This is more of a general question about whether we can do with Sage what we normally do as mathematicians on paper and in our minds. For example, if I do
V = VectorSpace(QQ,4)
W = VectorSpace(QQ,4)
I get: True. This is quite disturbing - while V and W are isomorphic they should not be identical. As I understand it, a vectorspace over QQ for Sage is just QQ^4, that's it. In other words, the Linear algebra package, while excellent, is not really about vector spaces but rather about arrays of numbers.
Any thoughts on this desire of mine to have a genuine "coordinate-free" approach?
asked Sep 06 '10marco
73 ● 1 ● 11
I like coordinate-free linear algebra, but your issue here may simply be that
sage: 3 == Mod(3,7) True sage: 3 == Mod(3,5) True sage: Mod(3,5) == Mod(3,7) False sage: Q = PolynomialRing(QQ,'t') sage: 3 == Q(3) True sage: 3 in Q True sage: R = PolynomialRing(RR,'w,v') sage: 3 == R(3) True sage: Q(3) == R(3) False
Given this behavior, I don't find it particularly surprising that
So it seems it's not even possible to make two separate copies of a free module with a given rank. That seems a little limiting, which is your original point, I guess :) Maybe it's more accurate to think of
Asked: Sep 06 '10
Seen: 200 times
Last updated: Sep 07 '10
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