#15552: enumerate_totallyreal_fields_prim does not return polynomial as
elements of
a polynomial ring
-------------------------------------+-------------------------------------
Reporter: ppurka | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.1
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers: Francis Clarke
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/ppurka/ticket/15552 | d67b6c35baf378c3362f38b8b8c8c8dcc661602f
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by ppurka):
This is still not completely ready for review -- need to verify that the
outputs are fine. But you can look into the changes if you want.
I am actually not confident that the functions give the output
corresponding to the documentation! The statements that we get with
`verbose=True` do not match the output (for example the discriminant
bound). I guess we can just fix the output here and leave the actual
program to someone who knows this stuff inside out.
Here is a sample run after my patches.
{{{
sage: ZZx = ZZ['x']
sage: F.<t> = NumberField(x^2-2)
sage: enumerate_totallyreal_fields_rel(F, 2, 2000, verbose=True) # m=2
==> [t - 1, t + 1, 1] has discriminant 2624 > B
==> [-1, t + 1, 1] has discriminant 2624 > B
==> [-2, 1, 1] is not absolutely irreducible
==> [-1, t, 1] has discriminant 2304 > B
==> [t - 1, t, 1] is not squarefree
==> [-t - 1, t, 1] is not squarefree
==> [-2, 0, 1] is not squarefree
==> [t - 2, 0, 1] has discriminant 2048 > B
==> [-t - 2, 0, 1] has discriminant 2048 > B
================================================================================
Polynomials tested: 9
Polynomials with discriminant with large enough square divisior: 6
Irreducible polynomials: 5
Polynomials with nfdisc <= B: 0
[1600, x^4 - 6*x^2 + 4, xF^2 + xF - 1]
[[1600, x^4 - 6*x^2 + 4, xF^2 + xF - 1]]
# return_seqs returns four numbers corresponding to the numbers above
sage: enumerate_totallyreal_fields_rel(F, 2, 2000, return_seqs=True)
[[9, 6, 5, 0], [[1600, [4, 0, -6, 0, 1], [-1, 1, 1]]]]
# Testing m=1 which wasn't working before
sage: enumerate_totallyreal_fields_rel(F, 1, 2000, verbose=True) # m=1
[[1, x - 1, [-2, 0, 1]]]
-------------------------- SECOND FUNCTION ----------------------------
Let us try the _all function which calls _rel
sage: enumerate_totallyreal_fields_all(2, 10, return_seqs=True)
[[0, 0, 0, 0], [[5, [-1, -1, 1]], [8, [-2, 0, 1]]]]
sage: enumerate_totallyreal_fields_all(2, 10)
[[5, x^2 - x - 1], [8, x^2 - 2]]
# the verbose output
sage: enumerate_totallyreal_fields_all(2, 10, verbose=True)
================================================================================
Polynomials tested: 0
Polynomials with sssd poldisc: 0
Irreducible polynomials: 0
Polynomials with nfdisc <= B: 0
[5, x^2 - x - 1]
[8, x^2 - 2]
================================================================================
Polynomials tested: 0
Polynomials with discriminant with large enough square divisior: 0
Irreducible polynomials: 0
Polynomials with nfdisc <= B: 0
[5, x^2 - x - 1]
[8, x^2 - 2]
[[5, x^2 - x - 1], [8, x^2 - 2]]
# the case n=1
sage: enumerate_totallyreal_fields_all(1, 10, verbose=True)
================================================================================
Polynomials tested: 0
Polynomials with discriminant with large enough square divisior: 0
Irreducible polynomials: 0
Polynomials with nfdisc <= B: 0
[1, x - 1]
[[1, x - 1]]
----------------------- THIRD FUNCTION --------------------------------
# the third function
sage: enumerate_totallyreal_fields_prim(5,5**7)
[[14641, x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1],
[24217, x^5 - 5*x^3 - x^2 + 3*x + 1],
[36497, x^5 - 2*x^4 - 3*x^3 + 5*x^2 + x - 1],
[38569, x^5 - 5*x^3 + 4*x - 1],
[65657, x^5 - x^4 - 5*x^3 + 2*x^2 + 5*x + 1],
[70601, x^5 - x^4 - 5*x^3 + 2*x^2 + 3*x - 1]]
sage: enumerate_totallyreal_fields_prim(5,5**7,verbose=True)
================================================================================
Polynomials tested: 953
Polynomials with sssd poldisc: 359
Irreducible polynomials: 191
Polynomials with nfdisc <= B: 38
[14641, x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1]
[24217, x^5 - 5*x^3 - x^2 + 3*x + 1]
[36497, x^5 - 2*x^4 - 3*x^3 + 5*x^2 + x - 1]
[38569, x^5 - 5*x^3 + 4*x - 1]
[65657, x^5 - x^4 - 5*x^3 + 2*x^2 + 5*x + 1]
[70601, x^5 - x^4 - 5*x^3 + 2*x^2 + 3*x - 1]
[[14641, x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1],
[24217, x^5 - 5*x^3 - x^2 + 3*x + 1],
[36497, x^5 - 2*x^4 - 3*x^3 + 5*x^2 + x - 1],
[38569, x^5 - 5*x^3 + 4*x - 1],
[65657, x^5 - x^4 - 5*x^3 + 2*x^2 + 5*x + 1],
[70601, x^5 - x^4 - 5*x^3 + 2*x^2 + 3*x - 1]]
# the case n = 1
sage: enumerate_totallyreal_fields_prim(1,7, verbose=True)
[[1, x - 1]]
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15552#comment:11>
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