On Thu, May 15, 2008 at 7:48 AM, Jason Grout
<[EMAIL PROTECTED]> wrote:
>
> Jason Grout wrote:
>> Based on some conversations with linear algebra people and classroom
>> demonstrations in a linear algebra class, people are confused that when
>> they create a matrix with matrix(3, range(9)), for example, that the
>> echelon_form is not the rref output that they get from most any other
>> program they have ever used, and certainly not what is taught in an
>> undergrad linear algebra class.  There is additional confusion if the
>> entries specified have a fraction in them; then the matrix defaults to
>> being over QQ, and the echelon_form functino gives the expected naive
>> rref!  The problem, of course, lies in the matrix defaulting to having
>> base_ring == ZZ (i.e., non-field).
>>
>>
>> What do people think about making the default ring for matrices QQ?
>> Additionally, if the ring R is determined from the elements provided,
>> then the matrix would be over R.fraction_field().  Of course, the
>> documentation for matrix() would clearly indicate what is happening if
>> the ring is not specified.
>>
>
>
> More concisely, this proposal could be worded:
>
> What do people think of making matrix() return a matrix over a field by
> default, unless a ring is explicitly specified.  The default field would
> either be the fraction field of the ring containing the specified
> elements, or would be QQ if no elements are specified.  This logic would
> *only* be applied if a ring is not specified.  The documentation of
> matrix() would also be changed accordingly.
>

+1

I suggested this idea.  I would never do this is Sage were "just for me",
but Sage isn't.  Please keep that in mind when reading the above proposal...

 -- William

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