#16653: immediately get all integral/ODE solutions instead of asking for
assumption
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-6.3
Component: symbolics | Resolution:
Keywords: assumption, desolve, | Merged in:
integrate, maxima | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by charpent):
So, we'd get something a bit like what Maxima's to_poly_solve returns
(that Sage somehow is able to digest in certain cases) or Mathematica's
Integrate returns (indigestible by sage). So, we'd divde the problem in
two :
1) parse the "assumptions" part of the answer, in order to keep it for
further computations.
2) ensuring somehow that the "assumption" list/tree is finite. I have seen
Maxima start a list of questions about a parameter (say zeta) known as
positive, asking if zeta-1 was positive, zeta-2 was positive, zeta-3 was
positive, ... until C-c C-c ("Shut the fuck up and stop '''that''' !" in
interactive-Maxima).
The first part probably entails a new class of symbolic expressions, which
is doable (i has been done by the author of to_poly_solve and by
Mathematica's developpers.
The second, I do not know. A '''human''' can catch the repetition pattern,
may examine the shape of the proposed solution and possibly set-up a
secondary computation in order to prove that the recurrence will solve
,say, for some majorant of zeta, which allows to shortcut the loop (and
implicitely uses some hypothetical declaration like "zeta is finite").
There '''are''' algorithms able to detect a circular (i. e. infinite)
list/tree/etc... (i.e. anything represented by dotted pairs, a. k. a. Lisp
lists) : ask your friendly local graph theorist or Lisp guru (the species
is not quite extinct yet...). The problem is to know when to call them.
And there might be tygers...
--
Ticket URL: <http://trac.sagemath.org/ticket/16653#comment:2>
Sage <http://www.sagemath.org>
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