Hp50g emu : graph abs(x)^3 gives negative y-values

[ramon_ea1gth]

(12-14-2020 10:38 AM)Gil Wrote:  The question is why two DIFFERENT behaviours
when -119 flag is set, I. e. "not rigorous" mode is on for

a) stack/programme calculation
b) drawing graphs.

Flag -119 controls symbolic operations with the CAS. I find it interesting when doing symbolic simplifications on the stack or in a program and using parameters with a physical meaning.

For example, the voltage across the terminals of an R-L series circuit can be written as: w·L·Ip·sin(w·t)+R·Ip·cos(w·t)
Let’s consider that all the symbols in this expression are always positive (or zero) in practical applications. In fact, Ip is the amplitude of the current across the circuit. We want to rewrite that expression into something more compact like cos(w·t + phase).
Let’s have the HP 50g in Real & Exact mode on (-103 CF -105 CF):

• Apply TCOLLECT with rigorous mode on (-119 CF). The result is: √(w²·L²+R²)·|Ip|·cos(w·t+...)
• Apply TCOLLECT with rigorous mode off (-119 SF). The result is: √(w²·L²+R²)·Ip·cos(w·t+...)
  

This second result (non-rigorous) discards the module of Ip. Hence, if by chance we require to divide this expression by Ip, further simplifications can be done. However, with the first result, it won’t be possible for the machine to further simplify |Ip|/Ip to 1.