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- TL;DR Summary
- Is there a standard numeric approach to finding the intersection of two algebraic curves?

Given two algebraic curves:

##f_1(z,w)=a_0(z)+a_1(z)w+\cdots+a_n(z)w^n=0##

##f_2(z,w)=b_0(z)+b_1(z)w+\cdots+b_k(z)w^k=0##

Is there a general, numeric approach to finding where the first curve ##w_1(z)## intersects the second curve ##w_2(z)##? I know for low degree like quadratic or cubics can find the intersection by brute force but was wondering if there is a more general approach for higher degrees say 10 or 12 each?

##f_1(z,w)=a_0(z)+a_1(z)w+\cdots+a_n(z)w^n=0##

##f_2(z,w)=b_0(z)+b_1(z)w+\cdots+b_k(z)w^k=0##

Is there a general, numeric approach to finding where the first curve ##w_1(z)## intersects the second curve ##w_2(z)##? I know for low degree like quadratic or cubics can find the intersection by brute force but was wondering if there is a more general approach for higher degrees say 10 or 12 each?