As I said, this weekend I was hoping to work on ‘systems of equations’, to make Math-o-mir able to solve simple systems by one click. But first I had to implement the ‘substitution of variables’ procedure into the Math-o-mir. This proved non-trivial, and I didn’t finish it yet.
For example, let say you have two equations:
and you want to eliminate the ‘y’, making one single equation containing ‘x’ and ‘C’ only.
The idea is that in Math-o-mir you pick up the first equation (mouse click on it) and then, carrying the first equation with mouse, righ-mouse-click on the ‘y’ variable in the second equation. The Math-o-mir will understand this as: extract the ‘y’ from the equaiton that is carried (the first one) and substitute it into the right-clicked equation. Note that all instances of ‘y’ will be substituted, not only the ‘y’ you clicked on.
This works fine, but I am not sure if I am happy with this approach. It may become confising. Look for the following, more awkward example:
We want to replace all ‘xy’ terms, so you pick-up the first equation, then touch the ‘xy’ term in the second equation and right-mouse-click. Math-o-mir will replace all ‘xy’ occurences with A/2, making the following result: A/2+y+zA/2=C…. But what if the first equation is ‘x+y=1’. In this case the Math-o-mir will not be able to propose any result. It doesn’t know how to make ‘xy’ from the ‘x+y=1’ equation.
In addition, the first equation doesn’t have to be an equation. But can be just a general expression, like in the example:
You pick-up the first expression, and right-click to the ‘y’ in the second equation. In this case the Math-o-mir should make ‘stupid’ replacement of the ‘y’ with the ‘x+y’ term. This gives: 5x(x+y)+2(x+y)=C.
I feel that there are too many different cases and this my confuse users.