On 29 May 2018 at 12:01, chris wuthrich <christian.wuthr...@gmail.com> 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. > This is not the only place in Sage where there is hidden structure which equality testing uses. sage: QuadraticField(2) == QuadraticField(8) False This looks wrong if you naively think that you are defining a subset of CC or RR. But number fields in Sage are all defined with a fixed generating element, i.e. they are not just QQ-algebras but QQ[X]-algebras. In the matrix subgroup case it is hard to see how H and the other subgroups are intended to be viewed if not as subsets of G. (By the way, your code raises an error for me in the assignment to H I get AttributeError: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'gap' ) > > > Chris > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
