"organize by subgroup" recolours the elements
Closed this issue · 3 comments
Let's look at the multiplication table for Q4:
not organized by any subgroup. If you organize by subgroup H1 you get a 2x2 square with red-orange row and orange-red. Switch back to organize by none and there is no row with orange-red.
What happened is that orange switched from i to -1.
If you pick organizing by subgroup H2, H3 and H4, you get the same colours for all the elements, just the labels change. The colours aren't revealing much information about how the subgroups are organized differently since they're the same for all subgroups of the same order.
I think it would be better to pick the colours for the set elements once (in the same order used when not organized by any subgroup) and keep the colour-element mapping invariant as the user changes the subgroups.
Here's another way of describing what you're seeing: the sequence of colors across the top row and down the left column are always the same, no matter how the group elements are ordered, and the squares in the rest of the table are colored consistently according to the multiplication table. The elements across the top can be re-ordered by organizing them by subgroup, or you can drag a row/column to an arbitrary new position, but it doesn't change the colors of the boxes. This behavior is unchanged since GE2.
But I agree that it's a bit unexpected, too. When I originally coded it my intuition was to do as you suggested, and I was a bit confused about how it was supposed to work. I've put a fork of group-explorer with a modified multtable at https://rayellis4.github.io/group-explorer-multtable-mod (see, e.g., https://rayellis4.github.io/group-explorer-multtable-mod/Multtable.html?groupURL=./groups/Q_4.group). This is what you're suggesting, right? It's definitely different, though I'm not sure that I learn anything from the difference. Perhaps an option, like drawing Cayley diagrams with left- or right-handed multiplication? What do you think, now that you can see it?
-- Ray
Yes, that's perfect!!
As a new user of GE, when I started selecting subgroups and looking for them in the original group, I didn't see the how the groups were formed and started to question my understanding of subgroups before, after some minutes, realising that the colours had simply changed. I agree with you that it doesn't reveal any new information per se, I merely think it would be less likely to confuse other people. (But I'm not a UI/UX person, so who knows!)
Putting an option in there would work too, of course, though I'm not sure it's worthwhile.
Take a look at the latest release (3.4.0), I think it does what you'd like. I left both ways of recoloring the elements in, there's an example in the documentation that illustrates how the old approach can be useful, too. I'm going to close this issue, but we can certainly open it again if needed.
And thanks for taking the time to make the suggestion, as a bit of a group theory newbie myself I was puzzled by the same thing you were. Let us know if you have any more good ideas!
-- Ray