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The relationship between entities designated by nouns (substantives and adjectives) can be expressed not only through a genitive construction but also by means of a Tatpuruṣa (तत्पुरुष). Similarly, attributive coordination of adjectives or appositional coordination of substantives can be expressed by a specific type of Tatpuruṣa, namely the so-called Karmadhāraya (m.) = कर्मधारय.
तत्पुरुषः = तस्य पुरुषः "his servant", i.e., as a designation for this type of compound, an example of such compounds is used.
In determinative compounds (Tatpuruṣa), a noun (substantive or adjective) is more precisely determined by another noun or adverb. The word being specified usually forms the second member of the compound.
The relationship between the first member (determining element) and the second member (specified element) can be:
The case relationship of both components of a compound is independent of the case in which the compound stands: for the compound is, after all, a single declinable word:
e.g.
Nom. sg. तत्पुरुषः = तस्य पुरुषः
Acc. sg. तत्पुरुषम् = तस्य पुरुषम्
Instr. sg. तत्पुरुषेण = तस्य पुरुषेण
Gen. sg. तत्पुरुषस्य = तस्य पुरुषस्य
Nom. pl. तत्पुरुषाः = तस्य पुरुषाः
etc.
The gender of a Tatpuruṣa is, with few exceptions, that of its second component.
When resolving a Karmadhāraya, both components of the compound stand in the same case.
e.g.
गुणवत्पुत्रः = गुणवान्पुत्रः = "a son with good qualities"
Acc. sg. गुणवत्पुत्रम्
Nom pl. गुणवत्पुत्राः पुण्यवत्क्षत्रिया = पुण्यवती क्षत्रिया = "a Kṣatriya woman of merit"
साधुजनाः = साधवो जनाः = "good people"
इष्टदेवता = इष्टा देवता = "the desired deity = the deity to which one has a special relationship of devotion and refuge"

Fig.: लक्ष्मी
(Image source: Details)
The following special rule applies to the sequence of components in a Karmadhāraya:
नरसिंहः = सिंह इव नरः = "a man like a lion"
पुरुषव्याघ्रः = व्याघ्र इव पुरुषः = "a man like a tiger"
नरसिंहः can also be resolved: नर एव सिंहः = "A lion, who (in reality) is a man."
Such appositional Karmadhārayas are resolved in the indigenous commentaries as well as in the example above using एव.

Fig.: नरसिंहः
(Image source: Details)
Tatpuruṣa combinations are possible for connections of nouns (nouns and adjectives), where the first member - according to the rules of syntax - can stand in any case. As expected, the first member most frequently represents a genitive (षष्ठी), since this is indeed the case for expressing the relationship between nouns.
e.g.
क्षत्रियपुत्रः = क्षत्रियस्य पुत्रः = "the son of a Kṣatriya", "a young Kṣatriya", "a member of the group of Kṣatriyas"
Acc. sg. क्षत्रियपुत्रम्
Gen. sg. क्षत्रियपुत्रस्य
etc.
गुरुभावः = गुरोर्भावः = "the nature of a teacher"
धनलोभः = धनस्य लोभः = "desire for wealth, greed"
लोकगतिः = लोकस्य गतिः = "the course of the world, the behavior of people"
Almost every genitive relationship can be replaced by a Tatpuruṣa. The few exceptions see e.g. in Kale, A higher Sanskrit grammar § 211; there you will also find the corresponding passages in Pāṇini.
However, the first member of a Tatpuruṣa can in principle represent any case. Nevertheless, not all syntactically possible case relationships can be replaced by a Tatpuruṣa. The corresponding rules can be found in Kale, A higher Sanskrit grammar § 203 - 217 or Pāṇini 2,1,22 - 2,2,22 in case of doubt.
The first member can stand in the singular, dual, or plural when resolving the compound. Which possibility is present must be inferred from meaning and context.
Examples:
The first member represents the accusative (द्वितीया): e.g. with certain PPPs to verbs of motion (Pāṇini 2,1,24):
ग्रामगतः = ग्रामं गतः = "one who has gone into the village"
नरकपतिता = नरकं पतिता = "one who has fallen into a hell"
The first member represents the instrumental (तृतीया): e.g. frequently the agent (कर्तृ) of nominal formations with kṛt suffixes (e.g. PPP):
देवकृतम् = देवेन / देवैः कृतम् = "made by a god / made by gods"
Also resolvable: देवस्य / देवानां कृतम् = "deed/action of a god / by gods; divine deed, deeds of the gods"
बुद्धरक्षिता = बुद्धेन रक्षिता = "the one who was protected by Buddha" (a proper name)
Although compounds of arbitrary length can be formed in Sanskrit and are also very frequently formed (compounds consisting of 10 to 30 members are no rarity!), nevertheless - with the exception of Dvandvas - all compounds must be decomposed progressively and hierarchically into two parts each:

