आप्ज्ञप्यृधामीत्

Operational rule vidhi

For the vowel of the roots 1. आप् 2. ज्ञपि and 3. ऋध् there is substituted long ई before सन् of the Desiderative when it begins with स्.

Word by word (padaccheda)

Target आप्ज्ञप्यृधाम् ṣaṣṭhī · bahuvacanaSubstitute / term ईत् prathamā · ekavacana

Target Ṣaṣṭhī (6th case): names what gets replaced, "in place of X" (1.1.49 षष्ठी स्थानेयोगा).
Substitute / term Prathamā (1st case): in operational rules, the substitute or the thing introduced; in definitions, the term or its referent.

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Full reading

आप्ज्ञप्यृधाम् ईत्

Pāṇini leaves out words that carry over from earlier sūtras. Expand to see the rule as a reader actually understands it.

As a rewrite rule (sketch from case endings)

आप्ज्ञप्यृधाम् → ईत्

Replace āpjñapyṛdhām with īt. Inherited words (anuvṛtti) may add further conditions.

Commentary

For the vowel of the roots 1. आप् 2. ज्ञपि and 3. ऋध् there is substituted long ई before सन् of the Desiderative when it begins with स्।
Thus आप्-ईप्सति, ज्ञपि-ज्ञीप्सति, ऋध्-ईर्त्सति 1.1.51. The reduplication is dropped by 7.4.58. In the Causative stem ज्ञपि there are two vowels, the इ (णि) is dropped by purva-vipratishedha (the prior debarring the subsequent) according to 6.4.51, and ई (substituted for अ according to the present sutra. The word सन् is to be read into the sutra, otherwise प्रापस्यति ॥ The सन् must begin with स् i.e should not take the इट् augment, as in जिज्ञपयिषति, अर्हिधिषति ॥ The roots ज्ञपि and ऋध् are optionally सेट् in the Desiderative by 7.2.49.

Śrīśa Chandra Vasu, The Ashtadhyayi of Panini (1897), via ashtadhyayi.com.