Using standard notation for vector magnitude

Question

The mathematical notation for the magnitude of a vector is $\vert x \vert$, but this does not work:

∥ {1, 2, 3} ∥

Is there any way to overload the DoubleVerticalBar symbol so my Mathematica code would look like a textbook formula?

Answer 1

If you only want to have the "nice" format for input, you could assign Norm to DoubleBracketingBar (which is equivalent to \[LeftDoubleBracketingBar] # \[RightDoubleBracketingBar] &)

DoubleBracketingBar := Norm
DoubleBracketingBar[x]
(* Norm[x] *)

Alternatively, and more usable, you could use the Notation package

Needs["Notation`"]
Notation[ParsedBoxWrapper[
RowBox[{"DoubleBracketingBar", "[", "x_", 
     "]"}]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[
RowBox[{"Norm", "[", "x_", "]"}]]]
Notation[ParsedBoxWrapper[
RowBox[{"\[LeftDoubleBracketingBar]", "x_", 
     "\[RightDoubleBracketingBar]"}]] \[DoubleLongLeftRightArrow] 
  ParsedBoxWrapper[
RowBox[{"Norm", "[", "x_", "]"}]]]

Which is displayed more readable as

The usage is then as expected:

DoubleBracketingBar[x] // FullForm
(* Norm[x] *)
\[LeftDoubleBracketingBar]x\[RightDoubleBracketingBar] \
// FullForm
(* Norm[x] *)
Norm[x]
(* \[LeftDoubleBracketingBar]x\[RightDoubleBracketingBar] *)

Edit: By the way, the reason I did not use \[DoubleVerticalBar] is because it is built in as an infix operator.

Answer 2

You could create an input alias for this:

CurrentValue[EvaluationNotebook[], {InputAliases, "norm"}] = TemplateBox[
    {"\[SelectionPlaceholder]"},
    "Norm"
]

The only downside is you have to tab to the placeholder.