Fig.: समासविच्छेदः
(Image source: Details)
etc. until one reaches the individual word stems.
e.g.
गुणवत्पुत्रकृतपुण्यम्
1. stage (main caesura): गुणवत्पुत्रकृतं ॥१॥ पुण्यम्
2. stage (first secondary caesura): गुणवत्पुत्रेण ॥२॥ कृतं ॥१॥ पुण्यम्
3. stage (second secondary caesura): गुणवता॥३॥ पुत्रेण ॥२॥ कृतं ॥१॥ पुण्यम्
= "the meritorious deed (merit) that my virtuous son has performed"
Various types of compounds can be mixed here, e.g. first member: Bahuvrīhi (बहुव्रीहि) - second member: Tatpuruṣa etc.
e.g.
ब्राह्मणक्षत्रियवैश्यधर्मः
1. stage: ब्राह्मणक्षत्रियवैश्यानां धर्मः (first member: Itaretaradvandva)
2. stage: ब्राह्मणानां क्षत्रियाणां वैश्यानां च धर्मः
= "the dharma of Brahmans, Kṣatriyas and Vaiśyas"
Very often there are various possibilities for resolving a compound. Which one is the correct or at least the best can only be decided from the context and content of the text. Sometimes such a decision is not possible. Often two resolution possibilities are presumably intended by the author. Then both resolution possibilities must be rendered in the translation (connected with "and", "or" "resp." and similar).
e.g.
पुण्यवत्पुत्रकृतम्
1. stage: either - or
2. stage: accordingly
In all types of compounds, the first member is generally the unchanged stem. Two-stem nouns stand in the weak stem. Feminine adjectives, which further specify a following member in the compound, generally stand in the masculine stem:
e.g.
पुण्यवत्क्षत्रिया = पुण्यवती क्षत्रिया = "a Kṣatriya woman who possesses merit"
गुणवत्पुत्रः = गुणवान् पुत्रः = "a son with good qualities"
पुष्कल 3: splendid, magnificent, abundant
वा : or (postposed)
अथवा : or (preposed)
चतुर्थ 3 (f.: चतुर्थी): fourth
विद् "to find" 6 U विन्दति ; Pass. विद्यते ; PPP विन्न / वित्त विद् "to know" 2 P वेत्ति ; Pass. विद्यते ; PPP विदित पत् "to fly, to fall" 1 P पतति ; Pass. पत्यते ; PPP पतित अर्ध 3: half, m.n. half
पूजा f.: honor, honorable reception, religious worship (Pūjā)

Fig.: पूजा
(Image source: Details)
कुल n.: herd, multitude, race, lineage, family
इन्द्र m.: prince, first, best among ; king of gods Indra

Fig.: इन्द्रः
(Image source: Details)
दास m.: slave, serf, servant
दासी f.: slave woman, serf, servant
काल m.: time, (right) moment ; fate, death ; god of death Kāla
काल 3: black, bluish-black, dark
पुरुष m.: human being, man, servant
-जन as the second member of Tatpuruṣas often expresses the plural
स्तु 2 स्तौति ; Pass. स्तूयते ; PPP स्तुत : to praise, extol
from this:
स्तुति f.: praise, hymn of praise
स्तोत्र n.: (means of praise =) hymn of praise, hymnus
सिंह m.: lion (Panthera leo persica)

Fig.: सिंहः
(Image source: Details)
व्याघ्र m.: tiger (Panthera tigris tigris) (lit.: growler)

