To get a quick sense of what people think about this, I've decided to
rephrase this as a survey.  To be clear, though this coincides with
Matlab syntax, the intent is not to try to make Sage a Matlab clone,
rather it is to add a missing feature to Sage.

Should [a, b; c, d] be a valid syntax for matrix construction in Sage?

[ ] Yes, I love this syntax! It would be make life better for me and
my students.
[ ] I wouldn't oppose, but may require some convincing.
[ ] No, that's a horrible idea.

Why?


Should the default basering be more linear-algebra friendly? E.g. R ->
Frac(R), RR -> RDF.

[ ] Yes, that would take away a lot of pain/be what I'd have to
specify manually anyway.
[ ] Could be handy, but the drawbacks are significant.
[ ] No, matrices over QQ are for sissies, real mathematicians work
over ZZ unless otherwise specified.

Why?



On Thu, Jan 26, 2012 at 6:12 AM, Jason Grout
<jason-s...@creativetrax.com> wrote:
> On 1/26/12 7:54 AM, Marco Streng wrote:
>>
>> 2012/1/26 Jason Grout<jason-s...@creativetrax.com>:
>>>
>>> That's part of the problem pointed out in an earlier message---our RR
>>> matrices really are pretty bad for numerical things, but RDF matrices are
>>> the way to go (the RDF matrices use standard numerical algorithms for the
>>> most part, whereas RR matrices use naive algorithms that can be really
>>> bad
>>> and slow).  This should be fixed, but for right now, RR matrices don't
>>> seem
>>> to be all that useful compared to RDF matrices.
>>
>>
>> Is RDF always better than 53-bit RR in this way? If so, perhaps
>> "RealNumber" or the preparser could be changed to use RDF if the
>> precision is sufficiently small. Most users typing 12.345 will want
>> the fastest implementation and not something generic.
>
>
> No, this is a linear algebra problem, not a general problem in Sage. Usually
> RR is better mathematically than RDF.
>
> Thanks,
>
> Jason
>
>
>
>
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