>> shouldn't UTS(F, x, 0) export EuclideanDomain if F is >> a Field?
At first I thought, how can we have a Euclidean algorithm without zero detection? But then ... that's not the definition of a Euclidean domain. All it needs is a Euclidean size function and a division step. As long as divide(f, g) does not get (potential) zeros as input, that looks like a computable problem to me. Anyway, I still think it's potentially more dangerous than its gain. > EuclideanDomain implies BasicType and this already > is a lie. Oh, now we enter a very dangerous field. In fact, currently UTS claims BasicType. UTS itself already lies. We have probably lies all over the place. > So question is if after lying several times we want > to keep lying, or if we want to clean up things. Since long I am in favour of removing our lies. When we say Ring, we actually mean a computable ring. So power series cannot claim to be of category Ring. AFAIR, the aldor library tried something in the direction of relaxing things. There are categories like AdditiveType, LinearCombinationType, etc. https://github.com/pippijn/aldor/blob/master/aldor/lib/aldor/src/arith/sal_arith.as https://github.com/pippijn/aldor/blob/master/aldor/lib/aldor/src/arith/sal_lincomb.as that just claim existence of operations, but without the respective properties. Yes, that makes the category structure a whole lot more complex. However, I guess when we can come up with a nice naming convention such a change should be doable and should be done. Clearly this will not happen overnight, but that should be a longterm goal for FriCAS. Ralf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/0046542c-1847-f042-f396-159e92e85bf0%40hemmecke.org. For more options, visit https://groups.google.com/d/optout.
