On Mon, Oct 20, 2008 at 12:38:56PM +0100, John Cremona wrote:
> 
> John Voight and I are having trouble with the patch I attached to
> #4249 (see below).  On my machines I get a doctest failure, while on
> his he does not.  Please could someone else try?  the patch should
> apply equally to 3.1.3 or 3.1.4.

I get this doctest failure too on 3.1.3rc0 on an amd64 machine. I ran
the failing example with verbose=2 pre-patch and post-patch, and get the
attached outputs, which are quite different in areas. Maybe this gives
a clue somehow?

-Willem Jan

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sage: F.<t> = NumberField(x^2-5)
sage: ls = enumerate_totallyreal_fields_rel(F, 2, 10^4,verbose=2)
0 : 0 -1/2*t + 1/2 1 
  bl, br: 8.0 27.0
  found copy!
  am2s: [-2*t - 4, -3/2*t - 9/2, -3/2*t - 7/2, -t - 5, -t - 4, -t - 3, -t - 2, 
-1/2*t - 11/2, -1/2*t - 9/2, -1/2*t - 7/2, -1/2*t - 5/2, -1/2*t - 3/2]
  betak: [[-1.82709091529, -0.809016994375, 0.209056926535], [-1.33826121272, 
0.309016994375, 1.95629520147]]
==> [-1/2*t - 3/2, -1/2*t + 1/2, 1] has discriminant 1125 and is new!
==> [-1/2*t - 5/2, -1/2*t + 1/2, 1] is not absolutely irreducible
==> [-1/2*t - 7/2, -1/2*t + 1/2, 1] has discriminant 5725 and is new!
==> [-1/2*t - 9/2, -1/2*t + 1/2, 1] has discriminant 9225 and is new!
==> [-1/2*t - 11/2, -1/2*t + 1/2, 1] has discriminant 13525 > B
==> [-t - 2, -1/2*t + 1/2, 1] has discriminant 725 and is new!
==> [-t - 3, -1/2*t + 1/2, 1] is not squarefree
==> [-t - 4, -1/2*t + 1/2, 1] has discriminant 6125 and is new!
==> [-t - 5, -1/2*t + 1/2, 1] has discriminant 10025 > B
==> [-3/2*t - 7/2, -1/2*t + 1/2, 1] has discriminant 2225 and is new!
==> [-3/2*t - 9/2, -1/2*t + 1/2, 1] has discriminant 5725 but is not new
==> [-2*t - 4, -1/2*t + 1/2, 1] is not absolutely irreducible
  finished
0 : -2*t - 4 -1/2*t - 1/2 1 
  bl, br: 8.0 27.0
  found copy!
  am2s: [-3/2*t - 9/2, -3/2*t - 7/2, -t - 5, -t - 4, -t - 3, -1/2*t - 11/2, 
-1/2*t - 9/2, -1/2*t - 7/2, -1/2*t - 5/2, -1/2*t - 3/2, -5, -4, -3, -2]
  betak: [[-1.75659825386, -0.309016994375, 1.13856426511], [-0.820249250653, 
0.809016994375, 2.4382832394]]
==> [-2, -1/2*t - 1/2, 1] has discriminant 2225 but is not new
==> [-3, -1/2*t - 1/2, 1] has discriminant 4525 and is new!
==> [-4, -1/2*t - 1/2, 1] has discriminant 7625 and is new!
==> [-5, -1/2*t - 1/2, 1] has discriminant 11525 > B
==> [-1/2*t - 3/2, -1/2*t - 1/2, 1] is not squarefree
==> [-1/2*t - 5/2, -1/2*t - 1/2, 1] has discriminant 2525 and is new!
==> [-1/2*t - 7/2, -1/2*t - 1/2, 1] has discriminant 5225 and is new!
==> [-1/2*t - 9/2, -1/2*t - 1/2, 1] has discriminant 8725 and is new!
==> [-1/2*t - 11/2, -1/2*t - 1/2, 1] has discriminant 13025 > B
==> [-t - 3, -1/2*t - 1/2, 1] is not absolutely irreducible
==> [-t - 4, -1/2*t - 1/2, 1] has discriminant 5125 and is new!
