argument and abs return type for complex numbers

[Grégory Vanuxem]

Hello,

Any idea why abs(complex(a,b)) return a complex type whereas argument not:

(74) -> abs complex(2.3,3.2)

   (74)  3.9408120990_476062027
                                        Type: Complex(Float)
(75) -> argument complex(2.3,3.2)

   (75)  0.9475969968_6083068824
                                                 Type: Float

[Grégory Vanuxem]

To explain, I am unable to overload abs in a descendant domain of the ComplexCategory. It always returns a Complex type and I would like by default a real type.

[Waldek Hebisch]

One possible guess is that 'abs' was defined in that way to have
similar signature as in Expression(Complex(INT)). But it is not
clear to me if there is any good reason. Defining 'abs' in
ComplexCategory with signature:

abs : % -> R

requires changes to algebra, but after changes apparently there
is no problem. And changes mostly are simplificantion.

Attached a patch

--
Waldek Hebisch