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\iteman{ZMATH 2011a.00058}
\itemau{Rice, Adrian}
\itemti{``To a factor pr\`es'': Cayley's partial anticipation of the Weierstrass $\wp$-function.}
\itemso{Am. Math. Mon. 117, No. 4, 291-302 (2010).}
\itemab
In a nutshell, this article presents -- apart from biographical material on Cayley and Weierstra\ss{} -- Cayley's transformation of an integral $\int \frac{dx}y$, where $y^2 = f_4(x)$ equals a quartic polynomial, into an integral of Weierstra\ss{} form $\int \frac{dx}{w}$, where $w^2 = f_3(x)$ equals a cubic polynomial. Neither the result nor Cayley's method of proof via invariants are as obscure as the author seems to believe: all of these classical results have found their way into modern presentations of the general $2$-descent on elliptic curves [see e.g. {\it J. E. Cremona}, J. Symb. Comput. 31, No. 1-2, 71--87 (2001; Zbl 0965.11025)]. For this reason, the article under review is recommended to number theorists who wonder where the invariants, covariants and syzygies they are using came from.
\itemrv{Franz Lemmermeyer (Jagstzell)}
\itemcc{A30 I80}
\itemut{invariants; Weierstrass $\wp$-function; elliptic functions; elliptic integrals}
\itemli{doi:10.4169/000298910X480766}
\end