On May 15, 2008, at 8:21 AM, Bjake Hammersholt Roune wrote:
>> [...] 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 [...]
>> What do people think about making the default ring for matrices QQ?
>>
> I have no objections to making QQ the defailt ring for matrices.
> However, I don't think this resolves the problem entirely.
>
> A part of the confusion stems from echelon_form doing entirely
> different things based on the type of argument it gets. I would prefer
> echelon_form to always use fractions, and have some other function
> avoid the fractions. Another solution I could get behind is for
> echelon_form to have a parameter for whether to use fractions, and
> have the default be to use them.
I would second this idea, I like it much better than matrix(3,range
(9) being over Q. I think that's the way it used to be. It seems odd
to make matrices by default over their fraction fields (if they
exist)--other than echelon form is there any other case that one
wants this. This could slow things down a lot too--matrices over QQ
have some overhead (only O(n^2)) over matrices over ZZ, but there is
a huge difference in performance for Z[x] and Frac(Z[x]). Also, then
sage: matrix(3, range(9).charpoly('x')
would return a polynomial over QQ rather than ZZ which I think is odd
and less efficient.
- Robert
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