With reference to the history of India, the 'Katapayadi system', the Parahita system' and the 'Drigganita system' are associated with

The 'Katapayadi', 'Parahita', and 'Drigganita' systems are integral components of Indian astronomical and mathematical traditions, particularly within the Kerala School. The Katapayadi system is an alphabetical notation where Sanskrit consonants are assigned numerical values to simplify the representation of large numbers in astronomical verses [2]. The Parahita system, introduced by Haridatta in the 7th century, simplified the computational cycles of the Aryabhatiya to improve accuracy in planetary calculations. The Drigganita (or Drik) system was a later refinement introduced by Parameshvara in the 15th century, which emphasized observational accuracy over purely theoretical constants to align calculated planetary positions with actual visual observations. These systems were primarily used for computing almanacs (Panchangas), predicting eclipses, and determining auspicious timings, marking significant advancements in the history of Indian astronomy [3].

Sources

1. [2] https://en.wikipedia.org/wiki/Drigganita
2. [3] https://ia801508.us.archive.org/7/items/in.ernet.dli.2015.205661/2015.205661.History-Of_text.pdf