Question

I am trying to create a function in Mathematica that takes in a list of pairs that are numeric and outputs a list of the first element of the pair raised to the inverse power of the second element e.g. {{1,3},{2,2}….} -> {1^(1/3),2^(1/2),…}.

This is what I have got so far:

pairsToRoots3[list : {{_, _} ..}] := 
list /. {p_Real, q_Real} :> p^(1/q)

It doesn’t seem to work with p_Real but if i put p_Integer it works fine. Not sure why. Ideally, I would like the condition to be expressed like

 pairsToRoots3[list : {{_Real, _Real} ..}]      

or somehting like this but everything I tried seemed not to work.

Answer 1

This works if your numbers have head Real:

pairsToRoots[list : {{_Real, _Real} ..}] :=  #^(1/#2) & @@@ list

pairsToRoots[{{1`, 3`}, {2`, 2`}}]

{1., 1.41421}

But these numbers do not have head Real:

Head /@ {1, 2, Pi 7/8}

{Integer, Integer, Integer, Symbol, Rational}

Therefore you probably want NumericQ as george used:

pairsToRoots[list : {{_?NumericQ, _?NumericQ} ..}] :=  #^(1/#2) & @@@ list

pairsToRoots[{{1, 3}, {2, 2}}]

{1, Sqrt[2]}