  We develop a diagrammatic calculus for representations of unrolled quantum
$\mathfrak{sl}_2$ at a fourth root of unity. This allows us to prove
Seifert-Torres type formulas for certain splice links using quantum algebraic
methods, rather than topological methods. Other applications of this
diagrammatic calculus given here are a skein relation for $n$-cabled double
crossings and a simple proof that the quantum invariant associated with these
representations determines the multivariable Alexander polynomial.
