Hi,
I'm getting a strange error message in the library that I'm having trouble
reproducing at the prompt for determinants over GF(2). The full commands to
create the message are below, using the sage in ~jonhanke/sage3.3.rc0_bad
directory on the sage.math machine. Thanks,
-Jon
=)
----------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------
| Sage Version 3.3.rc0, Release Date: 2009-02-11 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage:
sage:
sage: MM = matrix(ZZ, 6, 6, [0, 0, 1, 2, 2, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2,
3, 0, 2, 1, 2, 3, 1, 2, 2, 0, 3, 1, 1, 0, 2, 1, 0, 2, 0, 1])
sage: QQ = QuadraticForm(ZZ, 2*MM)
sage: QQ.maximal_form()
Watson lattice B = [0 0 2 4 4 4]
[0 0 0 2 0 2]
[2 0 4 4 6 0]
[4 2 4 6 2 4]
[4 0 6 2 2 0]
[4 2 0 4 0 2]
pp1 = [2, 3]
pp2 = [2, 3]
p = 2
small_gram = [15 7 12 6 3 6]
[ 7 5 6 6 0 3]
[12 6 9 6 3 6]
[ 6 6 6 6 0 3]
[ 3 0 3 0 0 0]
[ 6 3 6 3 0 0]
small_gram_det = -81
small_gram_ed = [1, 1, 1, 1, 1, 1]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/jonhanke/.sage/temp/
sage.math.washington.edu/20191/_home_jonhanke__sage_init_sage_0.py in
<module>()
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/quadratic_forms/quadratic_form__neighbors.pyc
in maximal_form(self)
308 print "small_gram_det = ", small_gram.det()
309 print "small_gram_ed = ", small_gram.elementary_divisors()
--> 310 Tp = find_basis_of_maximal_isotropic_subspace(matrix(GF(p),
small_gram))
311 TZ = matrix(ZZ,Tp).transpose() * dp_cols_small.transpose()
312 T_huge = T_huge.augment(cofacp*TZ)
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/quadratic_forms/extras.pyc
in find_basis_of_maximal_isotropic_subspace(G)
105
106 ## Find one isotropic vector
--> 107 v = find_isotropic_vector_at_prime(G)
108
109 ## Check if we're done.
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/quadratic_forms/extras.pyc
in find_isotropic_vector_at_prime(G)
38 p = G.parent().base_ring().characteristic()
39 ## Check that G % p is non-degenerate... or allow it an use the
kernel.
---> 40 G_det = G.det()
41 if G_det == 0:
42 raise NotImplementedError, "Must input a non-degenerate
matrix over GF(p)."
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.det (sage/matrix/matrix2.c:6331)()
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/matrix/matrix_modn_dense.so
in sage.matrix.matrix_modn_dense.Matrix_modn_dense.determinant
(sage/matrix/matrix_modn_dense.c:10704)()
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.determinant (sage/matrix/matrix2.c:5951)()
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/matrix/matrix_modn_dense.so
in sage.matrix.matrix_modn_dense.Matrix_modn_dense.charpoly
(sage/matrix/matrix_modn_dense.c:7109)()
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/matrix/matrix2.so
in sage.matrix.matrix2.Matrix.charpoly (sage/matrix/matrix2.c:7195)()
/home/jonhanke/sage-3.3.rc0/local/lib/python2.5/site-packages/sage/matrix/matrix_modn_dense.so
in sage.matrix.matrix_modn_dense.Matrix_modn_dense._charpoly_hessenberg
(sage/matrix/matrix_modn_dense.c:10131)()
TypeError: Cannot convert sage.matrix.matrix_mod2_dense.Matrix_mod2_dense to
sage.matrix.matrix_modn_dense.Matrix_modn_dense
sage:
-------------------------------------------------------------------------------------------------------------------------------------------------------
sage: G = matrix(GF(2),[1,1,0,0,1,0, 1,1,0,0,0,1, 0,0,1,0,1,0, 0,0,0,0,0,1,
1,0,1,0,0,0, 0, 1,0,1,0,0 ])
sage: G
[1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0]
sage: G = matrix(GF(2),6,6,[1,1,0,0,1,0, 1,1,0,0,0,1, 0,0,1,0,1,0,
0,0,0,0,0,1, 1,0,1,0,0,0, 0, 1,0,1,0,0 ])
sage: G
[1 1 0 0 1 0]
[1 1 0 0 0 1]
[0 0 1 0 1 0]
[0 0 0 0 0 1]
[1 0 1 0 0 0]
[0 1 0 1 0 0]
sage: G.det()
1
sage: type(G)
<type 'sage.matrix.matrix_mod2_dense.Matrix_mod2_dense'>
sage: G = matrix(ZZ,6,6,[1,1,0,0,1,0, 1,1,0,0,0,1, 0,0,1,0,1,0, 0,0,0,0,0,1,
1,0,1,0,0,0, 0, 1,0,1,0,0 ])
sage: G2 = matrix(GF(2),G)
sage: G2.det()
1
sage:
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