Consider the following example expression dependent on parameter t
:
expr= t a ((t b+t c+ d )(t e+ f)+t g (t k+ l)+m (t n+ p));
This is a very short expression, which stands as an example for more complicated ones that are much larger, more nested and of higher overall degree in t
.
Now I would like to take the limit:
Limit[expr/t^3,t->Infinity]
However, instead of doing it using this function, I would like to manipulate expr/t^3
such as to cancel most t
parameters without opening any brackets, so that we get:
expr2=myManipulate[expr/t^3]
a (( b+ c+ d/t )( e+ f/t)+ g ( k+ l/t)+m (n+ p/t)/t)
Now we can see that taking the limit amounts to just setting t->Infinity
:
expr2/.t->Infinity
a ( e ( b+ c )+ g k)
We did not have to open any brackets and did not have to use Limit
function. Is there a way to write an efficient myManipulate
function that does this for arbitrarily more complicated (larger and more nested) input? Thanks for any suggestion!