  The set of non-linear equations describing the Standard Model kinematics of
the top quark antiqark production system in the dilepton decay channel has at
most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its
most precise solution is of major importance for measurements of top quark
properties like the top quark mass and $t\bar{t}$ spin correlations. Simple
algebraic operations allow to transform the non-linear equations into a system
of two polynomial equations with two unknowns. These two polynomials of
multidegree eight can in turn be analytically reduced to one polynomial with
one unknown by means of resultants. The obtained univariate polynomial is of
degree sixteen. The number of its real solutions is determined analytically by
means of Sturm's theorem, which is as well used to isolate each real solution
into a unique pairwise disjoint interval. The solutions are polished by seeking
the sign change of the polynomial in a given interval through binary
bracketing.
