Question: Why is Maple mixing roots in this plot and how to avoid this?

In the below plot switches between to solutions of a RootOf expression when the plot range starts at zero.

plot3d on the other hand sticks to one root.

Why is that and how to get a plot starting at zero showing only one root?

restart

a := RootOf(JacobiCN(sqrt(2)*sqrt(alpha), (1/2)*sqrt(2)*_Z)^2*_Z^2+_Z^2-2)

RootOf(JacobiCN(2^(1/2)*alpha^(1/2), (1/2)*2^(1/2)*_Z)^2*_Z^2+_Z^2-2)

(1)

allvalues(a)

RootOf(JacobiCN(2^(1/2)*alpha^(1/2), (1/2)*2^(1/2)*_Z)^2*_Z^2+_Z^2-2)

(2)

plot(a, alpha = 0 .. .5)

 

eval(a, [alpha = 1/20])

RootOf(JacobiCN((1/20)*2^(1/2)*20^(1/2), (1/2)*2^(1/2)*_Z)^2*_Z^2+_Z^2-2)

(3)

evalf(allvalues(RootOf(JacobiCN((1/20)*2^(1/2)*20^(1/2), (1/2)*2^(1/2)*_Z)^2*_Z^2+_Z^2-2)))

1.024662619, -1.024662619

(4)

_ValuesMayBeLost

true

(5)

plot3d(a)

 

NULL

Download plot_of_RootOf.mw

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