Scalars, vectors, pseudo-scalars, pseudo-vectors

[captain]

This is a basic question about the scalars, vectors, pseudo-scalars, and pseudo-vectors. I know that scalars and pseudo-vectors don't change sign under parity and vectors and pseudo-scalars do, but does that imply that scalars have to be even function of x, y, z (like for example x^2+y^4+z^2) and pseudo scalars have to be odd in x, y, z and also correspondingly with vectors and pseudo vectors? Also if you have a function like x^3 +y^2+z^54, does that mean that this function can be broken up into a scalar and pseudo scalar part, just like how any function can be broken up into an even and an odd part? I think I am really confused about this. Thanks in advance to anyone who can really clarify this. (Also I didn't know where to post this question. So if its placed in the wrong section, then feel free to redirect it into the correct section.)

 

[tiny-tim]

Hi captain!

Just as you can't add scalars to vectors,

you can't add vectors to pseudovectors, or scalars to pseudoscalars.

In physics, it'll be a scalar or a vector or a pseudo-scalar or a pseudo-vector …

it won't be a mixture.