I have finished a first look through the examples of Laplace transforms
tabulated by EqWorld and A&S. To get correct results or a noun forms I have
suggested 12 bug fixes or extensions of the code. The test files and a diff is
attached to a bug report on SourceForge.net.
To get correct noun form in all cases I have introduced a simple method. In the
case a subroutine fails to calculate a Laplace transform a global variable is
set. The main integration routine of $SPECINT looks for this global flag and
returns if necessary a complete noun form. I had to indroduce this method
because we add up the returned symbols in the routine DISTRDEFEXEC. We can
construct integrals where this summation gives the wrong result 0.
This simple method no longer calculate the known parts of a sum. A simple
example would be:
specint(%e^(-s*t)*(t+u(t)),t);
The original code gives the result:
CASE 1: lt-arbow-failed+1/s^2
The simple method to get noun forms gives:
CASE 2: specint(%e^(-s*t)*(t+u(t)),t);
That is the complete integral, because one part of the sum fails. Perhaps the
best result would be:
CASE 3: specint(%e^(-s*t)*u(t),t)+1/s^2;
I think it is possible to program a general algorithm to get always the result
of CASE 3. To do this we have to modify the routine DISTRDEFEXEC.
Dieter Kaiser