Opened 3 years ago

Closed 8 months ago

#11783 closed defect (fixed)

bug in DirichletGroup and/or DirichletCharacter when the modulus is 1

Reported by: was Owned by: was
Priority: major Milestone: sage-6.2
Component: number theory Keywords:
Cc: Merged in:
Authors: Alex Ghitza Reviewers: Peter Bruin
Report Upstream: N/A Work issues:
Branch: 0693286 (Commits) Commit: 06932866de2e5308e2bdf58d137e6e9911f29460
Dependencies: Stopgaps:

Description

Observe that the value of chi(1) below depends on whether chi.values() is called first. Thus there is certainly a bug. I think we should always have chi(1)=1, since gcd(1,1)=1; this is also consistent with the rule that if psi is trivial but not primitive, then psi(n)=1 for all n coprime to the modulus of psi.

See this thread:
http://groups.google.com/group/sage-devel/browse_thread/thread/fa94a97612c7225b

wstein@ubuntu:~$ sage
----------------------------------------------------------------------
| Sage Version 4.7.2.alpha2, Release Date: 2011-08-18                |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------                                               
**********************************************************************                                               
*                                                                    *                                               
* Warning: this is a prerelease version, and it may be unstable.     *
*                                                                    *
**********************************************************************
sage: chi = DirichletGroup(1)[0]
sage: chi(1)
1
sage: chi.values()
[1]
sage: 
Exiting Sage (CPU time 0m0.09s, Wall time 0m18.02s).
wstein@ubuntu:~$ sage
----------------------------------------------------------------------
| Sage Version 4.7.2.alpha2, Release Date: 2011-08-18                |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
**********************************************************************
*                                                                    *
* Warning: this is a prerelease version, and it may be unstable.     *
*                                                                    *
**********************************************************************
sage: chi = DirichletGroup(1)[0]
sage: chi.values()
[0]
sage: chi(1)
0

Change History (7)

comment:1 Changed 16 months ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:2 Changed 11 months ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:3 Changed 8 months ago by AlexGhitza

This was fixed in #14368. In sage-6.1.1 we have:

sage: chi = DirichletGroup(1)[0]
sage: chi.values()
[1]
sage: chi(1)
1

I am adding a bit to the existing doctest to illustrate this.

comment:4 Changed 8 months ago by AlexGhitza

  • Branch set to u/AlexGhitza/ticket/11783
  • Modified changed from 04/24/14 01:22:09 to 04/24/14 01:22:09

comment:5 Changed 8 months ago by AlexGhitza

  • Authors set to Alex Ghitza
  • Commit set to 06932866de2e5308e2bdf58d137e6e9911f29460
  • Status changed from new to needs_review

New commits:

0693286doctest to verify fix of issue with DirichletCharacter of modulus 1

comment:6 Changed 8 months ago by pbruin

  • Reviewers set to Peter Bruin
  • Status changed from needs_review to positive_review

comment:7 Changed 8 months ago by vbraun

  • Branch changed from u/AlexGhitza/ticket/11783 to 06932866de2e5308e2bdf58d137e6e9911f29460
  • Resolution set to fixed
  • Status changed from positive_review to closed
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