Hi all,
I wanted to know which papers are best to implement Kovacic's Algorithm. I have gone through the following papers, but all of them seem to be quite old.
https://www.sciencedirect.com/science/article/pii/S0747717186800104 https://cs.uwaterloo.ca/research/tr/1984/CS-84-35.pdf https://www.math.fsu.edu/~hoeij/papers/issac05/f99HoeijWeil.pdf
Please suggest some recent papers if there are any. Also, what papers are implemented in CAS' like Maple, Mathematica?
Regards
Naveen
Hi all,
I wanted to know which papers are best to implement Kovacic's Algorithm. I have gone through the following papers, but all of them seem to be quite old.
https://www.sciencedirect.com/science/article/pii/S0747717186800104 https://cs.uwaterloo.ca/research/tr/1984/CS-84-35.pdf https://www.math.fsu.edu/~hoeij/papers/issac05/f99HoeijWeil.pdf
Please suggest some recent papers if there are any. Also, what papers are implemented in CAS' like Maple, Mathematica?
Concerning implementation, you can look at implementation is FriCAS,
in particular:
https://github.com/fricas/fricas/blob/master/src/algebra/kovacic.spad
which implements case 2. Case 1 is handled by general approach (factorization). Currently case 3 remains unimplemented
(I have code which theoretically solves case 3, but it is
so slow that I was not able to test it). Commercal competiton
probably have better implementation, but main improvements
are not in core algorithm, but in supporting parts, in
particular factorizer for differential operators and
solver for associated equations.
BTW: I do not know of system that fully implements case 3,
namely in case 3 "explicit" result is very large and
Hoeij&Weil suggest using shorthand notation to avoid
dealing with problematic expressions.
--
Waldek Hebisch
Currently case 3 remains unimplemented
(I have code which theoretically solves case 3, but it is
so slow that I was not able to test it).
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