The great Smath/Maple dual solver

This dual solver is most precious for Engineering/Scientific works. 1. given the independent, it solves for the dependent. 2. given the dependent, it solves for the independent. Just a matter of coding the respective 'solve' range appropriately. The AntColony was fitted Verhulst model and we use the result. sol(w):=root[f(t,β,colony)-w,t] is the Maple symbolic executable format wrt var [t] This format is "general" wrt 't', but it can be recast in term of either solving for 't' or 'w' by equating to 0 and specifying the variable to slove for and its respective bracketed 'solve' range.

maple("symbolicExpression") - evaluates symbolic expression.

<= a native Maple code, active in Smath but not documented.

1. The general coding to be adapted for each solver

2. Solving for 'w' [dependent] given 't' independent

3. Solving for 't' [independent] given 'w' dependent

4. At this point, the dual solver is done for use in-situ.

Next, we recast the original model from the symbolic 1. above and make 'w=0', that will plot and interpolate the dependent.

Sanity check wrt 2.

You can copy this part of the document, add the data set from the original Ant. Thus you will have a complete piece of scientific work for publishing in working maths, much superior to "Latex Papers".

Ants, rats, termites, bees ... when they migrate, they don't migrate "Dady & Momy". They form a 'base colony'. We just have the 'Ant' from American Scientists. Assume you have the "rats", you discover a rat colony installed in Australia. From your magic Smath, then using the solver, you can tell how old the colony is & future population [assuming you have the "rats model" fitted from a model function].