On 7/3/19 11:27 AM, Waldek Hebisch wrote:
> Ralf Hemmecke wrote:
>>
>> the test
>>
>> testEquals("omegapower(o2) + 7*omegapower(o1)", "o3")
>> https://github.com/fricas/fricas/blob/master/src/input/ord.input#L15
>> fails.
>
> What exactly are you doing? For me it works.
Ummm... well, I think, it might have something to do with a change in my
local FriCAS where I have exported the degree function for
PolynomialRing in a different way. That shouldn't actually be the case,
but it needs further investigation of what the real reason is.
>> Remark about notation:
>>
>> Although I can somehow understand you motivation to use * and + for
>> "natural" product and "natural" addition of ordinals (just reuse the
>> PolynomialRing domain), I would be more in favour of reserving * and +
>> for ordinal multiplication and ordinal addition.
>
> Well, it is more than that: '*' and '+' are (semi)ring operations.
> That fits nice into FriCAS category structure. "Ordered" operatations
> on ordinals have worse properties.
OK, that's an argument. And due to our problem with renaming monoid
operations, I can / must somehow live with it.
Still, it doesn't make me happy.
>> In fact, I would like to show \omega * 2 as the output of \omega +
>> \omega (ordinal addition), not 2*\omega.
>
> I think that this goes into user control of output. More precisely
> standard notation is 2*\omega, and this agrees with other domains.
> User may wish different output and it is resonable to provide
> some means for customization. And that is much more general
> problem: users should not be forced to change types to get
> y*x as output for polynomials. Sometimes x*2 may be better
> than 2*x...
Maybe, but since with a domain where coefficients commute with
variables, that shouldn't be much of a problem.
However, for SmallOrd, how do I interpret the * in the output 2*omega?
It can only be the "natural product, right? Or is it to be interpreted
as the Cantor normal form, but just with the coefficients on the wrong side?
https://en.wikipedia.org/wiki/Ordinal_arithmetic#Cantor_normal_form
Coming back to "semiring" operations. Aren't you lying when you claim
that SmallOrdinal is a SeminRing? Or do the ordinals form indeed a group
with respect to "natural" addition?
In fact, I wonder how the compiler actually creates code for
0 == 0$Rep
, since the representation is PolynomialRing(NNI, %).
I guess that can only work, because the representation of the 0 of
PolynomialRing is the empty list. Would it fail, if it were not the
empty list?
Ralf
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