Yogam and Karnam

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How yogam and Karnam are calculated mathematiccaly w.r.t thithi and nakshatra?

 

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27 Nithyayogas
1) Vishkambha, 2) Preethi, 3) Ayushman, 4)Soubhagya, 5) Shobhana, 6) Athiganda, 7) Sukarma, 8) Dhrithi, 9) Soolam, 10)Ganda, 11) Vridhi, 12) Dhruva, 13) Vyaghatha, 14) Harshana, 15) Vajra, 16)Siddhi, 17) Vyathipatha, 18) Variyan, 19) Parigha, 20) Shiva, 21) Siddha, 22)Sadhya, 23) Subhra, 24) Braahma, 25) Mahendra, 26) Vaidhruthi, 27) Shubha
Their length, as the length of the stars, is 13 degree 20 minutes.Nithyayoga is the sum of the longitudes of Sun and Moon.
Karanam
Karanam is half of Tithi. There are 28 Tithis from Shukla PradhamaUttarashada to Krishna Chathurdasi Purvashada. So there are 56 Karanams.
Charakaranas
1) Lion (Bava), 2) Tiger (Balava), 3) Pig(Koulava), 4) Ass (Taitila), 5) Elephant (Gara), 6) Cow (Vanija), 7) Vishti(Bhadra).
These 7 Charakaranas are repeated 8 times.
The four Karanas including Shukla Pradhama's Purvashada, KrishnaChathurdasi's Uttarashada and the two parts of Amavasi are permanent karanas.These come only once. They are 1) Bird (Sakuna) 2) Four-legged animal(Chatushpada) 3) Snake (Naga) 4) Worm (Kimstugna).
https://www.epanchang.com/daily-panchangam