#10281: Multimodular echelon form over cyclotomic fields fails
---------------------------------------+------------------------------------
Reporter: mraum | Owner: jason, was
Type: defect | Status: positive_review
Priority: critical | Milestone:
Component: linear algebra | Resolution:
Keywords: cyclotomic, echelon | Work issues:
Report Upstream: N/A | Reviewers: Martin Raum
Authors: William Stein | Merged in:
Dependencies: | Stopgaps:
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Description changed by was:
Old description:
> The following example comes from Eisenstein series. It leads to
> previous_prime being called with invalid arguments.
>
> {{{
> sage: K.<rho> = CyclotomicField(106)
> sage: coeffs = [(18603/107*rho^51 - 11583/107*rho^50 - 19907/107*rho^49 -
> 13588/107*rho^48 - 8722/107*rho^47 + 2857/107*rho^46 - 19279/107*rho^45 -
> 16666/107*rho^44 - 11327/107*rho^43 + 3802/107*rho^42 + 18998/107*rho^41
> - 10798/107*rho^40 + 16210/107*rho^39 - 13768/107*rho^38 +
> 15063/107*rho^37 - 14433/107*rho^36 - 19434/107*rho^35 - 12606/107*rho^34
> + 3786/107*rho^33 - 17996/107*rho^32 + 12341/107*rho^31 -
> 15656/107*rho^30 - 19092/107*rho^29 + 8382/107*rho^28 - 18147/107*rho^27
> + 14024/107*rho^26 + 18751/107*rho^25 - 8301/107*rho^24 -
> 20112/107*rho^23 - 14483/107*rho^22 + 4715/107*rho^21 + 20065/107*rho^20
> + 15293/107*rho^19 + 10072/107*rho^18 + 4775/107*rho^17 - 953/107*rho^16
> - 19782/107*rho^15 - 16020/107*rho^14 + 5633/107*rho^13 -
> 17618/107*rho^12 - 18187/107*rho^11 + 7492/107*rho^10 + 19165/107*rho^9 -
> 9988/107*rho^8 - 20042/107*rho^7 + 10109/107*rho^6 - 17677/107*rho^5 -
> 17723/107*rho^4 - 12489/107*rho^3 - 6321/107*rho^2 - 4082/107*rho -
> 1378/107, 1, 4*rho + 1), (0, 1, rho + 4)]
> sage: m = matrix(2, coeffs)
> sage: m.echelon_form()
> ---------------------------------------------------------------------------
> ValueError Traceback (most recent call
> last)
>
> /home/martin/<ipython console> in <module>()
>
> /opt/sage/local/lib/python2.6/site-
> packages/sage/matrix/matrix_cyclo_dense.so in
> sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense.echelon_form
> (sage/matrix/matrix_cyclo_dense.cpp:13469)()
>
> /opt/sage/local/lib/python2.6/site-
> packages/sage/matrix/matrix_cyclo_dense.so in
> sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense._echelon_form_multimodular
> (sage/matrix/matrix_cyclo_dense.cpp:14366)()
>
> /opt/sage/local/lib/python2.6/site-packages/sage/rings/arith.pyc in
> previous_prime(n)
> 1044 n = ZZ(n)-1
> 1045 if n <= 1:
> -> 1046 raise ValueError, "no previous prime"
> 1047 if n <= 3:
> 1048 return ZZ(n)
>
> ValueError: no previous prime
> }}}
>
> Apply:
> 1. [attachment:trac_10281-sage-5.0-beta9.patch​]
>
> Install:
> 1. http://wstein.org/home/wstein/patches/linbox-1.1.6.p8.spkg
New description:
The following example comes from Eisenstein series. It leads to
previous_prime being called with invalid arguments.
{{{
sage: K.<rho> = CyclotomicField(106)
sage: coeffs = [(18603/107*rho^51 - 11583/107*rho^50 - 19907/107*rho^49 -
13588/107*rho^48 - 8722/107*rho^47 + 2857/107*rho^46 - 19279/107*rho^45 -
16666/107*rho^44 - 11327/107*rho^43 + 3802/107*rho^42 + 18998/107*rho^41 -
10798/107*rho^40 + 16210/107*rho^39 - 13768/107*rho^38 + 15063/107*rho^37
- 14433/107*rho^36 - 19434/107*rho^35 - 12606/107*rho^34 + 3786/107*rho^33
- 17996/107*rho^32 + 12341/107*rho^31 - 15656/107*rho^30 -
19092/107*rho^29 + 8382/107*rho^28 - 18147/107*rho^27 + 14024/107*rho^26 +
18751/107*rho^25 - 8301/107*rho^24 - 20112/107*rho^23 - 14483/107*rho^22 +
4715/107*rho^21 + 20065/107*rho^20 + 15293/107*rho^19 + 10072/107*rho^18 +
4775/107*rho^17 - 953/107*rho^16 - 19782/107*rho^15 - 16020/107*rho^14 +
5633/107*rho^13 - 17618/107*rho^12 - 18187/107*rho^11 + 7492/107*rho^10 +
19165/107*rho^9 - 9988/107*rho^8 - 20042/107*rho^7 + 10109/107*rho^6 -
17677/107*rho^5 - 17723/107*rho^4 - 12489/107*rho^3 - 6321/107*rho^2 -
4082/107*rho - 1378/107, 1, 4*rho + 1), (0, 1, rho + 4)]
sage: m = matrix(2, coeffs)
sage: v = m.echelon_form()
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
/home/martin/<ipython console> in <module>()
/opt/sage/local/lib/python2.6/site-
packages/sage/matrix/matrix_cyclo_dense.so in
sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense.echelon_form
(sage/matrix/matrix_cyclo_dense.cpp:13469)()
/opt/sage/local/lib/python2.6/site-
packages/sage/matrix/matrix_cyclo_dense.so in
sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense._echelon_form_multimodular
(sage/matrix/matrix_cyclo_dense.cpp:14366)()
/opt/sage/local/lib/python2.6/site-packages/sage/rings/arith.pyc in
previous_prime(n)
1044 n = ZZ(n)-1
1045 if n <= 1:
-> 1046 raise ValueError, "no previous prime"
1047 if n <= 3:
1048 return ZZ(n)
ValueError: no previous prime
}}}
Apply:
1. [attachment:trac_10281-sage-5.0-beta9.patch​]
Install:
1. http://wstein.org/home/wstein/patches/linbox-1.1.6.p8.spkg
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10281#comment:14>
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