# Interval in a Coxeter group of type A6

let [a,b] be a smooth interval in a Coxeter group of type A6 such that every ascent of a is an ascent of b. Is there a way of computing such interval in sage math?

Welcome to Ask Sage! Thank you for your question.

Bruhat order ? weak order ? Shard-intersection order ? some other partial order ? And what does smooth mean ? And what do you mean by computing ? Are the elements a and b given ?

If you already have code for the setup, please provide it as a starting step for potential answerers.