Hi,

I'm getting rather frustrated with the lack of speed for simple arithmetic in 
number fields.   At the moment, I'm most interested in very fast cyclotomic 
fields.  (A comparison is in the P.S. to get a feel for it).  After some 
profiling and fiddling around a bit, it appears that the lack of speed is 
caused by little bits here and there.  Probably the biggest hit is that the 
polynomial representation is not stored in PARI format internally.

It appears to me that they really need to be moved to SageX and then optimized 
more aggressively.  Is PARI the best tool for the internal format?  Will this 
just be moved to FLINT later or will that be utilized through PARI?  Any 
other bits of advice for a move to SageX in this part?

And, just to make sure, no one else is already working on this are they?

--
Joel

P.S. The comparison:
sage: I=CC.gen()
sage: time for _ in xrange(10000): I+I
CPU times: user 0.05 s, sys: 0.00 s, total: 0.05 s
Wall time: 0.06
sage: I=CyclotomicField(4).gen()
sage: time for _ in xrange(10000): I+I
CPU times: user 1.71 s, sys: 0.01 s, total: 1.72 s
Wall time: 1.81

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