solve() problems

[C.Ret]

@rawi:
No, you don't have to indicate the variable to be search for when you use default x variable. It is mandatory only in case of several variables in the equation.

   

@HansB
I think the problem come from a confusion between the symbolic CAS variable x (lowercase) and the global variable X (uppercase). In the CAS windows, the later X is consider as a numeric constant.

In CAS mode, if you indicate to solve over global register X (uppercase) in solve, expected answer is display what ever the value store in X.

If you don't indicate variable to solve, default symbolic CAS variable x (lowercase) is used and the equation containing the X register is first numerically evaluated.

When X is not storing value 4, solve returns empty solution set [ ] since no symbolic x will ever made X-3 to be 1.
When X is storing the correct value 4, solve returns the infinite symbolic solution set { x } (lowercase) to indicate that any values of x will fit, since, whatever is x, (4-3) always eval to 1.

   

Concerning solve behavior in HOME, I have no explanation.

@Joe Horn
Sorry my post crossed yours. You are perfectly right when stating that solve is not intended to be used in HOME numeric environment.

The main goal of solve is symbolic solving and dependencies resolving: