Most concise performance ever! I love it.

I disagree with the sigma notation, the song isn't commutative )order of words does matter). should be pi notation. mmmm...pie...

Yeah, but Pi notation is lame.

Now that I think about it, I don't see how Pi notation could work anyway...

I think he's just referring to products being written as things being put next to each other. Although string concatenation is usually done as addition. Also, there's a corner case that gives a problem. Where's the "and" before g_1 for d != 1?

The song may not be commutative, but apparently those are 5 gold commutative rings.

@Mike Nicely done. Well played good man.

I'm swedish and don't know the song, since it is not traditional here. But I do think of the notation not as a string concatenation, but as description of what is sent. Hence, the Pi notation would be useless (you can't really give away products of different things). Also the "and" comes in from converting a sum described by mathematical notation to one described by text.

It might be better to replace the summation by another for-loop =)

no, 2g_2!=g_2+g_2. hence you're not working with the free abelian group generated by the g_i(i=1:12) as a Z=module, but rather with the free (non-abelian) group <Z,{g_i|i=1:12}>. it's a group, not a module, so it should be pi notation.

"On the first day of Christmas, my true love sent to me: 1 partridge E pear tree". (Ok.. we get it, Mr. Pedantic.)
No, it's pretty awesome anyways.

I like it, but it would be more correct in full-on pseudo-code. Of course it would have less joke value that way. Also, "d-i+1" is more concise, but "d-(i-1)" or "d-i" with i=0 to d-1 would be easier to conceptualize. Always having to think about that when writing source code.
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Furry cows moo and decompress.