Opened 7 years ago

Last modified 7 years ago

#18342 new defect

numerical integral is wrong in pari master

Reported by: vdelecroix Owned by:
Priority: major Milestone: sage-6.7
Component: packages: standard Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: Reported upstream. Developers deny it's a bug. Work issues:
Branch: Commit:
Dependencies: #18340 Stopgaps:

Status badges

Description (last modified by jdemeyer)

Within pari master, the gp numerical integral gives 

? intnum(x=0,13,sin(x)+sin(x^2) + x)
%1 = 84.181815392229652966739838357234264357

but should be 85.1885681951527 (as it was with previous pari release). Increasing the precision, it gets better but the relative error is incredibly huge 

? \p 30
   realprecision = 38 significant digits (30 digits displayed)
? intnum(x=0,13,sin(x)+sin(x^2) + x)
%2 = 84.1818153922296529667398383572
? \p 40
   realprecision = 57 significant digits (40 digits displayed)
? intnum(x=0,13,sin(x)+sin(x^2) + x)
%3 = 85.18860335415782535357810701961378283432
? \p 50
? intnum(x=0,13,sin(x)+sin(x^2) + x)
%4 = 85.188603354157825353578107019613782834315433312524

Tested on PARI master at commit 17795-d04cdd3 with an amd64.

See also #18340

Upstream ticket: ​http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1694

Change History (10)

comment:1 Changed 7 years ago by vdelecroix

  • Description modified (diff)

comment:2 Changed 7 years ago by jdemeyer

  • Description modified (diff)
  • Report Upstream changed from Not yet reported upstream; Will do shortly. to Reported upstream. No feedback yet.

comment:3 Changed 7 years ago by jdemeyer

  • Report Upstream changed from Reported upstream. No feedback yet. to Reported upstream. Developers acknowledge bug.

comment:4 Changed 7 years ago by jdemeyer

  • Report Upstream changed from Reported upstream. Developers acknowledge bug. to Reported upstream. Developers deny it's a bug.

Upstream has answered essentially that we need to live with it. I think we should close this as wontfix.

comment:5 follow-up: Changed 7 years ago by vdelecroix

I just read the answer from Karim. We should document that this function is not adaptative and is likely to lead to wrong results with oscillating functions (though sin(x^2) at x=13 is not terribly oscillating compared to sin(1/x) at 0).

Vincent

comment:6 Changed 7 years ago by leif

  • Dependencies set to #18340

comment:7 in reply to: ↑ 5 ; follow-up: Changed 7 years ago by jdemeyer

Replying to vdelecroix:

We should document

document where? intnum isn't available in the Sage interface for PARI (because it has a closure argument, see #18052 and #18038).

comment:8 in reply to: ↑ 7 ; follow-up: Changed 7 years ago by vdelecroix

Replying to jdemeyer:

Replying to vdelecroix:

We should document

document where? intnum isn't available in the Sage interface for PARI (because it has a closure argument, see #18052 and #18038).

In the pari interface 

sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x)")
85.1885681951527

comment:9 Changed 7 years ago by leif

Yep, e.g. 

sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x)")
84.1818153922297
sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x,1)")
85.1885681951527
sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x,2)")
85.1885681951527

with an explanation in a comment.

comment:10 in reply to: ↑ 8 Changed 7 years ago by jdemeyer

Replying to vdelecroix:

Replying to jdemeyer:

Replying to vdelecroix:

We should document

document where? intnum isn't available in the Sage interface for PARI (because it has a closure argument, see #18052 and #18038).

In the pari interface

The module docstring of pari_instance.pyx is not the place to document a specific function.

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