1. right after Startup: have hand symbol always activated ("move system")
> Did you know that you can hold down Shift as a shortcut to Move system?
Nope, and 99% of all new uses will not know either For usability reasons, please add this to the startup. Or make moving of the coordinate system by mouse default.
2. add a button on the left sidebar on the bottom "add function" (i saw just after weeks that there is a tiny icon in the menubar)
> What is wrong with the tiny icon on the toolbar? I don't think adding more buttons to do the same will help.
You say it yourself: "tiny icon". Regarding usability: I never saw it and so will 99 % of users. The most important feature of graph is adding a function, this main feature is underrepresented. There should be more ways to insert a function. At least one clear big button. Or the mouse feature (double click on white area in sidebar or right mouse click, add graph).
3. add context entry - right mouseclick on sidebar "add function" + "Insert point series"
> That doesn't seem to do anything you cannot already do with the toolbar buttons.
Again, for usability there should be "Add function" if you right-click with the mouse in the left sidepanel.
4. make labels draggable even if hand symbol is activated
> I am afraid that would be more confusing.
Then you need to add a button that represents the "drag". With the current version, if you have the hand symbol activated (most users will), as a user you have no idea how to activate the dragging. Other programs have buttons for that, see image editing software for example.
5. add below context menu when you right-click on a function the option "rename legend"
> That might be a good idea. I assume you are aware that you can change the legend text in the Description field in the function dialog.
I know after I asked here in the forum. Do you like all users to search for this feature? It should be intuitive.
6. double click on white area of the left sidebar should add a new function (!)
> You seem to want everything to add a new function. :-)
Again, this is the main feature of your software
7. having a function selected, the key "F2" should rename it or bring up the function dialog
> Did you know that you can use Enter to show the function dialog?
Well, again. As a usability expert I can only tell you what users expect. Of course, you can try to teach everybody new shortcuts, new ways of doing things with your software. But I am super sure, that a software is more attractive if a user can use it with the lowest learning curve needed
8. switch on the grid by default and use Arial as font-family by default
> Did you know that you can change the default by setting what you want and selecting Save as default in the Edit|Axes dialog?
Yes I know, this I found myself. I just thought you want your graph software look great on the first start? I mean Times New Roman is great for reading, but it should not be used for graphing purposes. Check out other plotter examples.
And the grid is activated by default in most of the plotters I know. Why to force the users to search settings, to change them, then not to forget to tick the little checkbox "save as default" in the dialog... Just give them what they want and expect on the first hand
9. each newly added function MUST have another name, starting from f, then g, h, ...
> Yes, I have been considering that. But as mentioned you can change the name shown in the legend to whatever you want.
Again, "I" as a user have to think of something that should be automated.
11. Shortcut CTRL+Q should be different (CTRL+Q and CTRL+W are usually for closing applications)
> I seem to be running out of shortcuts. However Alt+F4 are usually used for closing applications.
This is actually not so important. 1 to 10 are definitely of higher priority.
12. you might add a point tracer (mouse goes over a graph, mouse is pressed down, a point appears on the graph and follows the position of the mouse), see example https://www.desmos.com/calculator/3ruiyzjort
> You can do that by selecting Calc|Evaluate in the menu.
Oh, that was not obvious. Why to hide this feature? Just provide another button in the toolbar, P(x|y) or alike. // Update: Now I found the button on the toolbar...
What is missing: The coordinates should appear directly at the graph. With the recent implementation I always have to look on the left, lose focus, look again back to the graph, reposition the mouse, look again to the left, forth and backwards. Why not make it simpler for everybody?
PS: I would furthermore suggest to rename "graph" as it is not easy to find using google (and could be more unique). Maybe you ask your website visitors for ideas. .... what about "padograph", does not exist yet and is close to the word "pantograph" or you just make it "padowan graph"
> I have been considering changing the name, but I seem to have gotten used to the name Graph. I am surprised you don't find it easy to find with Google. It is usually one of the first results when you search for Graph, which is one of the reasons that I kept the name.
Okay, Google makes sense. From the human point of view, just imagine: if i ask a friend "hej do you know graph?" ... what will he think? ... if i asked a friend "hej do you know padowan graph?" that would be specific and he could google it. Furthermore, if a user enters "graph" in google, i think he does not want a software to graph, he wants probably an image of a graph. Maybe you consider it. Adding something to the existing title "graph" will do you no harm, but help your project.
Well, a big list. Thanks that you answered all points.
I really want to point out, that my goal is to improve your software! And only advices, "critics", tips can do so.
If I would be developping in C++ I would also try to help you. But it's not my language.