canonicalMultipliers -- Computes the canonical multipliers of a rational curves with nodes

This function is identical to the function "canonicalMultipliers" from the Macaulay2 package NodalCurves. Given g pairs of points P_i, Q_i, on P¹ computes the canonical series of the corresponding nodal curve of genus g and determines the g ratios A_i of the glueing data for the canonical bundle (note that A_i depends on the choice of the homogeneous coordinates of the point P_i and Q_i).

Step 1.We compute g quadrics q_i q_i :=det(P_i | (x₀,x₁)^t) * det(Q_i | (x₀,x₁)^t) and a basis of H⁰(C,ω_C) by {s_i :=∏^g_j≠i,j=1q_i | i=1,...,g }.

Step 2. We compute the multipliers a_i=s_i(P_i) and b_i=s_i(Q_i)