Work on the complex components: abs, carg, ...



Dieter, these changes all sound fantastic.

> Again I have done some work on the functions for the complex components.
> At first I would like to suggest 6 changes to improve the functions for
> the complex components. My first aim was to extend abs to handle complex
> expressions more carefully and to get more consistent results for
> realpart, imagpart and carg.
> 
> (1) 
> Limit knows the following limits for atan2:

> (2) 
> When the argument y is zero and x a positive real value, atan2 has the
> value zero. For a negative argument x we get %pi.

> (3) 
> Remove rectform from function $cabs

> (4) 
> Do not use the function asksign, but $sign and return a general noun
> form if the sign is not known.

> (5)
> The function abs calls cabs for expressions which looks like complex
> expressions. But the test with csign is very weak. If we add a test with
> $csign much more results would be correct for complex expressions, e.g.

> (6)
> We do not return an expression with $cabs in absarg, but use the noun
> form of the simplifying function abs. Because $cabs is a verb function
> it is much more consistent to return the noun form of abs. The results
> are more consistent and can further simplify.

> So what do you think. Should we do the improvements of the functions for
> the complex components.