Here is a link to the article: https://www.sciencedirect.com/science/article/pii/S0022314X85710888?ref=cra_js_challenge&fr=RR-1.
Pages 237-238 give polynomial expressions $X_3^{(2)}, Y_3^{(2)}, Z_3^{(2)}$ for the addition law on an elliptic curve $E$ over a field, which are valid on some open subset of $E \times E$. I am trying to implement the formulas in Magma, as a rational map from $E \times E \to E$. However, when I attempt to construct the map for a specific curve $E$, Magma gives me an error, saying that the rational function on $E \times E$ given by $[X_3^{(2)}:Y_3^{(2)}:Z_3^{(2)}]$ does not define a map into $E$. Notably, Magma has no such problem with the formula $[X_3^{(1)}:Y_3^{(1)}:Z_3^{(1)}]$ for the addition, where the definition of these terms immediately precedes the definition of $X_3^{(2)}$ in the paper.
After several laborious checks, I am certain that I correctly transcribed the formulas from the paper into my code. It therefore seems likely that there is a small typo in the formulas given in the paper (which would not be surprising, considering that the formulas are very complicated and the paper predates modern computer algebra systems). Is there an erratum for this paper, or correct formulas written down anywhere?
Failing that, does anyone know if there is publicly available Magma code implementing a complete system of addition laws for an elliptic curve, in the terminology of the paper? There are other examples of such complete systems in the literature, such as in https://eudml.org/doc/143215, but I don't think that one works in arbitrary characteristic. Some other explicit example of a complete system of expressions which works in arbitrary characteristic would also be helpful.
