Enhanced Laplace transforms and desolve for Maxima

Mark,

I think your Laplace transform work is great.  So at this 
point I'd like to revive an old discussion about the names, 
"laplace" and "ilt".  They are grossly mismatched.  Why not 
laplace and inverse_laplace?

			Kostas

On 01/25/11 11:51 AM, Mark H Weaver wrote:
> Hugo Coolens<coolens at kahosl.be>  writes:
>> Will the new code also deal with this:
>>   ilt(exp(-a*s)/s,s,t);
>
> I didn't modify ilt to do this, but my new pwilt does it:
>
> (%i2) load(pwilt)$
> (%i3) pwilt(exp(-a*s)/s,s,t);
> (%o3) hstep(t-a)
> (%i4) pwilt(%e^-s*(s*%e^s-s^2-2*s-2)/s^3, s,t), ratsimp;
> (%o4) t-t^2*hstep(t-1)
>
> It is also designed to handle periodic functions
> (though currently it fails to detect this in some cases):
>
> (%i5) assume(a>0);
> (%o5) [a>  0]
> (%i6) pwilt(1/(s*(1-%e^-(2*a*s)))-%e^-(a*s)/(s*(1-%e^-(2*a*s))), s,t);
> (%o6) 'sum(hstep(t-2*%k*a)-hstep(t-2*%k*a-a),%k,0,inf)
>
> pwilt stands for "piecewise inverse laplace transform".  I attached the
> code at the beginning of this thread.  In the other direction, my
> changes to laplac.lisp support taking laplace transforms of piecewise
> functions defined in terms of hstep or unit_step.
>
> Note that this is still a work in progress.
>
>      Best,
>       Mark
>
>
>> This would be great for (electronic) engineering students who want to
>> make the shift to Maxima
>>
>>
>> best regards,
>> hugo
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