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Question: which method to use to remove RootOf ?

Question:which method to use to remove RootOf ?

nm 10978 Maple 2025
rootof
April 07 2025
2

I know of 3 ways to remove RootOf, but sometimes they give different result. How does one decide which to use? This is done in code. So method to decide can't depend on looking at the screen and see which result one "likes" more than the other.

Is allvalues() the one to use all the time? Could one of these 3 methods fail, and then one has to try the next one?

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interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

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Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1859 and is the same as the version installed in this computer, created 2025, April 6, 14:34 hours Pacific Time.`

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restart
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e:=y*4^(1/3)*((4*x^2*RootOf(_Z^2*y - 4*_Z*x + y) - y^2*RootOf(_Z^2*y - 4*_Z*x + y) - x*y)/y^2)^(1/3) - _C2;

y*4^(1/3)*((4*x^2*RootOf(_Z^2*y-4*_Z*x+y)-y^2*RootOf(_Z^2*y-4*_Z*x+y)-x*y)/y^2)^(1/3)-_C2

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convert(e,radical)

y*4^(1/3)*((4*x^2*(2*x+(4*x^2-y^2)^(1/2))/y-y*(2*x+(4*x^2-y^2)^(1/2))-x*y)/y^2)^(1/3)-_C2

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DEtools:-remove_RootOf(e)

(1/16)*(c__2^3+4*x*y^2)^2/(y*(4*x^2-y^2)^2)-(c__2^3+4*x*y^2)*x/(y*(4*x^2-y^2))+y = 0

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allvalues( e)

y*4^(1/3)*((4*x^2*(2*x+(4*x^2-y^2)^(1/2))/y-y*(2*x+(4*x^2-y^2)^(1/2))-x*y)/y^2)^(1/3)-c__2, y*4^(1/3)*((-4*x^2*(-2*x+(4*x^2-y^2)^(1/2))/y+y*(-2*x+(4*x^2-y^2)^(1/2))-x*y)/y^2)^(1/3)-c__2


 

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