[HN Gopher] Does there exist a complete implementation of the Ri...
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Does there exist a complete implementation of the Risch algorithm?
Author : thechao
Score : 67 points
Date : 2023-08-14 17:43 UTC (5 hours ago)
(HTM) web link (mathoverflow.net)
(TXT) w3m dump (mathoverflow.net)
| Havoc wrote:
| No idea, but I am impressed by the clarity and preciseness of the
| question
| jjtheblunt wrote:
| I'd check Mathematica or Macaulay2...but how would you verify an
| implementation is complete?
| jychang wrote:
| It's written in the mathoverflow question, did you read it?
|
| > I have access to Maple 2018, and it doesn't seem to have a
| complete implementation either. A useful test case is the
| following integral, taken from the (apparently unpublished)
| paper Trager's algorithm for the integration of algebraic
| functions revisited by Daniel Schultz: [?]29x2+18x-3x6+4x5+6x4-
| 12x3+33x2-16x-----------------------------[?]dx Schultz
| explicitly provides an elementary antiderivative in his paper,
| but Maple 2018 returns the integral unevaluated.
| cvoss wrote:
| The question at hand is "how do you verify that an
| implementation is complete?", not "what is one test case
| whose failure would demonstrate that an implementation is
| incomplete?"
| jjtheblunt wrote:
| That's not what i asked.
|
| For example, you could have an implementation that handles
| the example you cited, but fails at others you did not
| mention. So would your comment claim "complete" for handling
| what you mentioned, when it is not?
| [deleted]
| irrep wrote:
| Mathematica does not have a complete implementation of the
| Risch algorithm. It actually cannot do the integral in the
| mathoverflow question.
|
| Macaulay2 has a focus on commutative algebra and algebraic
| geometry and doesn't have an implementation of the Risch
| algorithm either.
| 1letterunixname wrote:
| I wonder how Giac measures up as it's reportedly more general
| than HP48's Erable.
|
| https://en.wikipedia.org/wiki/Xcas#Giac
|
| PS: The HP 48 could also be used a very long distance remote to
| turn on and off all of the TVs in a lecture hall simultaneously.
| :)
| irrep wrote:
| Manuel Bronstein wrote a book [1] about symbolic integration, but
| unfortunately it only covers the transcendental part. There is
| also a shorter "tutorial" from some workshop [2].
|
| [1] Manuel Bronstein: Symbolic Integration I,
| https://doi.org/10.1007/b138171
|
| [2] https://www-
| sop.inria.fr/cafe/Manuel.Bronstein/publications/...
| slavapestov wrote:
| Sadly he passed away before completing Part 2.
| https://lists.gnu.org/archive/html/axiom-developer/2005-06/m...
| downvotetruth wrote:
| https://news.ycombinator.com/item?id=589004
|
| https://news.ycombinator.com/item?id=19291578
|
| Not sure of a connection between the failure of the high school
| axiom set / nonfiniteness of axioms and Rubi/rule based
| integration feasiblility or validity of Schanuel's conjecture.
| tehsauce wrote:
| Does this count?
|
| https://github.com/sympy/sympy/blob/master/sympy/integrals/r...
| owalt wrote:
| This does not - according to what I can see from the code and
| comments - implement the case of algebraic extensions. As
| someone only really familiar with the implementation of the
| transcendental case[1], my understanding is that the algebraic
| case is where the major difficulty lies.
|
| [1]: Manuel Bronstein, Symbolic Integration I. Online:
| https://archive.org/details/springer_10.1007-978-3-662-03386...
| irrep wrote:
| Unfortunately this is not complete, because it does not work
| with integrals that require algebraic extensions (they are more
| complicated than transcendental extensions).
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