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I am not sure about your exact question, but you might start with:

sage: x = Permutation([2,1,4,3])
sage: y = Permutation([3,2,1,4])
sage: x.cycle_tuples()
[(1, 2), (3, 4)]
sage: y.cycle_tuples()
[(1, 3), (2,), (4,)]

Regarding Kazhdan-Lusztig polynomial for Weyl groups, you can have a look at :

• https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/kazhdan_lusztig.html
• https://doc.sagemath.org/html/en/thematic_tutorials/lie/kazhdan_lusztig_polynomials.html