Today we will look at the form धौम्येन mIs from महाभारतम् 3.3.14.

जनमेजय उवाच
कथं कुरूणामृषभः स तु राजा युधिष्ठिरः । विप्रार्थमाराधितवान्सूर्यमद्‌भुतदर्शनम् ।। ३-३-१३ ।।
वैशम्पायन उवाच
शृणुष्वावहितो राजञ्शुचिर्भूत्वा समाहितः । क्षणं च कुरु राजेन्द्र सम्प्रवक्ष्याम्यशेषतः ।। ३-३-१४ ।।
धौम्येन तु यथा पूर्वं पार्थाय सुमहात्मने । नामाष्टशतमाख्यातं तच्छृणुष्व महामते ।। ३-३-१४ ।।

Translation – Janamejaya said: For the sake of the Brāhmaṇas, how did that foremost of the Kurus, King Yudhiṣṭhira, worship the Sun of wonderful appearance? (13) Vaiśampāyana said: O king, (first) purify yourself and being composed listen with attention. O king of kings, make some leisure. I shall (then) tell you everything in detail (14). O highly intelligent one, listen to the one hundred and eight names (of the Sun), as they were told earlier by Dhaumya to the very high-souled Yudhiṣṭhira (son of Pṛthā) (15).

The above verses have previously appeared in the following post – नामाष्टशतम्-nNs

धूमस्य गोत्रापत्यम् (पुमान्) = धौम्यः – a (male) descendant (but not the son) of the sage Dhūma
In the verses the विवक्षा is तृतीया-एकवचनम्, hence the form used is धौम्येन।

(1) धूम ङस् + यञ् । By 4-1-105 गर्गादिभ्यो यञ् – Following a syntactically related पदम् in which the सन्धिः operations have been performed, and which ends in a sixth case affix and has ‘गर्ग’ etc (listed in the गर्गादि-गण:) as its base, the तद्धित: affix ‘यञ्’ may be applied optionally to denote a descendant having the designation ‘गोत्र’ (ref: 4-1-162 अपत्यं पौत्रप्रभृति गोत्रम्‌।)
Note: The अनुवृत्तिः of गोत्रे comes down into the सूत्रम् 4-1-105 from the सूत्रम् 4-1-98 गोत्रे कुञ्जादिभ्यश्च्फञ्।
As per 4-1-162 अपत्यं पौत्रप्रभृति गोत्रम्‌ – The designation ‘गोत्र’ is assigned to a grandson/granddaughter onward when the intention is to express him/her as a descendant (अपत्यम्)।
As per the सूत्रम् 4-1-92 तस्यापत्यम् – Following a syntactically related पदम् in which the सन्धिः operations have been performed and which ends in a sixth case affix the तद्धिता: affixes already prescribed (by the prior rules 4-1-83 प्राग्दीव्यतोऽण् etc), as well as those that are going to be prescribed (by the following rules 4-1-95 अत इञ् etc), may be optionally applied to denote the sense of अपत्यम् (descendant.)

(2) धूम ङस् + य । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।

Note: ‘धूम ङस् + य’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 सुपो धातुप्रातिपदिकयोः to apply in the next step.

(3) धूम + य । By 2-4-71 सुपो धातुप्रातिपदिकयोः – A सुँप् affix takes a लुक् elision when it is a part of a धातुः or a प्रातिपदिकम्।

Note: The affix ‘यञ्’ is a ञित् (has the letter ‘ञ्’ as इत्)। This allows 7-2-117 तद्धितेष्वचामादेः to apply in the next step.

(4) धौम + य । By 7-2-117 तद्धितेष्वचामादेः – The first vowel among the vowels of a अङ्गम् which is followed by a तद्धित: affix (ref. 4-1-76 तद्धिताः) which is either a ञित् (has the letter ‘ञ्’ as a इत्) or a णित् (has the letter ‘ण्’ as a इत्) takes the वृद्धि: (ref. 1-1-1 वृद्धिरादैच्) substitute.

Note: The अङ्गम् ‘धौम’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-148 यस्येति च to apply in the next step.

(5) धौम् + य । By 6-4-148 यस्येति च – When the letter ‘ई’ or a ‘तद्धित’ affix follows, the (ending) इ-वर्ण: (letter ‘इ’ or ‘ई’) or the (ending) अवर्ण: (letter ‘अ’ or ‘आ’) of the अङ्गम् with the भ-सञ्ज्ञा takes elision (लोपः)।

= धौम्य । The प्रातिपदिकम् ‘धौम्य’ declines like राम-शब्दः।

(6) धौम्य + टा । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्‌।

(7) धौम्य + इन । By 7-1-12 टाङसिङसामिनात्स्याः – Following a अङ्गम् ending in the letter ‘अ’, the affixes ‘टा’, ‘ङसिँ’ and ‘ङस्’ are replaced respectively by ‘इन’, ‘आत्’ and ‘स्य’। As per 1-1-55 अनेकाल्शित्सर्वस्य the entire affix ‘टा’ is replaced.

(8) धौम्येन । By 6-1-87 आद्‍गुणः।

We can similarly derive the following –
१) पुलस्तेर्गोत्रापत्यम् (पुमान्) = पौलस्त्यः (रावणः) – a (male) descendant (but not the son) of (the sage) Pulasti
२) शकलस्य गोत्रापत्यम् (पुमान्) = शाकल्यः – a (male) descendant (but not the son) of Śakala
३) मुद्गलस्य गोत्रापत्यम् (पुमान्) = मौद्गल्यः – a (male) descendant (but not the son) of Mudgala
४) यज्ञवल्कस्य गोत्रापत्यम् (पुमान्) = याज्ञवल्क्यः – a (male) descendant (but not the son) of Yajñavalka