Problems with LaPlace transform when 'a' is negative in e^-at

asked 2012-04-20 00:39:03 +0100

tkillian
1 ●1 ●2 ●1

var('s t')
f = t^(-1)*exp(-t)-t^(-1)*exp((-3)*t)
f.laplace(t,s)

The above transform works as expected, however, when (-3) is changed to (3), I get the following error:

Traceback (click to the left of this block for traceback)
...
TypeError: ECL says: Maxima asks: Is  s-3  positive, negative, or zero?

The Solution that I am expecting is:

log((s - 3)/(s + 1))

I don't know how to specify if s-3 is positive, negative, or zero. Any ideas?

Thanks, Taylor Killian

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answered 2012-04-20 00:45:54 +0100

DSM

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You can use the assume command:

sage: var('s t')
(s, t)
sage: f = t^(-1)*exp(-t)-t^(-1)*exp((3)*t)
sage: f.laplace(t,s)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
[...]
TypeError: ECL says: Maxima asks: Is  s-3  positive, negative, or zero?

sage: assume(s-3>0)
sage: f = t^(-1)*exp(-t)-t^(-1)*exp((3)*t)
sage: f.laplace(t,s)
log((s - 3)/(s + 1))

This mostly works, at least for simple enough conditions.

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Comments

Emphasis on the "simple enough conditions".

kcrisman ( 2012-04-20 12:03:56 +0100 )edit

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Asked: 2012-04-20 00:39:03 +0100

Seen: 1,046 times

Last updated: Apr 20 '12

Problems with LaPlace transform when 'a' is negative in e^-at edit