combine radicals in products - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Expression Manipulation : Combining : combine/radical

combine/radical - combine radicals in products

Calling Sequence

combine(expr, radical)

combine(expr, radical, symbolic)

Parameters

expr

-

any expression

Description

• 

The combine/radical function is used to combine products of radicals of the same power that appear in an expression.

• 

The main transformation made by combine/radical is

...xmdynd......xmyn1d...

  

where x and y are both positive, (i.e. signumx&equals;signumy &equals;1) and 0<m&comma;n<d where m&comma;n&comma;d are integers.

  

For example: 212312612 

• 

If the condition 0<m<d above is not satisfied, then let m&equals;dq&plus;r where 0<r<d. Then expand xmd&equals;xdq&plus;rd &equals;xq&plus;rd as xq xrd so that the condition is now satisfied.  If x is an integer, Maple applies this transformation automatically.  

  

For example: 2322212.

• 

Suppose the sign of x is known to be negative, i.e. signumx&equals;1. Then expand xmd as 1md xmd so that the positive part xmd can now be combined.  

  

For example: 212312I212312I612 

• 

The new radical xmyn1d needs to be simplified. The new radicand xmyn is simplified by applying normal(x^m*y^n, expanded). For example:10+210210+2102normal/expanded98 which after simplification yields 72

• 

If the sign of x and y is not known, then combine will not combine the radicals because that is not correct for all x and y in general. For example xyxy for negative x and y.  The user has two possibilities to force Maple to combine radicals of unknown sign. The first is to use assume to tell Maple the sign of the radicands. The second is to specify the optional argument symbolic which will assume all radicands of unknown sign are real and positive.

• 

If the sign of one radicand is unknown -- for example, suppose that signumx&equals;1 and signumy is unknown -- then combine will still combine the radicands x and y because x is known to be positive.

Examples

f1:=26&plus;2x&plus;1

f1:=26&plus;2x&plus;1

(1)

combinef1&comma;radical

23&plus;2x&plus;2

(2)

f2:=434&plus;3

f2:=434&plus;3

(3)

combinef2&comma;radical

434&plus;3

(4)

normal&comma;expanded

13

(5)

f3:=xy&plus;2x&plus;13y

f3:=xy&plus;2x&plus;13&sol;2y

(6)

combinef3&comma;radical

xy&plus;x&plus;1y2x&plus;2

(7)

combinef3&comma;radical&comma;symbolic

xy&plus;x&plus;12x&plus;1y

(8)

assumex<0

combinef3&comma;radical

Ix~y&plus;x~&plus;1y2x~&plus;2

(9)

See Also

assume, normal/expanded, signum, simplify[radical], sqrt


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam