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Topic: An independent integration test suite
Replies: 128   Last Post: Dec 8, 2013 3:21 PM

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Waldek Hebisch

Posts: 227
Registered: 12/8/04
Re: where the air gets thin for Axiom & Co.
Posted: Mar 21, 2013 3:26 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

clicliclic@freenet.de wrote:
>
> I bumped into this and am surprised by 70% failures (and not just
> timeouts) of the Axiom integrator on algebraic integrals possessing
> logarithmic antiderivatives that involve the single simple radical
> SQRT(x^3+1) or SQRT(x^4+1):
>
> <http://www.risc.jku.at/publications/download/risc_3427/Ka01.pdf>
>
> This must be where the missing computation of the "splitting field of
> the Trager resultant" comes in.


If one wants to describe the reason in one sentence, then yes.
However, the actual Axiom limitation is more severe: it can
only handle integrals where Trager resultant has at most one
nonlinear factor. Additionally, Axiom can handle directly
only integrands with no poles at infinity. Kauers examples
have pole at infinity, which Axiom handles by change of
variables. After change of variables Trager resultant
changes and has two nonlinear factors and Axiom gives up.

What is surprising is 12% sucess rate: Kauers examples of
given series are variation of a single example -- only numerical
coefficients differ but structure remains the same unless
there is degeneracy. Apparently distribution of coefficients
(which Kauers did not gave) is such that degeneracies are
relatively frequent.

Axiom restriction on single nonlinear factor of Trager
resultant is quite severe. Namely, given logand with
no zero or pole at infinity it will lead to at least
_two_ residues (one corresponding to zero another one
correspondig to a pole). So typically we will get a
pair of nonlinear factors.

Main difficulty of Kauers examples were already observerd
by Davenport. Namely, given derivative of

r1*log(f1) + r2*log(f2)

where r1 and r2 are rationals Trager method will consider
both terms together. If r1 and r2 are integer this
leads to

log(f1^r2*f2^r1)

f1^r2*f2^r1 may be quite large even if f1 and f2 are small.

FYI, FriCAS contans code which in many cases avoids both
problems. Namely, FriCAS tries to split integral and
integrate parts separately. This handles the sqrt(1 + x^4)
cases. Currently in sqrt(1 + x^3) case FriCAS is unable
to find working split and gives up.

--
Waldek Hebisch
hebisch@math.uni.wroc.pl


Date Subject Author
2/24/13
Read An independent integration test suite
clicliclic@freenet.de
3/19/13
Read where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/21/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/22/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/26/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/26/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Nasser Abbasi
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/21/13
Read Re: An independent integration test suite
Waldek Hebisch
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/22/13
Read Re: An independent integration test suite
Axel Vogt
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/23/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
Richard Fateman
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Richard Fateman
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Axel Vogt
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/25/13
Read Re: An independent integration test suite
Peter Pein
4/25/13
Read Re: An independent integration test suite
Nasser Abbasi
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Richard Fateman
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Richard Fateman
6/30/13
Read Re: An independent integration test suite
clicliclic@freenet.de
6/30/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite / Chap 3
clicliclic@freenet.de
7/1/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite
Waldek Hebisch
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/5/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/5/13
Read Re: An independent integration test suite
Nasser Abbasi
7/9/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/10/13
Read Re: An independent integration test suite
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite/ Klerer?
Richard Fateman
7/10/13
Read Re: An independent integration test suite/ Klerer?
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite
clicliclic@freenet.de
8/6/13
Read Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/24/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/30/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/26/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/29/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
10/1/13
Read The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
10/11/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/22/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Richard Fateman
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Waldek Hebisch
4/21/13
Read Re: An independent integration test suite
G. A. Edgar
12/8/13
Read Re: An independent integration test suite
clicliclic@freenet.de
10/5/13
Read Re: An independent integration test suite
Albert D. Rich
10/6/13
Read Re: An independent integration test suite
clicliclic@freenet.de

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