On 02/18/2015 10:57 AM, Waldek Hebisch wrote:
Hi all,
Is there something else which I could do now - maybe related to the
project itself? I've been looking for some small functions which could
be useful for the factoring routine but aren't yet implemented without
much success. So, I've limited myself to reading the thesis. Any other
code sample ideas that I could work on?
Maybe routine for point 5.3.2 (page 93) in the thesis? That
is given nontrivial solution to
fr + lf = 0
find a right factor of f.
Um, I have a doubt here. I feel very silly right now, but I'm not able
to finish this routine.
The problem I'm having is this:
I'm able to find the basis of formal solutions at a regular point of f,
but after that the thesis mentions computing the matrix of map r in this
basis. I think I'm not quite sure about what this means.
For concreteness, take the example mentioned in the thesis
f=∂4+6x∂3+2(x2-1)x4∂2-2(3x2-1)x5∂+1x8f = \partial^4 +
\frac{6}{x}\partial^3 + \frac{2(x^2-1)}{x^4}\partial^2 -
\frac{2(3x^2-1)}{x^5}\partial + \frac{1}{x^8}
r=−x5∂3-x4∂2+2x3∂+x∂r =
\minusx^5\partial^3-x^4\partial^2+2x^3\partial+x\partial
Using these, I'm able to find the basis of formal solutions at x=1 as
1 4 1 3 1 2 1 23 1 4 2 3 2 1 5 1
2 1
[- -- x + - x - - x + - x + --, - x - - x + x + - x - -, - x
- x + -,
24 6 4 6 24 6 3 3 6
2 2
1 4 7 3 2 3 5
- - x + - x - 2x + - x - --]
4 6 2 12
but am not able to figure out what should I do to make operator r act on
this basis.
Just applying it to every element in the list and taking the
coefficients doesn't work as the matrix mentioned in the thesis is 4x4.
Could you please help me? What should I be do to the basis using r so as
to get the 4x4 matrix?
Thanks,
Abhinav.
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