Cadabra manual: Coordinate

Coordinate

Declare a symbol to be a coordinate label.

Declare a symbol to be a coordinate label (useful in combination with Depends). This is required if you want to write a derivative with respect to a coordinate: if you write

\partial{#}::PartialDerivative. ex:= A(x,y) + \partial_{x}{B(x,y)};

{\color{red}{

RuntimeError: Free indices in different terms in a sum do not match.

At:
  Notebook Cell (Line 2): ex = Ex(r''' A(x,y) + \partial_{x}{B(x,y)}'''); _=ex; display(ex)

}}

will by default be seen as incorrect because the $x$ in the second term will be considered an index label, not a coordinate. The input

{ x, y }::Coordinate. ex:=A(x,y) + \partial_{x}{B(x,y)};

$\displaystyle{}A\left(x , y\right) +\partial_{x}{B\left(x , y\right)}$

A(x , y) + \partial_{x}(B(x , y))

is allowed and interpreted in the right way.