convert radicals and I to RootOf notation - Maple Help

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convert/RootOf - convert radicals and I to RootOf notation

Calling Sequence

convert(expr, RootOf)

convert(expr, RootOf, form=selector)

Parameters

expr

-

expression

form=selector

-

selector could be one of the three values: index, interval, or numeric; this is an option to convert between RootOf selectors, namely range/interval selector, numeric selector, and the index selector. For information on these selectors, see RootOf.

Description

• 

The convert/RootOf function changes all occurrences of radicals (may be algebraic constants or functions), to indexed RootOf notation.

• 

Usually, the radical Apm, for integers p < m, is transformed into the expression RootOf(_Z^m-A,index=1)^p.

• 

I is replaced by RootOf(_Z^2+1,index=1)

• 

This function is mapped recursively over expressions. In particular, nested radicals are converted. If the input expression is an unnamed table then the conversion routine is mapped onto the elements of the table.

• 

This function uses radfield to convert radicals into independent RootOfs.

• 

To convert RootOf notation to I and radicals (where possible) use convert(expr, radical).

• 

To convert RootOf notation between different selectors, use form=selector to select the target selector format.

Examples

convert215&comma;RootOf

RootOf_Z52&comma;index&equals;1

(1)

convert1&plus;21213I&comma;RootOf

RootOf_Z2&plus;1&comma;index&equals;1RootOf_Z31RootOf_Z22&comma;index&equals;1&comma;index&equals;1

(2)

convert1&plus;212I&comma;RootOf

RootOf_Z2&plus;1&comma;index&equals;11&plus;RootOf_Z22&comma;index&equals;1

(3)

convert214&plus;213&comma;RootOf

RootOf_Z42&comma;index&equals;1&plus;RootOf_Z32&comma;index&equals;1

(4)

convertx2&plus;2x&plus;112&comma;RootOf

RootOf_Z2x22x1&comma;index&equals;1

(5)

convertx36x26x712&comma;RootOf

RootOfx3&plus;_Z2&plus;6x2&plus;6x&plus;7&comma;index&equals;1

(6)

convert&comma;radical

x36x26x7

(7)

a:=RootOfx3x1&comma;index&equals;1

a:=RootOf_Z3_Z1&comma;index&equals;1

(8)

converta&comma;&apos;RootOf&apos;&comma;form&equals;interval

RootOf_Z3_Z1&comma;103493597812500..662358981500000000

(9)

converta&comma;&apos;RootOf&apos;&comma;form&equals;numeric

RootOf_Z3_Z1&comma;1.324717957

(10)

b:=RootOf_Z5_Z1&comma;1

b:=RootOf_Z5_Z1&comma;1

(11)

convertb&comma;&apos;RootOf&apos;&comma;form&equals;index

RootOf_Z5_Z1&comma;index&equals;1

(12)

convertb&comma;&apos;RootOf&apos;&comma;form&equals;interval

RootOf_Z5_Z1&comma;11673039731000000000..11673039831000000000

(13)

See Also

allvalues, convert, convert/radical, evala/Algfield, radfield, RootOf


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