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I have defined a variable called y, this contains a huge equation, but when I look for the dimension of y it shows 3. How come a single expression has dimensions of 3? It is supposed to be 1 right?

y=39.25 ω^2 (1.00519 Subscript[a,4][1]^2+1.00102 Subscript[a,4][2]^2+2.19056 Subscript[a,4][1] Subscript[a,4][3]-1.07645 Subscript[a,4][2] Subscript[a,4][3]+1.5 Subscript[a,4][3]^2+0.55507 Subscript[a,4][1] Subscript[a,4][4]+1.54742 Subscript[a,4][2] Subscript[a,4][4]+1.5 Subscript[a,4][4]^2);;
Dimensions[y]
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  • $\begingroup$ Well, it is a product of three things. A one-dimensional list, of three elements. $\endgroup$
    – Per Alexandersson
    Jan 10, 2020 at 13:56
  • $\begingroup$ Dimensions needs a full array as argument (see documentation) . If you apply it to a scalar surprising results like Dimension[a+b] (* 2*) occur. $\endgroup$
    – Ulrich Neumann
    Jan 10, 2020 at 14:00
  • $\begingroup$ It is a single expression right. Is it possible to make one expression with dimension 1 $\endgroup$
    – acoustics
    Jan 10, 2020 at 14:00
  • $\begingroup$ Yes, something like {a +b} $\endgroup$
    – Ulrich Neumann
    Jan 10, 2020 at 14:05
  • 1
    $\begingroup$ Perhaps you would be interested in LeafCount which gives the total number of indivisible subexpressions. In this case, 78 $\endgroup$
    – Bob Hanlon
    Jan 10, 2020 at 15:53

2 Answers 2

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Maybe what you are looking for is LeafCount. TreeForm is also useful for visualizing expressions.

TreeForm @ y

enter image description here

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From the point of view of tensor analysis, a scalar has no dimensions at all. You can make your own function that reflects this:

arrayDimensions[x_?ArrayQ] := Dimensions[x]
arrayDimensions[x_] := {}
arrayDimensions[{1, 2}]
(* {2} *)
arrayDimensions[a + b]
(* {} *}
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