अध्यायिन्यदेशकालात्

Operational rule vidhi

The affix ठक् comes in the sense of 'who studies there' after a word in the Locative -7th case in construction, denoting an improper place or time.

Word by word (padaccheda)

Right context अध्यायिनि saptamī · ekavacanaLeft context अ- देश- कालात् pañcamī · ekavacana

Right context Saptamī (7th case): "when X follows", the operation applies to what precedes (1.1.66 तस्मिन्निति निर्दिष्टे पूर्वस्य). Also a condition or domain ("in the sense of").
Left context Pañcamī (5th case): "after X", the operation applies to what follows (1.1.67 तस्मादित्युत्तरस्य). Also used for limits and sources.

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Full reading

अध्यायिनि अ-देश-कालात्

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

Commentary

The affix ठक् comes in the sense of 'who studies there' after a word in the Locative -7th case in construction, denoting an improper place or time.
The word अदेशकाल means the time or place of study, which is prohibited by sacred institutes. अध्यायिन् means one who studies. Thus श्मशानेऽधीते = श्माशानिकः 'who reads in a funeral ground.' चतुष्पथिकः 'who studies where four roads meet.' So also चतुर्दश्यामधीते = चातुर्दशिकः, 'who reads on the 14th lunar day.' So also आमावास्यिकः ॥

Why do we say 'improper time and place ?' Observe स्रुघ्नेऽधीते, पूर्वाह्णेऽधीते ॥

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