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LREtools

  

shift

  

integer shift of an expression

  

delta

  

single or iterated differencing of an expression

 

Calling Sequence

Parameters

Description

Examples

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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