Fig.: व्याघ्रः
(Image source: Details)
इव (postposed): as it were, like (in comparisons: व्याघ्र इव पुरुषः = "a man like a tiger", "a tiger-like man"
एव (postposed): emphasizes the preceding, in German often corresponds to emphasis, a kind of emoticon \<!\>, e.g. सत्यमेव जयति "only the truth prevails", "precisely the truth prevails", "the truth prevails"
अरि m.: enemy (according to Thieme, Der Fremdling im Ṛgveda: originally = foreigner)
आर्य 3: Aryan, noble ; m. Aryan (self-designation of the Sanskrit-speaking ancient Indians, lit.: hospitable (Thieme)) ; nobleman, gentleman
to जन्
जाति f.: birth, kind, caste (for caste as जाति see Basham, Wonder, p. 148ff.)
मृ 4 Ā म्रियते ; Pass. म्रियते ; PPP मृत : to die (according to Indian grammarians: 6 Ā)
from this:
मरण n.: dying, death
मृति f.: dying, death
मृत्यु m.: death ; personified: god of death
Resolve the following compounds as Tatpuruṣa in Sanskrit and provide a German translation. Provide all resolutions and translations that seem possible to you. Also indicate which case and number the entire compound represents.
१. देवेन्द्रस्य २. दुःखदग्धा ३. मोक्षधर्मः ४. अन्नजातानि ५. गृहकरणम् ६. शूद्रकृतेन ७. ईश्वरपूजा ८. देवेश्वरः ९. क्षत्रिययज्ञम् १०. वैश्यभावेन ११. देवगुरोः १२. धनलोभः १३. गृहदासी १४. दुःखमोहः १५. ग्रामेश्वरम् १६. नगरजनाः १७. यज्ञकालस्य १८. देवगृहाणि १९. देवपुत्राणाम् २०. पश्विष्टिः २१. स्मृत्युक्तम् २२. गुरुगृहम् २३. सोमयज्ञेन २४. स्वर्गगताः २५. सुखप्रश्नम् २६. पशुधर्मः २७. स्वर्गलोकः २८. ऋषियज्ञैः २९. तत्कालम् ३०. सत्यवदनम्
Resolve the following Tatpuruṣa as in Exercise 1:
१. देवतागृहम् २. देवीस्तोत्रम् ३. ब्राह्मणगृहम् ४. वैश्यापुत्राः ५. शूद्रधर्मः ६. अग्निगृहम् ७. साधुगता ८. सत्यवचनेन ९. धर्मयज्ञानाम् १०. सत्यधर्मः ११. अनृतवदनस्य १२. देवीदासः
१३. द्विजदासान् १४. अग्निदग्धम् १५. साधुवादः १६. बालमृगः १७. धनसर्गः १८. अन्नद्वेषम् १९. देवदेवम् २०. देवप्रश्नेन २१. गृहजनानाम् २२. गुरुपूजायाः २३. गुरुगतैः २४. स्वर्गमार्गेण २५. नरकदेवतया २६. गृहेश्वरः २७. ग्रामधर्मः २८. देवीपूजाम् २९. देवदर्शनम् ३०. देवपादान् ३१. धनजाता ३२. बालभावेन ३३. लोकगुरोः ३४. देवपुत्रः ३५. देवमार्गम् ३६. स्वर्गसुखम् ३७. सोमसुतिः ३८. देवपूजायाः ३९. लोकधर्मेण ४०. देवजनाः ४१. पापलोकः ४२. पुण्यफलानि ४३. सत्यवादः ४४. ऋषिपुत्रः ४५. पुत्रपुत्राः ४६. धर्मवादः ४७. देवलोकम् ४८. यज्ञेश्वरः ४९. ग्रामदेवता ५०. दुःखलोकः ५१. देवशत्रुणा ५२. क्षत्रियधर्मः ५३. द्विजेन्द्रः ५४. अग्निकृतम् ५५. साधूक्तानि ५६. ब्राह्मणभावेन ५७. देवधर्मः ५८. गृहदेवता ५९. कारुकुशीलवकृतम् ६०. द्विजातिशुश्रूषया

Abb.: ग्रामदेवता
(Bildkälla: Details)
A) Translate the proverb at the beginning of the lesson
B) Resolve the following Tatpuruṣa compounds:
१. बलकृतः २. बालधनस्य ३. नरककाकम् ४. लोकगुरोः ५. जलेश्वरेण ६. जनपानम् ७. वाक्यसारथीन् ८. गुणवचनानि ९. मृगेश्वरैः १०. बुद्धिकृतायाः ११. धर्मयज्ञेन १२. यज्ञाङ्गानि १३. गृहजनेन १४. ग्रामलेखकाः १५. नागदेवः १६. पुण्यजिताभिः १७. पापलोकम् १८. सत्यवदनस्य १९. दानधर्मेण