Testing for a vector of reals

Question

Suppose I define:

RealVector[expr_]:=VectorQ[expr,NumberQ[#]&&Head[#]===Real)];

Then:

RealVector[{1,2,3}];  RealVector[{1.,2.,3.}];

should evaluate to False and True, resp. But I get False and False. Why?

Answer 1

In Mathematica, Element[1,Reals] returns True since integers are subset of the reals. But Head[1] is Integer. So, since you need to check for Head of each element. One way might be

realVector[x_List] := VectorQ[x, NumericQ] && (AllTrue[x, (Head[#] === Real) &])

Now

 realVector[{1., 2., 3.}]  (*True*)
 realVector[{1, 2, 3}]  (*False*)
 realVector[{1., 2., 3}] (*False, since one element is not Real*)
 realVector[{Pi, 1., 2.}] (*False*)

btw, you do not need VectorQ[x, NumericQ] in the above, but I thought it might be faster to short circuit the test. You can also just use

 realVector[x_List] := AllTrue[x, (Head[#] === Real) &]

And this should work also.

Answer 2

Does this fit your needs?

RealVector = MatchQ[#, {__Real}] &

Answer 3

You have syntax errors (e.g., no & for making a function). Moreover, there is no need to check if an element is a number if you're also checking whether it is in the set of Reals.

This should work for you:

realVector[expr_] := VectorQ[expr, # \[Element] Reals &];