I've added this into Trac.
http://trac.sagemath.org/sage_trac/ticket/5135
Jason - thanks for the heads-up on 3058.
William - someplace you *have* to turn rows into columns. ;-) In my
book, I think it is all buried into "column space of A = row space of
transpose(A)" or something similar. Wou
I've added this into Trac.
http://trac.sagemath.org/sage_trac/ticket/5135
Jason - thanks for the heads-up on 3058.
William - someplace you *have* to turn rows into columns. ;-) In my
book, I think it is all buried into "column space of A = row space of
transpose(A)" or something similar. Wou
Rob Beezer wrote:
> William,
>>
>> I think the right change for your application would be to change this
>> line in left_kernel:
>>
>> W = V.submodule(basis)
>>
>> to
>>
>> if echelonize:
>> W = V.submodule(basis)
>> else:
>> W = V.submodule_with_basis(basis)
>>
>
On Wed, Jan 28, 2009 at 3:55 PM, Rob Beezer wrote:
>
> William,
>
> Thanks for the reply. I hadn't dug deep enough to find the
> "with_basis" variant of the submodule constructor, so I like the
> suggested approach. Barring anymore significant conversation here,
> I'll take on submitting this w
William,
Thanks for the reply. I hadn't dug deep enough to find the
"with_basis" variant of the submodule constructor, so I like the
suggested approach. Barring anymore significant conversation here,
I'll take on submitting this with a ticket and a patch. It'll be a
learning experience for me
On Wed, Jan 28, 2009 at 3:07 PM, Rob Beezer wrote:
>
> A question about computing bases for kernels or null spaces of
> matrices.
>
> When working with students studying linear algebra for the first time,
> I like to construct basis vectors for the (right) kernel by working
> through the indices
