Agniveshyagrihyasutra 3.7.4

Now, for these [kinsmen]—for the water-givers, sapiṇḍas, maternal relatives from maternal blood-relations, and for paternal relations up to the seventh generation, and for the teacher and his pupil, along with their wives and children—for the sapiṇḍas, [the impurity lasts] ten nights.

For the others, it lasts three nights.

In the case of a child or one in a distant land, purification is immediate, according to some.

Thus, in the regular offering of water, there is the commemoration of women, sacrificers, and pupils.

For those who die before the tonsure ceremony, there is no cremation.

The seizing of a cow is for animal-sacrificers; there is no curd mixture for those who do not offer the Sānnāyya; there is no pile for those who have not piled the fire altar.

For women, there is no shaving of the hair, no pile, no bricks, and no re-cremation.

The vessels for women are made of wood.

In the ancestral sacrifice of the Ṛgvedins, one should omit these mantras for women:

'This woman [goes] to the realm of her husband'; 'Arise, woman, to the world of the living'; 'Taking the gold from the hand of the dead'; 'Taking the bow from the hand of the dead'; 'Taking the jewel from the hand of the dead'; 'Do not burn him completely, O Agni, do not scorch him'; 'When thou hast made him cooked, O Jātavedas'; 'The unborn portion—warm that with thy heat'; 'This indeed art thou, born from him'; 'This one is thine, another is beyond'; 'Thy two dogs'; 'What the black bird has pecked'; 'Arise, go forth, run away, make a home'; 'From him thou art born'; 'Go away, depart, crawl aside from here'; [and] 'Open wide, O Earth, do not press down upon him.'

A widower, wishing to perform soma sacrifices, should marry a wife and establish the sacred fires.

And it is taught: 'Therefore, one man obtains two wives.'

For a widow, the ancestral sacrifice is performed with the domestic fire.

For she has no husband, so establishing the sacred fires cannot take place again.

And it is known [from scripture]: "Therefore one [woman] does not find two husbands."

"They cremate the one who has established the sacred fires with the fires and with the sacrificial vessels"—because of this lack of distinction, this statement applies to both wife and husband who have established the sacred fires.

Of the two, whoever dies first, their ancestor-rite is performed with the triad of fires and sacrificial vessels; whoever [dies] later, theirs is performed with the domestic fire.

When they die together, their ancestor-rite is single and performed together.

And the domestic fire should serve the purpose of a firebrand.

For a man who has not established the sacred fires, [it is performed] with the domestic fire, and for a woman, with churned fire.

Some teach [that it is performed] with heated fire.

They should cremate a woman and a child with churned fire, according to some.

When the wife is cremated with fires common to the widower, what is the disposal of the domestic fire?

If he intends to undertake a solemn sacrifice, he should make it the rice-fire for the Brahmins.

If he goes to the forest, the domestic fire alone should be worshipped.

Now if he renounces, he should pay no regard to it.

An impure person must not practice optional austerity, must not sacrifice, must not recite personal sacred study; elsewhere than for the Agnihotra and the New and Full Moon sacrifices, he may make gifts.

He may give at will to the officiating priests.

As for the statement, "Approaching the houses, he prepares," it is indeed said that he will take up his own householder duties.

How, now, should the ancestor-rite be performed: by one wearing the sacred thread over the right shoulder or by one wearing the sacred thread [normally]?

He should state: "By one wearing the sacred thread over the right shoulder."

"This is the sacrifice for the ancestors; other sacrifices are for the gods."

And wearing the sacred thread suspended around the neck, they should carry this out, and they should place it on the funeral pyre; they should place it on the funeral pyre.