==> [-t - 5, -1/2*t - 1/2, 1] is not squarefree
==> [-3/2*t - 7/2, -1/2*t - 1/2, 1] has discriminant 725 but is not new
==> [-3/2*t - 9/2, -1/2*t - 1/2, 1] has discriminant 4225 and is new!
  finished
0 : -3/2*t - 9/2 -1 1 
  bl, br: 8.0 26.0
  found copy!
  am2s: [-3/2*t - 9/2, -3/2*t - 7/2, -t - 5, -t - 4, -t - 3, -t - 2, -1/2*t - 
11/2, -1/2*t - 9/2, -1/2*t - 7/2, -1/2*t - 5/2, -1/2*t - 3/2, -6, -5, -4, -3, 
-2]
  betak: [[-1.0, 0.5, 2.0], [-1.0, 0.5, 2.0]]
==> [-2, -1, 1] is not absolutely irreducible
==> [-3, -1, 1] has discriminant 4225 but is not new
==> [-4, -1, 1] has discriminant 7225 and is new!
==> [-5, -1, 1] has discriminant 11025 > B
==> [-6, -1, 1] is not absolutely irreducible
==> [-1/2*t - 3/2, -1, 1] has discriminant 725 but is not new
==> [-1/2*t - 5/2, -1, 1] has discriminant 2525 but is not new
==> [-1/2*t - 7/2, -1, 1] has discriminant 5125 but is not new
==> [-1/2*t - 9/2, -1, 1] has discriminant 8525 and is new!
==> [-1/2*t - 11/2, -1, 1] has discriminant 12725 > B
==> [-t - 2, -1, 1] is not absolutely irreducible
==> [-t - 3, -1, 1] has discriminant 2225 but is not new
==> [-t - 4, -1, 1] has discriminant 5225 but is not new
==> [-t - 5, -1, 1] is not absolutely irreducible
==> [-3/2*t - 7/2, -1, 1] has discriminant 1125 but is not new
==> [-3/2*t - 9/2, -1, 1] has discriminant 4525 but is not new
  finished
0 : -3/2*t - 9/2 0 1 
  bl, br: 8.0 25.0
  found copy!
  am2s: [-2*t - 5, -3/2*t - 11/2, -3/2*t - 9/2, -3/2*t - 7/2, -t - 6, -t - 5, 
-t - 4, -t - 3, -1/2*t - 11/2, -1/2*t - 9/2, -1/2*t - 7/2, -1/2*t - 5/2, -6, 
-5, -4, -3, -2]
  betak: [[-1.41421356237, -0.0, 1.41421356237], [-1.41421356237, -0.0, 
1.41421356237]]
==> [-2, 0, 1] has discriminant 1600 and is new!
==> [-3, 0, 1] has discriminant 3600 and is new!
==> [-4, 0, 1] is not absolutely irreducible
==> [-5, 0, 1] is not squarefree
==> [-6, 0, 1] has discriminant 14400 > B
==> [-1/2*t - 5/2, 0, 1] has discriminant 2000 and is new!
==> [-1/2*t - 7/2, 0, 1] has discriminant 4400 and is new!
==> [-1/2*t - 9/2, 0, 1] has discriminant 7600 and is new!
==> [-1/2*t - 11/2, 0, 1] has discriminant 725 but is not new
==> [-t - 3, 0, 1] has discriminant 1600 but is not new
==> [-t - 4, 0, 1] has discriminant 4400 but is not new
==> [-t - 5, 0, 1] has discriminant 8000 and is new!
