problem with division

Question

Suppose i define a variable l:=k_{c}p_{c}, where k and c are vectors and usual summation is assumed. Then I define m to be the inverse of l i.e. m:=1/l (or I defined m:=l**{-1}). Then I computed m*l but i am not getting unity (1).

Instead I am getting output as ml.

Whats the mistake I am doing.

What should i do for the simplication involving fractions like this..please help

Answer 1

If you do

 m:= l**{-1};

you create an expression 'm' (a Python object) which contains the mathematical expression $l^{-1}$. The thing on the left of the := is a Python name, while the thing on the right is a Cadabra expression.

Now if you write

ex:= m l;

you create another expression, called 'ex', which contains the mathematical expression $m l$.

If you want to tell Cadabra that it should use the content of the m object to build this expression, you need to do

ex:= @(m) l;
collect_factors(_);

(the 2nd line is there to reduce $l^{-1} l$ to $1$).

A cleaner (more Cadabra-esque) way of writing this is

 mrule:= m = l^{-1};
 ex:= m l;
 substitute(ex, mrule);
 collect_factors(ex);

Here I defined an object which contains the rule which tells Cadabra how to replace $m$. The reason why this is cleaner is that it generalises better to replacement rules with indices. You cannot write

 A_{\mu} := B_{\mu};    # not possible

(to replace $A{\mu}$with$B{\mu}$), because Python objects need to have names consisting of alphanumeric characters only (and$A_{\mu}$ contains other stuff as well). But you can write

Arule:= A_{\mu} = B_{\mu};

and then

ex:= A_{\mu} C^{\mu};
substitute(ex, Arule);

to get $B_{\mu} C^{\mu}$.