On 27 October 2016 at 18:47, William Stein <wst...@gmail.com> wrote:
> Just curious: what choice does magma (or maple or Mathematica etc) make
> regarding this?
Using Magma V2.22-3 I am not impressed:
> A:=Matrix([[1,2],[3,4]]);
> B:=Matrix([[1,2],[3,4]]);
> Parent(A);
Full Matrix Algebra of degree 2 over Integer Ring
> Parent(B);
Full Matrix Algebra of degree 2 over Integer Ring
> IsSimilar(A,B);
>> IsSimilar(A,B);
^
Runtime error in 'IsSimilar': Coefficient ring of argument 1 is not an
exact field
I can get it to give true by replcing the first entries by 1/1.
If B has a different size it gives
> B:=Matrix([[1/1,2],[3,4],[5,6]]);
> IsSimilar(A,B);
>> IsSimilar(A,B);
^
Runtime error in 'IsSimilar': Bad argument types
Argument types given: AlgMatElt[FldRat], ModMatFldElt[FldRat]
which is a not very easy to understand error message.
>
>
> On Thursday, October 27, 2016, Dima Pasechnik <dimp...@gmail.com> wrote:
>>
>> AA
>> (but make sure docs make sense after the change)
>>
>> On Thursday, October 27, 2016 at 4:21:02 PM UTC, Travis Scrimshaw wrote:
>>>
>>> I am for BB because:
>>>
>>> 1 - the definition (as even given in the docstring) still makes full
>>> sense if the matrices are not the same size or if they are not square. There
>>> does not exist such a matrix P.
>>
>>
>> this is an argument for changing the docs, yes.
>>
>>>
>>> 2 - It puts an unnecessary burden on the average user. They have to deal
>>> with errors on a true/false question. You then also have to explain why
>>> there is the error message to your linear algebra students, provided you
>>> were very careful with your definition of similar matrices.
>>
>>
>> Just as they have to deal with errors from multiplying matrices of
>> different sizes.
>>
>>>
>>> 3 - It is a backwards incompatible change that (IMO) is not a bug and we
>>> cannot deprecate.
>>>
>>
>> well, a wrong decision was made at some point. Do you mean to say one has
>> to keep suffering from it forever? :-)
>>
>> Cheers,
>> Dima
>>
>>> Best,
>>> Travis
>>>
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>
>
>
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