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Rev

$\begingroup$ Very nice, thanks a lot! From the reformulation $0=f(z,w)$ I guess one could express these graphs as affine algebraic plane curves, such that the two components are defined through real polynomials $0=P_1(x,y)P_2(x,y)$ with $w=x+iy$? $\endgroup$

El Rafu
– El Rafu

2021-01-06 20:51:56 +00:00
Commented Jan 6, 2021 at 20:51
$\begingroup$ The function f(z,w)=w^2-z^8=0 is an algebraic curve and we could even plot the solution contours, the solutions to the DEs, over the branches of this curve to clearly show how the DE solutions provide an analytically-continuous route over the sheets of the curve. $\endgroup$

Dominic
– Dominic

2021-01-06 22:45:49 +00:00
Commented Jan 6, 2021 at 22:45

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