==> [-t - 6, 0, 1] has discriminant 12400 > B
==> [-3/2*t - 7/2, 0, 1] is not absolutely irreducible
==> [-3/2*t - 9/2, 0, 1] has discriminant 3600 but is not new
==> [-3/2*t - 11/2, 0, 1] has discriminant 7600 but is not new
==> [-2*t - 5, 0, 1] has discriminant 2000 but is not new
  finished
================================================================================
Polynomials tested: 118
Irreducible polynomials: 55
Polynomials with nfdisc <= B: 46
[725, x^4 - x^3 - 3*x^2 + x + 1, xF^2 + (-1/2*t - 7/2)*xF + 1]
[1125, x^4 - x^3 - 4*x^2 + 4*x + 1, xF^2 + (-1/2*t - 7/2)*xF + 1/2*t + 3/2]
[1600, x^4 - 6*x^2 + 4, xF^2 - 2]
[2000, x^4 - 5*x^2 + 5, xF^2 - 1/2*t - 5/2]
[2225, x^4 - x^3 - 5*x^2 + 2*x + 4, xF^2 + (-1/2*t + 1/2)*xF - 3/2*t - 7/2]
[2525, x^4 - 2*x^3 - 4*x^2 + 5*x + 5, xF^2 + (-1/2*t - 1/2)*xF - 1/2*t - 5/2]
[3600, x^4 - 2*x^3 - 7*x^2 + 8*x + 1, xF^2 - 3]
[4225, x^4 - 9*x^2 + 4, xF^2 + (-1/2*t - 1/2)*xF - 3/2*t - 9/2]
[4400, x^4 - 7*x^2 + 11, xF^2 - 1/2*t - 7/2]
[4525, x^4 - x^3 - 7*x^2 + 3*x + 9, xF^2 + (-1/2*t - 1/2)*xF - 3]
[5125, x^4 - 2*x^3 - 6*x^2 + 7*x + 11, xF^2 + (-1/2*t - 1/2)*xF - t - 4]
[5225, x^4 - x^3 - 8*x^2 + x + 11, xF^2 + (-1/2*t - 1/2)*xF - 1/2*t - 7/2]
[5725, x^4 - x^3 - 8*x^2 + 6*x + 11, xF^2 + (-1/2*t + 1/2)*xF - 1/2*t - 7/2]
[6125, x^4 - x^3 - 9*x^2 + 9*x + 11, xF^2 + (-1/2*t + 1/2)*xF - t - 4]
[7225, x^4 - 11*x^2 + 9, xF^2 - xF - 4]
[7600, x^4 - 9*x^2 + 19, xF^2 - 1/2*t - 9/2]
[7625, x^4 - x^3 - 9*x^2 + 4*x + 16, xF^2 + (-1/2*t - 1/2)*xF - 4]
[8000, x^4 - 10*x^2 + 20, xF^2 - t - 5]
[8525, x^4 - 2*x^3 - 8*x^2 + 9*x + 19, xF^2 - xF - 1/2*t - 9/2]
[8725, x^4 - x^3 - 10*x^2 + 2*x + 19, xF^2 + (-1/2*t - 1/2)*xF - 1/2*t - 9/2]
[9225, x^4 - x^3 - 10*x^2 + 7*x + 19, xF^2 + (-1/2*t + 1/2)*xF - 1/2*t - 9/2]

sage: F.<t> = NumberField(x^2-5)
sage: ls = enumerate_totallyreal_fields_rel(F, 2, 10^4,verbose=2)
0 : 0 -1/2*t + 1/2 1 
  bl, br: 8.0 27.0
  found copy!
  am2s: [-2*t - 4, -3/2*t - 7/2, -3/2*t - 9/2, -t - 2, -t - 3, -t - 4, -t - 5, 
-1/2*t - 3/2, -1/2*t - 5/2, -1/2*t - 7/2, -1/2*t - 9/2, -1/2*t - 11/2]
  betak: [[-3.0532260997, -0.809016994375, 1.43519211095], [-2.28203018612, 
0.309016994375, 2.90006417487]]
==> [-1/2*t - 11/2, -1/2*t + 1/2, 1] has discriminant 13525 > B
==> [-1/2*t - 9/2, -1/2*t + 1/2, 1] has discriminant 9225 and is new!
==> [-1/2*t - 7/2, -1/2*t + 1/2, 1] has discriminant 5725 and is new!
==> [-1/2*t - 5/2, -1/2*t + 1/2, 1] is not absolutely irreducible
==> [-1/2*t - 3/2, -1/2*t + 1/2, 1] has discriminant 1125 and is new!
==> [-t - 5, -1/2*t + 1/2, 1] has discriminant 10025 > B
==> [-t - 4, -1/2*t + 1/2, 1] has discriminant 6125 and is new!
