integer shift of an expression - Maple Help

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LREtools[shift] - integer shift of an expression

LREtools[delta] - single or iterated differencing of an expression

Calling Sequence

shift(e, var)

shift(e, var, i)

delta(e, var)

delta(e, var, n)

Parameters

e

-

expression

var

-

variable name

i

-

(optional) integer

n

-

(optional) positive integer

Description

• 

shift returns the expression equivalent to subsvar=var+i,e, where i is assumed to be 1 in the two argument case.

• 

This procedure knows about various Maple constructs, like diff, where the variable must not be simply substituted.  Currently shift knows about diff, Diff, int, Int, sum, Sum, product, and Product.

• 

Additional constructs can be added by the user.  If the procedure `LREtools/shift/f` is defined then the function call LREtools[shift](f(n,x), n, 3) will invoke `LREtools/shift/f`(f(n,x), n, 3) to compute the shift.

• 

delta(e, var) is defined to be shift(e, var, 1)-e and delta(e, var, n) is defined to be delta(shift(e, var, 1)-e, var, n-1).  Thus differencing is also user-extensible by providing the extension for shift.

Examples

withLREtools:

shiftx5,x

x+15

(1)

shiftx5,x,3

x+35

(2)

shiftfx,x,2

fx2

(3)

shiftⅆⅆxfx,x

Dfx+1

(4)

δsinn,n

sinn+1sinn

(5)

δcosn,n,2

cosn+22cosn+1+cosn

(6)

δxgx,x

xgx+1xgx

(7)

See Also

diff, LREtools


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