Pāṇini sūtras

The Dative case ending is not elided after ātman when the compound is the name of a technical term of grammar.

1. vaiyākaraṇa+ākhyāyāmवैयाकरण+आख्यायाम्

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   vव्	vaiyākaraṇवैयाकरण्	vaiyākaraṇaवैयाकरण	grammatical	vaiyākaraṇवैयाकरण् + plus aअ
   āआ	ākhyāआख्या	ākhyāyāmआख्यायाम्	term	ākhyआख्य् + plus āyआय्

2. caturthyāḥचतुर्थ्याः

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   cच्	caturthīचतुर्थी	caturthyāḥचतुर्थ्याः	dative	caturthचतुर्थ् + plus yāया

Anuvṛtti

1. uttara+padeउत्तर+पदे 6·3·1

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   uउ	uttaraउत्तर	uttaraउत्तर	last	uttarउत्तर् + plus aअ
   pप्	padaपद	padeपदे	word	padपद् + plus eए

2. ātmanaḥआत्मनः 6·3·6

   Part	Lexeme	Sandhi form	Meaning	Stem + termination
   āआ	ātmanआत्मन्	ātmanaḥआत्मनः	ātman [word]आत्मन् [wओर्द्]	ātmआत्म् + plus anaḥअनः