==> [-t - 3, -1/2*t + 1/2, 1] is not squarefree
==> [-t - 2, -1/2*t + 1/2, 1] has discriminant 725 and is new!
==> [-3/2*t - 9/2, -1/2*t + 1/2, 1] has discriminant 5725 but is not new
==> [-3/2*t - 7/2, -1/2*t + 1/2, 1] has discriminant 2225 and is new!
==> [-2*t - 4, -1/2*t + 1/2, 1] is not absolutely irreducible
  finished
0 : -2*t - 4 -1/2*t - 1/2 1 
  bl, br: 8.0 27.0
  found copy!
  am2s: [-3/2*t - 7/2, -3/2*t - 9/2, -t - 3, -t - 4, -t - 5, -1/2*t - 3/2, 
-1/2*t - 5/2, -1/2*t - 7/2, -1/2*t - 9/2, -1/2*t - 11/2, -2, -3, -4, -5]
  betak: [[-2.56633653374, -0.309016994375, 1.94830254499], [-1.56890405082, 
0.809016994375, 3.18693803957]]
==> [-5, -1/2*t - 1/2, 1] has discriminant 11525 > B
==> [-4, -1/2*t - 1/2, 1] has discriminant 7625 and is new!
==> [-3, -1/2*t - 1/2, 1] has discriminant 4525 and is new!
==> [-2, -1/2*t - 1/2, 1] has discriminant 2225 but is not new
==> [-1/2*t - 11/2, -1/2*t - 1/2, 1] has discriminant 13025 > B
==> [-1/2*t - 9/2, -1/2*t - 1/2, 1] has discriminant 8725 and is new!
==> [-1/2*t - 7/2, -1/2*t - 1/2, 1] has discriminant 5225 and is new!
==> [-1/2*t - 5/2, -1/2*t - 1/2, 1] has discriminant 2525 and is new!
==> [-1/2*t - 3/2, -1/2*t - 1/2, 1] is not squarefree
==> [-t - 5, -1/2*t - 1/2, 1] is not squarefree
==> [-t - 4, -1/2*t - 1/2, 1] has discriminant 5125 and is new!
==> [-t - 3, -1/2*t - 1/2, 1] is not absolutely irreducible
==> [-3/2*t - 9/2, -1/2*t - 1/2, 1] has discriminant 4225 and is new!
==> [-3/2*t - 7/2, -1/2*t - 1/2, 1] has discriminant 725 but is not new
  finished
0 : -3/2*t - 7/2 -1 1 
  bl, br: 8.0 26.0
  found copy!
  am2s: [-3/2*t - 7/2, -3/2*t - 9/2, -t - 2, -t - 3, -t - 4, -t - 5, -1/2*t - 
3/2, -1/2*t - 5/2, -1/2*t - 7/2, -1/2*t - 9/2, -1/2*t - 11/2]
  betak: [[-1.65220027211, 0.5, 2.65220027211], [-2.12069341754, 0.5, 
3.12069341754]]
==> [-1/2*t - 11/2, -1, 1] has discriminant 12725 > B
==> [-1/2*t - 9/2, -1, 1] has discriminant 8525 and is new!
==> [-1/2*t - 7/2, -1, 1] has discriminant 5125 but is not new
==> [-1/2*t - 5/2, -1, 1] has discriminant 2525 but is not new
==> [-1/2*t - 3/2, -1, 1] has discriminant 725 but is not new
==> [-t - 5, -1, 1] is not absolutely irreducible
==> [-t - 4, -1, 1] has discriminant 5225 but is not new
==> [-t - 3, -1, 1] has discriminant 2225 but is not new
==> [-t - 2, -1, 1] is not absolutely irreducible
==> [-3/2*t - 9/2, -1, 1] has discriminant 4525 but is not new
==> [-3/2*t - 7/2, -1, 1] has discriminant 1125 but is not new
  finished
0 : -3/2*t - 7/2 0 1 
  bl, br: 8.0 25.0
  found copy!
  am2s: [-2*t - 5, -3/2*t - 7/2, -3/2*t - 9/2, -3/2*t - 11/2, -t - 3, -t - 4, 
-t - 5, -t - 6, -1/2*t - 5/2, -1/2*t - 7/2, -1/2*t - 9/2, -1/2*t - 11/2]
  betak: [[-2.09331459921, -0.0, 2.09331459921], [-2.5725539817, -0.0, 
2.5725539817]]
==> [-1/2*t - 11/2, 0, 1] has discriminant 725 but is not new
==> [-1/2*t - 9/2, 0, 1] has discriminant 7600 and is new!
