|
Calling Sequence
|
|
ConvertRootOf(f, options)
|
|
Parameters
|
|
f
|
-
|
any Maple object
|
options
|
-
|
(optional) equation(s) of the form keyword = value, where keyword is either 'makeindependent' or 'substitutions'
|
|
|
|
|
Options
|
|
•
|
If the option 'makeindependent' = true is given, ConvertRootOf will attempt to rewrite all algebraic objects, including RootOfs that are present in f, in terms of independent RootOfs, using the command evala/Algfield. Note that this computation can be very expensive. If 'makeindependent' = false is given, then ConvertRootOf will not perform any independence checking, and the RootOfs in the output may not be independent. By default, 'makeindependent' = FAIL is assumed, and a rewrite in terms of independent RootOfs will only be attempted if there are at most distinct algebraic objects in f.
|
•
|
If the option 'substitutions' = true is given (or 'substitutions' for short), then ConvertRootOf does not actually perform the conversion but instead returns an expression sequence F, B, S, where
|
–
|
F is a set of forward substitutions, such that the result of subs(F, f) is equal to what ConvertRootOf returns without option substitutions,
|
–
|
B is a set of backward substitutions, essentially the inverse of the substitution induced by F, and
|
–
|
S, of type boolean, indicates whether the RootOfs in subs(F, f) are independent.
|
|
|
Description
|
|
•
|
Usually, the radical , for integers , is transformed into the equivalent expression .
|
•
|
The imaginary unit is replaced by , unless it occurs in the second or third argument of a RootOf.
|
•
|
This command descends recursively into subexpressions, including tables. In particular, nested radicals are converted.
|
•
|
By default, this command performs a limited amount of independence checking, for efficiency reasons, unless the option 'makeindependent' is given (see below).
|
•
|
If the input is a single algebraic object, then ConvertRootOf always returns an irreducible RootOf.
|
|
|
Examples
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
>
|
|
| (4) |
The imaginary unit is replaced by , unless it occurs in the second or third argument of a RootOf:
>
|
|
| (5) |
If there are at most 4 algebraic numbers in the input, the output RootOfs will be independent by default:
>
|
|
| (6) |
>
|
|
| (7) |
If the input contains more than 4 algebraic objects, the output RootOfs are not necessarily independent:
>
|
|
| (8) |
>
|
|
| (9) |
ConvertRootOf recognizes trigonometric algebraic numbers:
>
|
|
| (10) |
Unless the only algebraic object in the input is a trigonometric algebraic number, ConvertRootOf first converts to radicals and then to RootOfs:
>
|
|
| (11) |
|
|
|