Ticket #6393 (closed defect: fixed)

Opened 4 years ago

Last modified 4 years ago

[with patch, positive review] Jacobi sums incorrect when exactly one character is trivial

Reported by: wdj Owned by: craigcitro
Priority: major Milestone: sage-4.1.1
Component: modular forms Keywords:
Cc: Work issues:
Report Upstream: Reviewers: David Loeffler
Authors: David Joyner Merged in: sage-4.1.1.alpha0
Dependencies: Stopgaps:

Description

Example: 

sage: G=DirichletGroup(5); X=G.list(); Y=X[0]; Z=X[1] 
sage: # Y is trivial and Z is quartic
sage: sum([Y(x)*Z(1-x) for x in IntegerModRing(5)])
 -1
sage: # The value -1 above is the correct value of the Jacobi sum J(Y, Z).
sage: Y.jacobi_sum(Z);    Z.jacobi_sum(Y)
0
0
sage: #The 0 values above are incorrect values of J(Y, Z).

Attachments

trac_6393-jacobi-sum.patch Download (1.4 KB) - added by wdj 4 years ago.
applies to 4.0.2.rc3 passes sage -testall

Change History

Changed 4 years ago by wdj

applies to 4.0.2.rc3 passes sage -testall

comment:1 Changed 4 years ago by wdj

  • Owner changed from tbd to craigcitro
  • Summary changed from Jacobi sums incorrect when exactly one chacater is trivial to [with patch, needs review] Jacobi sums incorrect when exactly one character is trivial
  • Component changed from algebra to modular forms
  • Milestone set to sage-4.1

comment:2 Changed 4 years ago by davidloeffler

  • Reviewers set to David Loeffler
  • Summary changed from [with patch, needs review] Jacobi sums incorrect when exactly one character is trivial to [with patch, positive review] Jacobi sums incorrect when exactly one character is trivial
  • Authors set to David Joyner

Looks good to me, and doctests pass. I'm surprised this went so long without being spotted.

comment:3 Changed 4 years ago by davidloeffler

BTW, in the course of reviewing this I've realised that our Jacobi sum algorithm is absurdly slow, vastly slower than calculating the sums directly! I've just opened #6534 for this.

comment:4 Changed 4 years ago by davidloeffler

I'm about to upload a patch at #6534 which totally changes the way we calculate Jacobi sums, thus superseding this patch somewhat. I've made sure that it takes into account the issue you raised here.

comment:5 Changed 4 years ago by mvngu

Just to let people know, this has been merged in sage-4.1.1-alpha0. I can't close this ticket because I don't have the privilege to do so. Sorry, folks :-(

comment:6 Changed 4 years ago by mvngu

  • Status changed from new to closed
  • Resolution set to fixed
  • Merged in set to sage-4.1.1.alpha0

comment:7 Changed 4 years ago by mvngu

See #6613 for a follow up to this ticket.

Note: See TracTickets for help on using tickets.