(Bug?) HP48 Equation Library

[Han]

(02-14-2017 04:29 PM)rprosperi Wrote:  Thanks are due mostly to you for your ongoing contributions to the folks here; access to the 48 Eq Lib on Prime will likely get me to use it again, so thanks for that too!

In the interest of providing a useful list of equations, how should we approach the provision of these formulas? Would users find it more useful to have a single formula using piecewise functions as shown in one of the examples above? Or would it be better to separate the single formula into several "copies", and then allow the user to select the one that best fits their parameters?

In other words, provide a single formula:
\[ Mx = \begin{cases}
P\cdot (x-a), & x \le a\\
0, & x>a
\end{cases} \quad + \quad
\begin{cases}
M, & x\le c\\
0, & x>c
\end{cases} \quad + \quad
\frac{w}{2}\cdot (L^2−2\cdot L \cdot x+x^2) \]
or provide all the cases and have the user pick one among
\begin{align}
Mx & = P\cdot (x-a) + M + \frac{w}{2}\cdot (L^2−2\cdot L \cdot x+x^2) \\
Mx & = P\cdot (x-a) + \frac{w}{2}\cdot (L^2−2\cdot L \cdot x+x^2) \\
Mx & = M + \frac{w}{2}\cdot (L^2−2\cdot L \cdot x+x^2) \\
Mx & = \frac{w}{2}\cdot (L^2−2\cdot L \cdot x+x^2)
\end{align}
These formulas, in context, are most likely going to used in the fashion of computing \( Mx \) while knowing the other parameters (not really solving as much as evaluating). However, as an equation, one could in theory provide a value for \( Mx \) and solve any of the other variables. (Again, unlikely in this context, but theoretically possible). The HP48 fails spectacularly, solving for \( c \) to be 9.999...E499 and I imagine the solver I have implemented to do no better using the first formula (the one with piecewise functions).

I will definitely have to include some warnings either way about using the solver for such problems. In the former case, we have discontinuities that would make Newton's method possibly fail. In the latter case, these formulas, taken individually, imply \( Mx \) is continuous in the remaining variables (which is clearly not the case for \(x \)).