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Question: Does function Solve have limitations by output form RootOf?

Question:Does function Solve have limitations by output form RootOf?

lcz 994 Maple 2020
solve implicit rootof
December 26 2020
0

 The code

s:=solve(sin(x)=3*x/Pi,x)

gives us following output:

s := RootOf(-sin(_Z)*Pi + 3*_Z)

The allvalues command attempts to find symbolic representations of the roots using solve.
But  the code:

allvalues(s);
solve(sin(x)=3*x/Pi,x,AllSolutions)

gives us 

RootOf(-sin(_Z)*Pi + 3*_Z, 0.5235987756), RootOf(-sin(_Z)*Pi + 3*_Z, -0.5235987756), 0

RootOf(-sin(_Z)*Pi + 3*_Z)

To see the roots of sin(x)-3*x/Pi   we use plot

plot(sin(x)-3*x/Pi,x=-100..100)

 

plot(sin(x)-3*x/Pi,x=-Pi/4..Pi/4)

And we can also figure out  three roots of this function are 0 ,  Pi/6 and -Pi/6. 

High probability it has no other root.

seq(eval(sin(x)-3*x/Pi,x=i),i in [-Pi/6,0,Pi/6])

0, 0, 0

Why doesn't Maple do anything about it

 

 

 
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