Assigning the result of `get_component`

Question

I'm using the get_component function to obtain an expression. I'd like to assign the expression to a variable, in order for further processing it.

I've tried things like

A00 := get_component(A, $t,t$);

and

get_component(A, $t,t$)
A00 := _;

but I get a SyntaxError message.

Any ideas?

Answer 1

The get_component function returns a Python object, which you can directly assign to another symbol, e.g. A00. So a complete example would be

from cdb.core.component import *

{t,x}::Coordinate;
{i,j}::Indices(values={t,x});
ex:= a_{i};
evaluate(ex, $a_{t}=1, a_{x}=2$);

A00=get_component(ex, $x$)

and then A00 is a cadabra Ex object as usual.

Comments

Dear Kasper, thank you for the answer. Actually, as you pointed, the equal sign assigns the value to A00. However, it seems that I cannot use the value for further manipulations.

I'm trying to write a demo notebook for students, and it occurs to me that it might be possible to solve the Schwarzschild spacetime. I got inspired by your notebook, but used

ss:= { g_{t t} = - \exp(A),
 g_{r r} = \exp(B),
 g_{\theta\theta} = r**2,
 g_{\phi\phi}=r**2 \sin(\theta)**2 }. 

for the metric.

After calculating the Ricci tensor rc, I call the components,

from cdb.core.component import *
r00=get_component(rc, $t,t$)[1];
r11=get_component(rc, $r,r$)[1];

but then I cannot use those expressions (it seems)

See image

---

Both r00 and r11 are Cadabra expressions. If you want to pull those into a mathematical expression elsewhere, you need to use @, as in

 exp1:= r  \exp( B - A ) @(r00) - @(r11);

Here r, A and B are mathematical symbols (not Python objects), and if you do not write @ then r00 and r11 would be seen as such too. If you want Cadabra to look up a Python expression, you need to say that explicitly with @.

---

I completely forgot the (at) symbols! Thank you again Kasper.