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convert/radical

convert RootOf and trig functions to radicals and I

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

convert( expr, radical, n )

Parameters

expr

-

expression

n

-

(optional) positive integer

Description

• 

The convert(expr, radical) calling sequence replaces RootOfs of polynomials by appropriate expressions in radical notation if possible.

  

The conversion can fail if Maple cannot find radical expressions for the roots or if the correct radical expression cannot be selected. If the conversion fails, the RootOf remains unchanged.

• 

If a root of unity cannot be expressed in terms of radicals, it is converted to an equivalent expression involving sin and cos terms.

• 

If the argument n is included, the n-th root with respect to the ordering used by solve is returned. Otherwise, the following rules are applied to choose the root.

  

Binomials

  

An indexed RootOf of the form RootOf(P(_Z), index=i), where P_Z=A_Zm+B for some integer m is replaced by (-B/A)^(1/m)*(-1)^(2*(i-1)/m). If no index is given, then i=1 is assumed and BA1m is returned. In particular, RootOf(_Z^2+1) and RootOf(_Z^2+1, index=1) are transformed into I.

  

If the argument n is included, indexed RootOf can be converted to radical only if n equals the index i. Otherwise, an error is generated.

  

Other cases

  

Labeled RootOfs are converted by the same rules as unlabeled.

  

If a RootOf can be evaluated numerically by using evalf, then the radical expression with the closest numerical approximation is returned, which is the value of RootOf with index=1. If numerical evaluation fails, for example, if the RootOf has symbolic coefficients, then the cause is one of the following.

1. 

The RootOf has only one argument. That is, it has the form RootOf(P(_Z)). The first radical expression for the ordering used by the solve command is returned.

2. 

The RootOf is indexed. The conversion usually fails because Maple is unable to find a radical expression equal to the input RootOf for all values of the parameters.

• 

To a limited extent, the RootOf notation can be restored by using convert/RootOf.

• 

If the argument of a trigonometric function is of the form nπ120 where n is an integer, then Maple converts the function to radical form.

Examples

convertRootOf_Z32,index=1,radical

21/3

(1)

convertRootOf_Z32,index=2,radical

21/312/3

(2)

convertRootOf_Z32,index=2,radical,2

1221/3+12I321/3

(3)

The following command produces an error.

convertRootOf_Z32,index=2,radical,3

Error, (in `convert/radical`) indexed RootOf can only be converted to the same root number

convertRootOf_Z32,1.2,radical

21/3

(4)

convertRootOf_Z2+1,index=2,radical

I

(5)

convertRootOf_Z2+1,radical

I

(6)

convertRootOf_Z3+_Z+1,index=1,radical

112108+12931/31108+12931/312I316108+12931/32108+12931/3

(7)

convertRootOf_Z3+_Z+1,radical

112108+12931/31108+12931/312I316108+12931/32108+12931/3

(8)

convertRootOf_Z3+_Z+x,radical

16108x+1281x2+121/32108x+1281x2+121/3

(9)

In the following case, radical expressions exist, but viewed as functions of x none of them is equal to the RootOf.

convertRootOf_Z3+_Z+x,index=1,radical

RootOf_Z3+_Z+x,index=1

(10)

In general, there is no radical expression for the roots of a degree 5 polynomial.

convertRootOf_Z5+_Z+3,index=1,radical

RootOf_Z5+_Z+3,index=1

(11)

The following RootOf represents a seventh root of unity. It cannot be expressed in radical form, but it can be converted to a form involving trigonometric functions.

convertRootOf_Z6+_Z5+_Z4+_Z3+_Z2+_Z+1,index=1,radical

cos27π+Isin27π

(12)

Trigonometric functions of a rational multiplied by Pi can, in some cases, be converted to radical form.

sinπ30

sin130π

(13)

convert,'radical'

18235518185

(14)

convertsec5π24,'radical'

48+2622

(15)

convertcot323π20,'radical'

14514+255

(16)

See Also

allvalues

convert/RootOf

evalf

radfield

radnormal

RootOf

solve

trig

type/radical

 


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