Closing Prayers in vedic traditions are done so that both the students, the teachers and the activity (in this case the study of the Ashtanga Hrdayam) feel complete with the time and the conversation. The people involved can move on to their next activity and/or move into the next phase of study which is contemplation and application. Closing prayers usually end with chanting Shanti or peace three times to signify the three worlds in which we live.

We have chosen the Purnamada chant to end our study group with.

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पुर्णमुदच्यते
पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥
ॐ शान्तिः शान्तिः शान्तिः ॥

Om Puurnnam-Adah Puurnnam-Idam Puurnnaat-Purnnam-Udacyate
Puurnnasya Puurnnam-Aadaaya Puurnnam-Eva-Avashissyate ||
Om Shaantih Shaantih Shaantih ||

There are many translations and commentaries on this verse, each of which adds a different slant on the vast meaning. In some sense, a complete explanation of the nature of Reality and the entire wisdom of the path of Self-Realization is contained in this short summary. Here are several translations:

Om.
That is infinite, this is infinite;
From That infinite this infinite comes.
From That infinite, this infinite removed or added;
Infinite remains infinite.
Om. Peace! Peace! Peace!

Om.
That is full; this is full.
This fullness has been projected from that fullness.
When this fullness merges in that fullness,
all that remains is fullness.
Om. Peace! Peace! Peace!

Om.
Completeness is that, completeness is this,
from completeness, completeness comes forth.
Completeness from completeness taken away,
completeness to completeness added,
completeness alone remains.
Om. Peace! Peace! Peace!

Om.
Brahman is limitless, infinite number
of universes come out
and go into the infinite Brahman,
Brahman remains unchanged.
Om. Peace! Peace! Peace!

Om.
That is the whole, this is the whole;
from the whole, the whole becomes manifest;
taking away the whole from the whole,
the whole remains.
Om. Peace! Peace! Peace!

Om.
That is the absolute, this is the absolute;
from the absolute, the absolute becomes manifest;
when the absolute is added to or taken away from the absolute,
the absolute remains.
Om. Peace! Peace! Peace!

Om.
That is reality, this is reality;
from the reality, the reality becomes manifest;
adding or subtracting reality from reality,
only reality remains.
Om. Peace! Peace! Peace!

Om.
That is perfect,
This is perfect.
When perfection is taken from the perfect,
Perfect alone remains.
Om, peace, peace, peace