Use the Exponential field of the Options > Mode Settings > Simplification command19_L5FP to control the collection or expansion of expressions involving exponentials.  The transformation

 z  w      z+w 
ê ·ê  ⇐⇒ ê    

is valid if z and w are real or complex expressions.  The transformation

  z k      k·z 
(ê )  ⇐⇒ ê    

is valid if k is an integer, or if k is a fraction and z is a real or complex expression whose imaginary part lies in the interval (-π, π].  The Exponential field provides the following options:

•        Select the Collect option to apply both transformations to the right when simplifying expressions.

•        Select the Expand option to apply both transformations to the left when simplifying expressions.

•        Select the Auto option to apply the transformations in such a way as to produce the most compact and attractive form when simplifying expressions.  Auto is the factory default exponential mode setting.


For example, if the Collect option is selected, the expression

x^a·ê^(b + c)

simplifies to

 a·LN(x) + b + c 
ê                

whereas if the Expand option is selected, it simplifies to

 b  c  a 
ê ·ê ·x  

whereas if the Auto option is selected, it simplifies to

 b + c  a 
ê     ·x  


When a new exponential transform direction is selected, this command generates an expression of the form

Exponential := direction

where direction is Auto, Collect, or Expand.  The exponential transform direction can also be changed by entering an expression of the above form using upper and lower case exactly as shown on the expression entry line.


Other Options > Mode Settings > Simplification command19_L5FP fields

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