What is the relationship between singular points of algebraic curves (as described here or here), singular points of ode's (as described here or here) and singular points in complex analysis (as described here or here)? They seem like three completely distinct ideas, yet I'd wager that the last two definitions fall out of the Taylor expansions of $f(x,y,y')$ or $f(z)$, i.e. that they come out of the definition that allows for ideas like crunodes & acnodes & that theses ideas potentially relate to the other definitions - any thoughts?
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