Hi,

On 2017-02-20, Daniel Krenn <kr...@aon.at> wrote:
> On 2017-02-19 17:57, rjf wrote:
>> It might be comparing the real parts.  What did you expect?  Perhaps
>> Error "<" requires that both operands be members of the same ordered
>> field  ??
>> Or perhaps just
>> False
>
> I, for sure, did not expect "True".

It is clear that there is no mathematical meaning associated with the
comparison "I<1" --- so, I wouldn't have any expectation of mathematical
meaning here. "bool(I<1)" is a different story: It *has* to return
True/False for political reasons (Python decided against using "Unknown"
or "Alternative" as truth values). Or it could raise an error.
Indeed it would be a good idea to have a switch as in Maxima.

I believe it would be good to have an "Ordered" axiom for fields, so that
one can easily check "CC in Fields.Ordered()" respectively
"QQ in Fields.Ordered()".

Also, for an *ordered* field K, it might be a good idea to have a method
K.cmp (implemented via Fields.Ordered.ParentMethods) so that K.cmp(x,y)
returns -1,0,+1, according to how the elements x,y of K compare (and
raises an error if x,y do not coerce into K): Explicit is better than
implicit.

Best regards,
Simon


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