==> [-1/2*t - 7/2, 0, 1] has discriminant 4400 and is new!
==> [-1/2*t - 5/2, 0, 1] has discriminant 2000 and is new!
==> [-t - 6, 0, 1] has discriminant 12400 > B
==> [-t - 5, 0, 1] has discriminant 8000 and is new!
==> [-t - 4, 0, 1] has discriminant 4400 but is not new
==> [-t - 3, 0, 1] has discriminant 1600 and is new!
==> [-3/2*t - 11/2, 0, 1] has discriminant 7600 but is not new
==> [-3/2*t - 9/2, 0, 1] has discriminant 3600 and is new!
==> [-3/2*t - 7/2, 0, 1] is not absolutely irreducible
==> [-2*t - 5, 0, 1] has discriminant 2000 but is not new
  finished
================================================================================
Polynomials tested: 98
Irreducible polynomials: 46
Polynomials with nfdisc <= B: 40
[725, x^4 - x^3 - 3*x^2 + x + 1, xF^2 + (-1/2*t - 7/2)*xF + 1]
[1125, x^4 - x^3 - 4*x^2 + 4*x + 1, xF^2 + (-1/2*t - 7/2)*xF + 1/2*t + 3/2]
[1600, x^4 - 6*x^2 + 4, xF^2 - t - 3]
[2000, x^4 - 5*x^2 + 5, xF^2 - 1/2*t - 5/2]
[2225, x^4 - x^3 - 5*x^2 + 2*x + 4, xF^2 + (-1/2*t + 1/2)*xF - 3/2*t - 7/2]
[2525, x^4 - 2*x^3 - 4*x^2 + 5*x + 5, xF^2 + (-1/2*t - 1/2)*xF - 1/2*t - 5/2]
[3600, x^4 - 2*x^3 - 7*x^2 + 8*x + 1, xF^2 - 3/2*t - 9/2]
[4225, x^4 - 9*x^2 + 4, xF^2 + (-1/2*t - 1/2)*xF - 3/2*t - 9/2]
[4400, x^4 - 7*x^2 + 11, xF^2 - 1/2*t - 7/2]
[4525, x^4 - x^3 - 7*x^2 + 3*x + 9, xF^2 + (-1/2*t - 1/2)*xF - 3]
[5125, x^4 - 2*x^3 - 6*x^2 + 7*x + 11, xF^2 + (-1/2*t - 1/2)*xF - t - 4]
[5225, x^4 - x^3 - 8*x^2 + x + 11, xF^2 + (-1/2*t - 1/2)*xF - 1/2*t - 7/2]
[5725, x^4 - x^3 - 8*x^2 + 6*x + 11, xF^2 + (-1/2*t + 1/2)*xF - 1/2*t - 7/2]
[6125, x^4 - x^3 - 9*x^2 + 9*x + 11, xF^2 + (-1/2*t + 1/2)*xF - t - 4]
[7600, x^4 - 9*x^2 + 19, xF^2 - 1/2*t - 9/2]
[7625, x^4 - x^3 - 9*x^2 + 4*x + 16, xF^2 + (-1/2*t - 1/2)*xF - 4]
[8000, x^4 - 10*x^2 + 20, xF^2 - t - 5]
[8525, x^4 - 2*x^3 - 8*x^2 + 9*x + 19, xF^2 - xF - 1/2*t - 9/2]
[8725, x^4 - x^3 - 10*x^2 + 2*x + 19, xF^2 + (-1/2*t - 1/2)*xF - 1/2*t - 9/2]
[9225, x^4 - x^3 - 10*x^2 + 7*x + 19, xF^2 + (-1/2*t + 1/2)*xF - 1/2*t - 9/2]



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