The <math>l</math>th [[division polynomial]] is such that its roots are precisely the <math>x</math> coordinates of points of order <math>l</math>. Thus, to restrict the computatiocomputation of <math>(x^{q^{2}}, y^{q^{2}}) + \bar{q}(x, y)</math> to the <math>l</math>-torsion points means computing these expressions as functions in the coordinate ring of <math>E</math> ''and'' modulo the <math>l</math>th division polynomial. I.e. we are working in <math>\mathbb{F}_{q}[x,y]/(y^{2}-x^{3}-Ax-B, \psi_{l})</math>. This means in particular that the degree of <math>X</math> and <math>Y</math> defined via <math>(X(x,y),Y(x,y)):=(x^{q^{2}}, y^{q^{2}}) + \bar{q}(x, y)</math> is at most 1 in <math>y</math> and at most <math>(l^2-3)/2</math>
