# Mathematical Notation

If we use Mathematica notation the following works:

Div[Grad[u[x, y], {x, y}], {x, y}]


also if we multiply the gradient with a scalar:

Div[scal[x,y] Grad[u[x, y], {x, y}], {x, y}]


But when I use graphical mathematical notation with the Del operator (EscdelEsc), the first still works, but the second screws up (sorry, I can not paste the input here, because if I paste the graphical input it gets translated into: Subscript[\[Del], x, y] what is interpreted differently in Mathematica ). I denote therefore the operator symbolically by: delxy:

delxy.(scal[x,y] delxy u[x,y])


This gives an error message, complaining that one can not take the divergence of a scalar. Obviously scal[x,y] delxy u[x,y] is considered a scalar.

Does anybody have an explanation and possibly a way around for this?

• Interesting, didn't know ∇ can be used in this way, but "because if I paste the graphical input it gets translated into: Subscript[\[Del], x, y]" seems to suggest that you're not making it correct in 1st case, either. Perhaps you can create a GIF to illustrate what you've done? – xzczd Oct 9 at 10:52
• BTW you may want to read this: mathematica.stackexchange.com/a/139647/1871 – xzczd Oct 9 at 12:01

Note that you have to use Subscript[∇, {x,y}] instead of Subscript[∇, x, y] to make it work. If you do that, I don't get any problems:

Copyable input for the left side:

\!$$\*SubscriptBox[\(∇$$, $${x, y}$$] .
$$(scal[x, y] \*SubscriptBox[\(∇$$, $${x, y}$$]\ u[x, y])\)
\)


If you don't want to type the braces around the subscripts, you can use the notation package (see below for copyable version of the Notation[...] inputs):

### Copyable inputs

Copy the following, and select "Yes" when it asks you whether the text should be interpreted:

Cell[BoxData[{
RowBox[{"Notation", "[",
RowBox[{
TemplateBox[{RowBox[{
SubscriptBox["\[Del]",
RowBox[{"x_", ",", "y__"}]], "f_"}]},
"NotationTemplateTag"], " ", "\[DoubleLongLeftRightArrow]", " ",
RowBox[{"f_", ",",
RowBox[{"{",
RowBox[{"x_", ",", "y__"}], "}"}]}], "]"}]},
"NotationTemplateTag"]}], "]"}], "\[IndentingNewLine]",
RowBox[{"Notation", "[",
RowBox[{
TemplateBox[{RowBox[{
SubscriptBox["\[Del]",
RowBox[{"x_", ",", "y__"}]], ".", "f_"}]},
"NotationTemplateTag"], " ", "\[DoubleLongLeftRightArrow]", " ",
TemplateBox[{RowBox[{"Div", "[",
RowBox[{"f_", ",",
RowBox[{"{",
RowBox[{"x_", ",", "y__"}], "}"}]}], "]"}]},
"NotationTemplateTag"]}], "]"}]}], "Input"]


Example input:

\!$$\*SubscriptBox[\(∇$$, $$x, y$$] .
$$(scal[x, y] \*SubscriptBox[\(∇$$, $$x, y$$]u[x, y])\)
\)

• Thanks a lot for your answer. The braces do the job. Playing around with the braces, I found, that there is even an easier way, without using the notation package. One can type: Esc,d,e,l,Esc,Ctrl-,{,x,y,},Ctrl Space. – Daniel Huber Oct 10 at 8:10
• @DanielHuber Isn't that the first example in my answer? Or am I missing something? – Lukas Lang Oct 10 at 8:16