Re: LaPlace Monsters: TI92's Laplace92 wrestles HP48's Erable 3.2
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Re: LaPlace Monsters: TI92's Laplace92 wrestles HP48's Erable 3.2
>
> 3rd Function: exp(5*t-3)+4*t^2*sin(7*t-Pi/3)+2*t^3/5
>
> HP+Erable3.2) LaPlace: 09.27 sec InvLaPlace: Using LAP took 305 sec and did
> not returned original expression form. Using LAP and EXPAND took 308 sec and
> did not returned original expression form. Using PARTIALFRAC and LAP took a
> long time and I cancelled it. (If I am ignoring a flag or something, please
> tell me)
>
Well, I have tried with ILAP alone and I get
-2*sqrt(3)*t^2*cos(7t)+2t^2*sin(7t)+exp(-3)*exp(5t)+2t^3/5
that is equal to the original expression since
4t^2*sin(7t-Pi/3)=2t^2*sin(7t)-2*sqrt(3)*t^2*cos(7t).
It tooks a very long time. Looking at the code, I discovered that
I did not test for linearity for invert laplace transform, we have
ILAP(f(x)+g(x))=ILAP(f(x)+g(x))
Instead of doing so, ILAP factors f(x)+g(x) globally and does partial
fraction expansion after. On your example, there are square roots *and*
a multiple root (0 of order 4 in fact). Hence factorization requires
taking 4 times the gcd of the denominator, a polynomial of order 11,
and since square roots are involved the fast heuristic gcd algorithm
can not be used (the evry slow euclidean sub-resultant algorithm is used
instead).
Conclusion: ILAP is not bugged (at least on this example) and it will
be very easy to improve the timings on your example. Expect a timing
of about 9 seconds (that's the time you need using OBJ-> and ILAP on
each term).
Bernard Parisse
References: