2 Nov
2011
2 Nov
'11
6:34 p.m.
On November 2, 2011 18:00:05 Paterson, Ross wrote:
The two concepts are similar for Int and Integer, except that signum 0 = 0 while unit 0 = 1, but the meanings of abs and signum on other types generalize in a different way.
These functions are pretty common in computer algebra systems.
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The Euclidean function is the measure function into a well-ordered set (the naturals) used in the proof that gcd terminates. You don't actually use it in the code. On the other hand you do need to be able to get a canonical associate.
Am I correct in understanding then that there could actually be euclidean domains that don't have good definitions unit and associate? Thanks! -Tyson