Re: [isabelle-dev] Euclidean Ring

2015-07-10 Thread Florian Haftmann
Hi Manuel, On 27/06/15 09:06, Florian Haftmann wrote: What about: »a = unit_factor a * normalize a« Sounds reasonable. See now cb21b7022b00 ff. After accepting that gcd must always target a normalized segment of the underlying ring structure, it is quite obvious how the abstract

Re: [isabelle-dev] Euclidean Ring

2015-06-27 Thread Florian Haftmann
As for the terminology, I think I did not find this concept in the literature and just invented names that seemed reasonable to me at the time. I agree that normalization_factor perhaps gives the wrong idea; if you want to change it to something else, I have no objections, but I do think

Re: [isabelle-dev] Euclidean Ring

2015-06-27 Thread Manuel Eberl
On 27/06/15 09:06, Florian Haftmann wrote: What about: »a = unit_factor a * normalize a« Sounds reasonable. I still had the hope that it would be possible to develop an abstract specification for gcd which would form a lattice: »gcd a a = a«. But now I cam to realize that for Gcd :: 'a set =

Re: [isabelle-dev] Euclidean Ring

2015-06-25 Thread Manuel Eberl
Hallo, thanks for all the good work. It's nice to finally see my work integrated so neatly into HOL. 1. Normalization. Currently, there is normalization_factor such that a div normalization_factor a yields the normalized elements. My impression is that the latter should be an operation on