How to find out if two cubic bezier curves intersect using an algorithm (not brute force)?

Question

Algorithms

Greetings!
There is a need to calculate whether two cubic Bezier curves intersect on the plane given by the coordinates of the reference points.
The intersection points themselves and their coordinates are not important.
First of all, I discard all those in which the shells do not intersect at the reference points.
But what to do next?
Is there any algorithm that would allow you to unambiguously answer whether they intersect or not without using division into segments?

Answer 1

Curve equations?
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