Appendix A: Options for the Transform Rule Bases

All 10 transform rule bases support the <#725#>Dialogue<#725#> and <#726#>TransformLookup<#726#> options. The <#727#>Dialogue<#727#> option indicates how much information the transform rule bases give to the user: <#728#>False<#728#> means to print no information, <#729#>True<#729#> means to tell about strategies when used and about parts of the expression that could not be transformed (if any), and <#730#>All<#730#> means to display each step of the transformation process. (This <#731#>Dialogue<#731#> option is also supported by the difference and differential equation solvers <#732#>ZSolve<#732#> and <#733#>LSolve<#733#>.) The <#734#>TransformLookup<#734#> option allows users to specify their own transform pairs. This means that users can transform general (undefined) signals: e.g., letting #math261#y(t)↔Y(s): 

verbatim197#
(The region of convergence is significant because #math262##tex2html_wrap_inline3392#{y''(t)}↔s2 Y(s)<#1#> for <#1#> - ∞ ;SPMlt; ℜe(s) ;SPMlt; ∞ but #math263##tex2html_wrap_inline3394#{y''(t)u-1(t)}↔s2 Y(s) - s y(0+) - y'(0+)<#1#> for <#1#>0 ;SPMlt; ℜe(s) ;SPMlt; ∞.) The following table lists and explains these and other options.


<#3440#>Table<#3440#>: <#3441#><#764#>Meaning of the Options for the Transform Rule Bases<#764#><#3441#>
<#1028#>
Option Possible Values Meaning
Apart Rational, All Partial fraction decomposition only
applies to polynomials with real or
rational coefficients
Definition True, False Use the transform definition if all
else fails to find the transform
(does not apply to the inverse z
or Laplace transforms)
Dialogue False, True, All Ascending levels of justification
Simplify True, False Apply SPSimplify to result
Terms False or integer Number of terms in series expansion
(False means none)
TransformLookup list of rules Users can specify their own transform
pairs, like 106 or
107
<#1028#>



<#3536#>Table<#3536#>: <#3537#>Options for the Transform Rule Bases. <#775#>Definition<#775#> always defaults to <#776#>False<#776#> and <#777#>TransformLookup<#777#> always defaults to an empty list.<#3537#>
<#1030#>
Transform Option Default Value
CTFTransform Dialogue False
Simplify True
DFTransform Dialogue False
InvDFTransform Dialogue False
Terms False
DTFTransform Dialogue False
LaPlace Dialogue True
Simplify True
InvCTFTransform Apart Rational
Dialogue False
Simplify True
Terms False
InvDTFTransform Dialogue False
Terms False
InvLaPlace Apart Rational
Dialogue True
Simplify True
Terms 10
InvZTransform Dialogue True
Terms 10
ZTransform Dialogue True
<#1030#>