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numapprox

  

chebsort

  

sort the terms in a Chebyshev series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

chebsort(e)

Parameters

e

-

expression assumed to be a Chebyshev series

Description

• 

The input expression e is assumed to be a polynomial expressed in terms of a Chebyshev basis T0,x,....

• 

First the expression e is collected in 'T'. Then the terms in the collected polynomial expression are sorted in ``Chebyshev order'';  i.e. the Tk,x basis polynomials are ordered in ascending order with respect to the first argument.

• 

If some basis polynomials Tk,x have non-numeric first argument then ordering will be attempted using the ``is'' predicate. If that is not successful then ordering is performed only with respect to numeric first arguments (other terms are left as trailing terms).

• 

Note that chebsort is a destructive operation because it invokes the Maple sort function (see sort);  i.e. the input expression is sorted ``in-place''.

• 

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

Examples

withnumapprox:

Digits3:

achebyshevsinx,x:

bchebyshevcosx,x:

ca+b

c:=0.880T1,x0.0391T3,x+0.000500T5,x+0.765T0,x0.230T2,x+0.00495T4,x

(1)

chebsortc

0.765T0,x+0.880T1,x0.230T2,x0.0391T3,x+0.00495T4,x+0.000500T5,x

(2)

assume5<j&comma;j<k

d1.2y&plus;cjTj&comma;x&plus;a&plus;ckTk&comma;x

d:=1.2y&plus;cjTj~&comma;x&plus;0.880T1&comma;x0.0391T3&comma;x&plus;0.000500T5&comma;x&plus;ckTk~&comma;x

(3)

chebsortd

0.880T1&comma;x0.0391T3&comma;x&plus;0.000500T5&comma;x&plus;cjTj~&comma;x&plus;ckTk~&comma;x&plus;1.2y

(4)

See Also

collect

is

numapprox[chebyshev]

orthopoly[T]

sort

 


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