convert to continued-fraction form - Maple Help

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convert/confrac - convert to continued-fraction form

Calling Sequence

convert(expr, confrac)

convert(expr, confrac, maxit)

convert(expr, confrac, 'cvgts' )

convert(expr, confrac, maxit, 'cvgts')

convert(expr, confrac, 'subdiagonal')

convert(expr, confrac, var)

convert(expr, confrac, var, ctype)

convert(expr, confrac, var, order)

convert(expr, confrac, var, order, 'subdiagonal')

Parameters

expr

-

algebraic expression

maxit

-

(optional) non-negative integer

cvgts

-

(optional) name

var

-

(optional) variable

ctype

-

(optional) one of 'monic', 'regular', or 'simple'. The default is 'monic'.

order

-

(optional) non-negative integer

Description

• 

The convert(expr, confrac) command converts a number, series, rational function, or other algebraic expression to a continued-fraction approximation.

• 

If expr is numeric then maxit (optional) is the maximum number of partial quotients to be computed, and cvgts (optional) will be assigned a list of the convergents. A list of the partial quotients is returned as the function value.

• 

If expr is a series and no additional arguments are specified, a continued-fraction approximation (to the order of the series) is computed.  It is equivalent to either an n,n or n,n1 Pade approximant (depending on the parity of the order). By specifying 'subdiagonal' as an optional third argument, the continued-fraction computed will be equivalent to a n,n or n1,n Pade approximant.

• 

If expr is a ratpoly (quotient of polynomials) in x, the calling sequence is convert(expr, confrac, x). The rational form is converted into its associated continued-fraction form as required for efficient evaluation of numerical subroutines.

• 

If expr is any other algebraic expression, the third argument specifies a variable and (optionally) the fourth argument specifies order. The series function is applied to the arguments to obtain a series and then case series applies.

• 

By default, a rational polynomial is converted to a monic continued fraction, that is, one with monic polynomials in the non-fractional part of the denominator.  If the option regular or simple is specified then a regular or a simple continued fraction is returned, respectively.

• 

Otherwise, `convert/confrac` is applied to each component of a non-algebraic structure.

• 

For information on the inverse transformation, see numtheory[cfrac].

Examples

convert2.3,confrac

2,3,3

(1)

convert2113,confrac,'convergents'

1,1,1,1,1,2

(2)

convergents

1,2,32,53,85,2113

(3)

convertⅇx,confrac,x

1+x1+x2+x3+x2+15x

(4)

convertⅇx,confrac,x,subdiagonal

11+x1+x2+x3+x215x

(5)

r:=3x3+10x2+123x32x2+12

r:=3x3+10x2+123x32x2+12

(6)

convertr,confrac,x

1+4x23+4x2

(7)

convertr,confrac,x,regular

1+123x2+12x2

(8)

convertr,confrac,x,simple

1+114x16+1x2

(9)

See Also

convert/ratpoly, numtheory[cfrac]


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