[Math] The Intersection of Two Implicit Functions in Maple

maple

How would I find the intersection between the system of equations $2x^4-2y^3+y=0$ and $2x^2y+3y^4-2x=0$? The section in my book hasn't covered plot3d yet, so I was thinking perhaps implicitplot would be good, but I'm not sure if that's right command to use or not.If it is the right command, would the typical fsolve() method work on finding the points of intersection? Usually when I find solutions to a system of equations, I define the equations as functions,( say f and g) and then use fsolve(f(x)=g(x),x=-5..5) to find the solutions. But this isn't possible for an implicit function. How would I define something that isn't a function (such as a circle) in terms of a function in Maple? I change the last option accordingly to search for the solution, as I usually have the plot open in front of me. If anyone could offer any ideas, that would be appreciated.

Best Answer

restart:

ee:=2*x^4-2*y^3+y=0;

ff:=2*x^2*y+3*y^4-2*x=0;

plots:-display(
   plots:-implicitplot(ee,x=-4..4,y=-2..2, color=red),
   plots:-implicitplot(ff,x=-4..4,y=-2..2, color=blue) );

sols:=solve({ee,ff}):
rsols := remove(hastype,evalf(map(op,{allvalues({sols})})),nonreal);

fsol1 := fsolve({ee,ff},{x=-4..4,y=-2..2});

seq( eval([ee,ff], s), s in rsols );
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