Solution to the problem of pre-assigned variables to 0

[compsystems]

Solution to the problem of pre-assigned variables A, ... Z, Z0, ..., Z9, F0, F9, ..., V0, ..., V9 etc. to 0

Hello HPPrimeTEAM and users, one of the difficulties of the HPPrime calculator, is that there is no integration between CAS and NUM/HOME mode and especially in applications, since they are using predefined variables, in addition students have problems in differentiating X with x, since X is predefined to zero, they always call me, I do not get what I expected, another student asks me if X is set to zero, because when creating the function does not evaluate it.

There is no consistency in the hpprime system

X [enter] returns 0
F1(X) := 8 * X - 5 This should return -5
solve((right(F1)) = 0,X,'=') returns [] // synonym of no solution.


x:=0 [enter] returns 0
assume(x,symbol) // Remove the value of 0, changing the data type to symbolic
x [enter] returns x
F10(x) := 8 * x - 5

One solution that I propose is that the variables are predefined with 'noValue' instead of zero, in this way

X + 3 [enter] in NUM/Home mode returns "Syntax error" // ok, because it can not evaluate X, X has symbolic value
X + 3 [enter] in CAS mode returns X + 3 // ok because X is considered a symbolic variable

then:
X:=5
X + 3 [enter] in NUM/Home mode returns 8
X + 3 [enter] in CAS mode returns 8

restore(X) [enter] returns 'noValue'
X + 3 [enter] in NUM/Home mode returns "Syntax error" // ok

What do you think of this idea?

Another Case:

V1(X,Y) := (X²/3 - Y²/5 = 1); [enter] returns (X,Y)->(((X^2/3)-(Y^2/5))==1) // error
(X,Y)->((X^2/3)-(Y^2/5))=1 // ok
right(V1) [Enter] returns 0 // (0 synonymous of false), error because although ((X^2/3)-(Y^2/5) == 1 is false, this should not be compared, it must be interpreted as equation (X,Y) -> ((X^2/3)-(Y^2/5))=1

I do not use x in lowercase because the internal user variable V1 requires it [SYMB KEY], I also want to perform analytical [CAS], graphical [PLOT KEY] and numeric analyzes [NUM KEY] using the same definition.

Thanks