updated arg, re, im, conj, sign (now working also with Lists and Units)

[mipa83]

Proposal - functions work also with units, lists, vectors, matrix:

{ 230∡0° V 230∡120° V 230∡-120° V } re --> { 230 V -115 V -115 V }
{ 230∡0° V 230∡120° V 230∡-120° V } im --> { 0 V 199.18584 287 V -199.18584 287 V }
{ 230∡0° V 230∡120° V 230∡-120° V } arg --> { 0 ° 120 ° -120 ° }
{ 230∡0° V 230∡120° V 230∡-120° V } abs --> { 230 V 230 V 230 V }
{ 230∡0° V 230∡120° V 230∡-120° V } conj --> { 230∡0° V 230∡-120° V 230∡120° V }

{ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V } re --> { 1 V 3 V -5 V -7 V }
{ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V } im --> { 2 V 4 V 6 V -8 V }
{ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V } arg --> { 63.4349 ° 53.1301 ° 129.8056 ° -131.1859 ° }
{ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V } abs --> { 2.2361 V 5.0000 V 7.8102 V 10.6301 V }
{ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V } conj --> { 1-2ⅈ V 3-4ⅈ V -5-6ⅈ V -7+8ⅈ V }

[ 230∡0° V 230∡120° V 230∡-120° V ] re --> [ 230 V -115 V -115 V ]
[ 230∡0° V 230∡120° V 230∡-120° V ] im --> [ 0 V 199.18584 287 V -199.18584 287 V ]
[ 230∡0° V 230∡120° V 230∡-120° V ] arg --> [ 0 ° 120 ° -120 ° ]
[ 230∡0° V 230∡120° V 230∡-120° V ] abs --> 0.0000 V
[ 230∡0° V 230∡120° V 230∡-120° V ] conj --> [ 230∡0° V 230∡-120° V 230∡120° V ]

[ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V ] re --> [ 1 V 3 V -5 V -7 V ]
[ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V ] im --> [ 2 V 4 V 6 V -8 V ]
[ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V ] arg --> [ 63.4349 ° 53.1301 ° 129.8056 ° -131.1859 ° ]
[ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V ] abs --> 5.0856+7.8653ⅈ V
[ 1+2ⅈ V 3+4ⅈ V -5+6ⅈ V -7-8ⅈ V ] conj --> [ 1-2ⅈ V 3-4ⅈ V -5-6ⅈ V -7+8ⅈ V ]

[[ 1+2ⅈ V 3+4ⅈ V][ -5+6ⅈ V -7-8ⅈ V ]] re --> [[ 1 V 3 V ] [ -5 V -7 V ]]
[[ 1+2ⅈ V 3+4ⅈ V][ -5+6ⅈ V -7-8ⅈ V ]] im --> [[ 2 V 4 V ] [ 6 V -8 V ]]
[[ 1+2ⅈ V 3+4ⅈ V][ -5+6ⅈ V -7-8ⅈ V ]] arg --> [[ 63.4349 ° 53.1301 ° ] [ 129.8056 ° -131.1859 ° ]]
[[ 1+2ⅈ V 3+4ⅈ V][ -5+6ⅈ V -7-8ⅈ V ]] abs --> 5.0856+7.8653ⅈ V
[[ 1+2ⅈ V 3+4ⅈ V][ -5+6ⅈ V -7-8ⅈ V ]] conj --> [[ 1-2ⅈ V 3-4ⅈ V ] [ -5-6ⅈ V -7+8ⅈ V ]]

The bolded text shows the inconsistance of abs for vectors and matrixes.
Just a proposal form my side: split/introduce a new function:

• abs --> abs of each element
• norm --> Frobenius norm or the Hilbert–Schmidt norm
  https://en.wikipedia.org/wiki/Matrix_norm
  https://www.mathworks.com/help/symbolic/sym.norm.html

The propsed functions are programmed with switch-case.
Is it preferable to code the proposed functions with switch-case rather than if(should_be_symbolic(xt))?

[c3d]

Thanks @mipa83. As a general rule, changing the style locally is not a good idea.

• if statements are preferable when we deal with larger categories, because the types in the categories tend to evolve over time, and it's much better to change one place than many.
• Using switch makes sense in cases where the expectation is that the treatment is specific to a given type and not to a category of types. For example, decimal promotion is really specific to each individual type, as is the Cycle command.

Neg and Abs fall into the latter category because the way to compute the opposite is very specific to individual types. You don't get the abs of a neg_integer like the abs of a integer. So there aren't broad category types that fit.

[c3d]

Thanks a lot @mipa83. I've used your test cases but I implemented the changes using a slightly different approach that takes advantage of existing DB48x infrastructure a bit more efficiently. Closing this PR for now.