If we just fix the bug in the corresponding Homspace's __call__method to
make sure the domains match by pre/postcomposing using the appropriate
coercion maps when the objects are equal-but-not-identical, then it will
fix the problem because things would be described in terms of the same
basis.
Dear Travis,
I basically agree with you, in the sense to fix that what equality means.
At this time, equality of vector spaces does not imply equality of
associated vectors. I think both choices have good reasons. I am not sure
how to collaborate with these issues but I am ready to. Best, Enriqu
We need to be very careful here about what "same" means, and the category
we want to work in is vector spaces with a distinguished basis. By similar
I really meant up to a change-of-basis, and I should have been more
precise. Although perhaps it is a more simple problem than I was thinking
beca
Not exactly, when one asks if two linear maps are equal it is not the same
thing to ask if they are similar, I mean equal as maps. In my example, if
you enter:
K=GF(2)
V=K^2
B=V.basis()
B1=[vector(K,[i,j]) for i,j in [(1,0),(1,1)]]
V1=V.subspace_with_basis(B1)
and you ask V==V1 the answer is T
What you're asking for is checking if two matrices defining the linear
transformations are similar, which involves computing the Smith normal
forms of the matrices. This is computationally expensive. Instead, what we
do is == becomes a weaker form of equality that is fast (equivalently has
stro
