be considered to be the starting points. Only one of them is not sufficient to preserve them.
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\frametitle{Vik\d{r}tis}
{\dv जटा माला शिखा रेखा ध्वजो दण्डो रथो घनः } \textbar \\
{\dv अष्टौ विकृतयः प्रोक्ताः क्रमपूर्वा महर्षिभिः} \textbar\textbar 1 \textbar\textbar\\
(a\d{s}\d{t}vik\d{r}tilak\d{s}{\=a}\d{n}{\=a}ni)
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\frametitle{Lak\d{s}a\d{n}a for Ja\d{t}{\=a}}
Jat{\=a} (matted hair)\\
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{\dv क्रमं यथोक्तं प्रब्रूयाद् व्युत्क्रमेण क्रमेण च }\textbar \\
{\dv सलक्षणं सर्वसंधौ जटा सा प्रोच्यते बुधैः}\textbar\textbar 2 \textbar\textbar\\
(a\d{s}\d{t}vik\d{r}tilak\d{s}{\=a}\d{n}{\=a}ni) \\
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If there are 5 words 1 2 3 4 5 then the ja\d{t}{\=a} p{\=a}\d{t}ha will be\\
1 2 2 1 1 2; \\
2 3 3 2 2 3; \\
3 4 4 3 3 4; \\
4 5 5 4 4 5; \\
5 iti 5\\
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\frametitle{Lak\d{s}a\d{n}a for m{\=a}l{\=a}}
There are two types of m{\=a}l{\=a}: pu\d{s}pam{\=a}l{\=a} and kramam{\=a}l{\=a}\\

\textbf{pu\d{s}pam{\=a}l{\=a}}\\
{\dv माला मालेव पुष्पाणां पदानां ग्रन्थिनी हि सा}\textbar\\
{\dv आवर्तन्ते त्रयस्तस्यां क्रमव्युत्क्रमसंक्रमाः }\textbar\textbar\\
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If there are 5 words 1 2 3 4 5 then the pu\d{s}pam{\=a}l{\=a} will be\\
1 2; 2 1; 1 2; \\
2 3; 3 2; 2 3; \\
3 4; 4 3; 3 4; \\
4 5; 5 4; 4 5;\\
5 iti 5\\
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Note that this is exactly same as the ja\d{t}{\=a}, except that now there is a pause after every pair of words, and thus there is no sandhi taking place between the consecutive pair of words.
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\frametitle{Lak\d{s}a\d{n}a for m{\=a}l{\=a}}
\textbf{Kramam{\=a}l{\=a}}\\
{\dv ब्रूयातक्रमविपर्यासावर्धर्चस्यादितोऽन्ततः}\textbar \\
{\dv अन्तं चादिं नयेदेवं क्रममालेति गीयते}\textbar \textbar\\
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If there are 7 words 1 2 3 4 5 6 7 then the kramam{\=a}l{\=a} will be\\
1 2; 7 iti 7\\
2 3; 7 6\\
3 4; 6 5\\
4 5; 5 4\\
5 6; 4 3\\
6 7; 3 2\\
7 iti 7; 2 1\\
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