On 30/05/2018 08:14, Travis Scrimshaw wrote:
On Tuesday, May 29, 2018 at 9:01:51 PM UTC+10, chris wuthrich wrote:
As a simple-minded user I stumbled over exactly this last week. I don't
understand much of what this thread is discussing, but I know what a
simple-minded user wants.
sage: G = GL(2,13)
sage: G = G.as_matrix_group()
sage: H = G.subgroup([ matrix(GF(13),[[1,0],[1,1]]) ])
sage: H2 = G.subgroup([ matrix(GF(13),[[1,1],[0,1]]) ])
sage: H3 = G.subgroup([ matrix(GF(13),[[1,0],[2,1]]) ])
I expect H == H3 to say True as they are the same subgroup.
I expect H = H2 to say False, since they are not the same subgroup, even
though they are isomorphic.
Instead
sage: H == H3
False
sage: matrix(GF(13),[[1,0],[1,1]]) in H3
True
sage: matrix(GF(13),[[1,0],[2,1]]) in H
True
sage: H.is_isomorphic(H3)
True
sage: H.is_isomorphic(H2)
True
sage: matrix(GF(13),[[1,0],[1,1]]) in H2
False
I though of working around it by checking if they are the same as sets,
but to my surprise:
sage: Set( h for h in H ) == Set( h for h in H3 )
False
sage: Set( h.matrix() for h in H ) == Set( h.matrix() for h in H3 )
True
In short: I consider this a bug. No matter how this is done at the back,
the user expects == to mean mathematical equality, here equality of
subgroups. Otherwise the function should be called
subgroups_with_given_generators.
I think it is a bad thing in this case for == to be equality as sets.
Imagine if these are two really big, equal, but differently constructed
subgroups. This would be a really long and expensive check, whereas in most
cases, checking the defining objects are sufficient. I believe we have
other places in Sage where == is not strict mathematical equality for
similar reasons. -1 on changing the == semantics here.
But what if you *do* want to compare the subgroups (as Chris does). When
I ask "How many apples in my basket?" to Sage I don't want an answer
like "red bikes are nicer than blue ones" because it is faster to do so.
The problem here is definitely *not* to discuss whether equality of
subgroups is decidable or fast but what "==" should be.
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