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What does 'RootOf' mean and can I get rid of it?

RootOf() is a command used as a placeholder for roots of equations, helping Maple (and users) to simplify expressions. Generally, an expression with RootOf() represents multiple values.

When you apply allvalues() to an expression involving at least one RootOf(), Maple attempts to compute all possible values explicitly.

Another useful command is remove_RootOf(), which is in the DEtools package. This will attempt to rewrite an expression in a form that does not include RootOf(), commonly resulting in implicit expressions.

Below is an example from the remove_RootOf help page that illustrates the differences:

with( DEtools ):

eq := y / x + RootOf( _Z + exp(_Z) ) = C; 
remove_RootOf( eq ); 
allvalues( eq );

In some cases, using solve() can generate a sequence of expressions that use RootOf().  In such situations, using Maple's indexing notation and/or explicit option can be used:

s := solve({(x-11)^2+(y-5)^2 = 75, (x-7)^2+(y-2)^2 = 100}, {x, y});
solve({(x-11)^2+(y-5)^2 = 75, (x-7)^2+(y-2)^2 = 100}, {x, y}, explicit);

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