Billinghurst, David (RTATECH) wrote:
>> From: Richard Fateman>
>> I just had occasion to try hgfred. There are errors in
>> simplification in this program that allow it to generate
>> subexpressions like (1- -x) or even (1 - -36). Someone is producing
>> expressions with incorrect ((mtimes simp)..) headers.
>> Unfortunately I didn't catch the examples before my system
>> crashed. But there are other probs.
>>
>> as an example, consider
>> i3(m,k,a,x):=(x^(1 + m)*(a^2 + x^2)^k*hgfred([(1 + m)/2, -k],
>> [1 + (1 + m)/2], -(x^2/a^2))/((1 + m)*(1 + x^2/a^2)^k));
>>
>> i3(m,k,a,x)
>> should, I think, be the integral of x^m*(x^2+a^2)^k.
>>
>> The following example (and many others) give odd messages
>> like SIMP2F1-WILL-CONTINUE-IN
>>
>> i3(2,3/2,a,x)
>>
>> i3(0,1,a,x) [also says FAIL-1-IN-C-1-CASE]
>> i3(1,1/2,a,x) [gives "non-variable 2nd argument to diff, -x^2/a^2]
>>
>> also some of the answers come out in terms of jacobi_p
>> functions, but diff does not know about them.
>>
>
> Coincidentally I was looking through the code in hypgeo.lisp as I
> want to document the special functions defined and used by hgfred
> and specint there. I also downloaded a copy of Yannis Avgoustis'
> thesis from http://dspace.mit.edu/handle/1721.1/16269
>
>
After skimming over the thesis, I see that somethings are broken in
maxima compared to the thesis.
For example, on page 66, we have 2F1[3/4, 5/4; 1/2; z^2]. Maxima says
this is 1/2*((z+1)^(-3/2)+(1-z)^(-3/2)), which is different from the
expected answer of 1/6*(1+z)^(-3/2)+5/6*(1-z)^(-3/2).
On page 84, we have 2F1(a+5/6, a+7/3; 2*a+23/3; 4*z*(1-z)). Maxima
gives an error about 2nd arg to diff is a non-variable. (I probably
introduced that bug). If we repalce 4*z*(1-z) with z, maxima now
returns something long expression with false in it. That's clearly wrong.
The thesis also describes various quadratic and cubic transformations.
I don't think hgfred does any of those, except in specific cases a
quadratic transformation is done.
Anyway, having this document will certainly help to improve what we have
now.
Ray