convert to continued-fraction form
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')
(optional) non-negative integer
(optional) one of 'monic', 'regular', or 'simple'. The default is 'monic'.
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,n−1 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 n−1,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 NumberTheory[ContinuedFraction].
r ≔ 3⁢x3+10⁢x2+123⁢x3−2⁢x2+12
The option subdiagonal can be used together with the optional argument var as of Maple 16.
The subdiagonal option was updated in Maple 16.
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