How to create and implement a small database on Mathematica?

Question

I have a function

f[x_,y_,z_]:= a^x b^y c^z

and I want to evaluate it for various values of x,y,z always coming in triples. This means I have a database with columns x,y,z and rows vectors say A,B,C. (Sorry I could not write a Latex table here for some reason!)

How does one create such a table on Mathematica and then asks the function to directly compute 1) f[vector A] instead f[x,y,z] and 2) say the sum or product of vectors A,B, and C?

Answer 1

I recommend looking into Dataset.

Here is a test dataset:

data = Dataset@
  Table[<|"x" -> RandomReal[], "y" -> RandomReal[], 
    "z" -> RandomReal[]|>, {i, 9}]

Then you can apply your function like this:

f[data[1, "x"], data[1, "y"], data[1, "z"]]

or shorter:

f @@ data[1]

Which applies your function to the first row (or row vector A in your question).

With a dataset you can use Total like this to get a sum per row:

data[1, Total]