confracform - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

numapprox

  

confracform

  

convert a rational function to continued-fraction form

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

confracform(r)

confracform(r, x)

Parameters

r

-

procedure or expression representing a rational function

x

-

(optional) variable name appearing in r, if r is an expression

Description

• 

This procedure converts a given rational function r into the continued-fraction form which minimizes the number of arithmetic operations required for evaluation.

• 

If the second argument x is present then the first argument must be a rational expression in the variable x. If the second argument is omitted then either r is an operator such that  yields a rational expression in y, or else r is a rational expression with exactly one indeterminate (determined via indets).

• 

Note that for the purpose of evaluating a rational function efficiently (i.e. minimizing the number of arithmetic operations), the rational function should be converted to continued-fraction form. In general, the cost of evaluating a rational function of degree  when each of numerator and denominator is expressed in Horner (nested multiplication) form, with the denominator made monic, is

 mults/divs   and    adds/subtracts

  

whereas the same rational function can be evaluated in continued-fraction form with a cost not exceeding

  

 

 mults/divs   and    adds/subtracts

• 

The command with(numapprox,confracform) allows the use of the abbreviated form of this command.

Examples

(1)

The Horner form can be evaluated in 4 mults/divs

(2)

whereas the continued-fraction form can be evaluated in 2 mults/divs

(3)

(4)

(5)

(6)

(7)

See Also

convert/confrac

indets

numapprox[hornerform]

 


Download Help Document