There is currently no way to show all variable dependencies that still exist in a given variable. The dynamic assistance (which is not permanent and is sometimes cumbersome) shows what variables are originally assigned to a variable but some variables may themselves be assigned dependencies later. Also, explicit dependencies are not seen in the -> calculation because any variables with a value substituted in will be lost in favor the calculated value of the -> output string. This makes debugging hard and causes a lot of confusion when making even simple math sheets. I request some feature that will identify any explicit dependencies that a variable may have at the current location in the sheet.

eg., a b c
a := 3
b := a
b -> 3
which is correct as b is not dependent on a, however

b := a
a := 3
b -> 3
is not correct because b is dependent on a and if a changes, so will b

a := 3
b := 4 + c + a
b -> 7 + c
is correct because b depends solely on c

b := 4 + c + a
a := 3
b -> 7 + c
is not correct because b depends both on a and c, but -> shows all substitutions

I would rather see in a dependency display (using => as the symbol to mean depends on)

b => 4 + c + a
=> (undefined) (3)
where the second line shows assigned values.

c := a
b := 4 + c + a
a := 5
b -> 14, c -> 5, a -> 5
is not correct because b depends on a, and also c depends on a but -> shows only the calculated result of all substitutions

I would rather see for the three separate inquiries:
b => 4 + a + a , c => a , a => 5
=> (5) (5) , => (5)

Or if the simplification routines are working right
b => 4 + 2a , c => a , a => 5
=> (5) , => (5)

If there is hierarchical dependency, show the dependency tree.
b := 4 + c + a
c := a
a := 5
b -> 14
b => 4 + c + a
=> (a) + (5)
=> (5)

For more complex formulas and expressions, it will be hard to format the equation in a visually clarifying way, but the tool will be very useful and well worth the effort to develop.

I have thought of a further extension to this idea based on my experience with excel. In excel (actually I use openoffice Calc), I can highlight a cell and see its formula and color coded highlights on all other cells connected to the formula. smath sheets become long and cumbersome. I would like to be able to highlight an expression and see color coded highlights on all the prior expressions in the global sheet that the highlighted expression directly depends on. If I could hyperlink to them (and hyperlink back), that would also be very useful. It may also be useful to draw lines from the highlighted expression to its ancestors. This would allow me to quickly assess the thinking that smath is going through when is makes its substitutions and calculations and allow me to discover inadvertent errors in the sheet (especially larger sheets) much more easily.

I was thinking of a feature more for documentation and checking errors than for examining complete dependencies, for example:
- when a teacher writes a resolved problem, this would be useful to avoid writing expansions by hand.
- when checking errors on specific expressions, this way one could set up the exact sequence of terms in the same order as the user entered an expresion, i.e. there wouldn't be symbolic simplifications made by smath.

I would like some additional equal operators to set up a user defined symbolic sequence, for example using some unicode signs (see other equal symbols on this javascript bookmarklet 'mathematical 2' symbols)

y ≡ A*x
I tell smath to remember the sequence in that exact order
when I call ≡ again I want it to output that exact expansion:
y ≡ A*x = 5*8 = 40
what if X had more dependencies whose expansions I want to show ?
then again we could use the ≡ operator
x ≡ 4*z
x ≡ 4*z = 4*2 = 8
If we wanted to make the entire expansion from y with a certain number of expansions, then we could type ≡(x..)
where ≡ is followed by the list of ≡definitions enclosed by parentheses.
y ≡(y,x)
would result in
y ≡ A*4*z = 5*4*2 = 40
SMath's Dynamic Assistance could show the definitions associated with the variable y on this example.

Edited by user 21 January 2013 16:36:52(UTC)  | Reason: Not specified