As a first step to improve the code of $specint I would like to present five
changes:
1. Function DEFEXEC
If we cant't find a parameter, we apply factor to the expression. Now Maxima
finds the result for expressions like t/(x+y) --> 1/(s^2(x+y)) where x and y
are free of the integration variable.
2. Function arbpow1
I have specialized the pattern match to be sure that in the expression c*t^v the
parameter c is free of the integration variable. This condition now will fail if
we enter $specint with expression like u(t) or t^(1/2)*(a+t)^(-1) and with the
changes below we get nice and correct noun forms.
3. Function LT-SF-LOG
Because we have specialized the pattern match we add at the end of the function
as return value a noun form.
4. Function lt-arbpow
A lot of integrals fail at this point. We add as the return value a noun form.
5. Function LT-SF-LOG, Condition ONEI
This is an example how we can avoid additional phase factors. If we use %i
directly in the calculation all additional phase factors in the calculations
vanish and the results are correct. There are more places we can apply this
change to obtain easier results.
With this changes Problem 55 and Problem 157 of rtest14.mac will produce
different results. In both cases the noun form is improved and now more correct.
The numbers of correct results of the test file test_eqworld.mac is increased to
60. If Maxima can't evaluate the integral but returns a correct noun form I
declared the test as "(OK noun form)". There are even more correct results with
changes, but I had only a look at the first 30 examples.
I have added a diff and the test file test_eqworld.mac with some changes.
Dieter Kaiser
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