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#>
|