How to apply assumptions to pattern matching?

Question

I'm trying to remove terms whose exponents are positive in a polynomial. I tried this one;

Assuming[t > 0, x^t /. {x^a_ /; Positive@a -> 0}]

but the result becomes;

x^t

I want to get 0 instead of this result.

How to do so?

Thank you.

Answer 1

For some reason Mathematica doesn't apply the assumption automatically, but you can enforce it like this:

Assuming[t > 0, x^t /. {x^a_ /; Simplify[Positive@a] -> 0}]

a minimal example:

Assuming[t > 0, t > 0]
(*t>0*)

Assuming[t > 0, Simplify[t > 0]]
(*True*)