Today we will look at the form शैवम् nAs from श्रीमद्वाल्मीकि-रामायणम् 1.27.6.

तानि दिव्यानि भद्रं ते ददाम्यस्त्राणि सर्वशः । दण्डचक्रं महद्दिव्यं तव दास्यामि राघव ∥ १-२७-४ ∥
धर्मचक्रं ततो वीर कालचक्रं तथैव च । विष्णुचक्रं तथात्युग्रमैन्द्रमस्त्रं तथैव च ∥ १-२७-५ ∥
वज्रमस्त्रं नरश्रेष्ठ शैवं शूलवरं तथा । अस्त्रं ब्रह्मशिरश्चैव ऐषीकमपि राघव ∥ १-२७-६ ∥

Gita Press Translation – “I deliver to you all those celestial missiles, may good betide you! I shall deliver to you, O scion of Raghu, the great and ethereal Daṇḍa-Cakra and then the Dharma-Cakra, O gallant prince, as well as the Kāla-Cakra, also the Viṣṇu-Cakra as well as the most formidable Indra-Cakra and the missile in the shape of a thunderbolt, O jewel among men, similarly the Śūla (of Śiva), the best among all, presided over by Lord Śiva, as well as the missile called Brahmaśirā and even the Aiṣīka (that employed through the medium of a reed, rush or stem of grass). O scion of Raghu!” (4-6)

शिवो देवतास्‍येति = शैवम् (शूलम्) – (The trident) of which Lord Śiva is the presiding deity.
In the verses the विवक्षा is द्वितीया-एकवचनम्। Hence the form is शैवम्।

(1) शिव सुँ + अण् । By 4-2-24 सास्य देवता – To denote something of a particular deity, the तद्धित: affix ‘अण्’ (prescribed by 4-1-83 प्राग्दीव्यतोऽण्) may be optionally applied following a syntactically related पदम् in which the सन्धिः operations have been performed, provided the पदम् ends in a nominative case affix and has a base denoting the name of that presiding deity.

(2) शिव सुँ + अ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।

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

(3) शिव + अ । 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 ‘अण्’ is a णित् (has the letter ‘ण्’ as इत्)। This allows 7-2-117 तद्धितेष्वचामादेः to apply in the next step.

(4) शैव + अ । 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 ‘शैव’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-148 यस्येति च to apply in the next step.

(5) शैव् + अ । 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)।

= शैव । Note: The प्रातिपदिकम् ‘शैव’ is an adjective. In the present example, it is qualifying the neuter noun शूलम्। Hence, it declines like वन-शब्दः।

We can similarly derive the following –
१) इन्‍द्रो देवतास्‍येति = ऐन्‍द्रम् (हविः) – (an oblation) of which Indra is the presiding deity.