#10063: Some determinants can not be computed
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Reporter: tmonteil | Owner: AlexGhitza
Type: defect | Status: new
Priority: critical | Milestone:
Component: algebra | Keywords: determinant, ring, ideal
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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To use some fast algorithms that only work for fields, the `determinant`
method uses the `is_field` method for rings which uses the `is_maximal`
method for ideals. Unfortunately, this method is not always implemented.
The determinant is a very fundamental function, and there are many
division-free algorithms that work in every ring, hence this method should
never raise an error.
Here is an example of the bug i encountered while testing a conjecture in
combinatorics:
{{{
sage: A = GF(2)['x,y,z']
sage: A.inject_variables()
Defining x, y, z
sage: R = A.quotient(x^2 + 1).quotient(y^2 + 1).quotient(z^2 + 1)
sage: R.inject_variables()
Defining xbarbarbar, ybarbarbar, zbarbarbar
sage: M =
matrix([[1,1,1,1],[xbarbarbar,ybarbarbar,1,1],[0,1,zbarbarbar,1],[xbarbarbar,zbarbarbar,1,1]])
sage: M.determinant()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
/tmp/<ipython console> in <module>()
/opt/sagemath/sage-4.5.3/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.determinant
(sage/matrix/matrix2.c:6942)()
1092 # TODO: Find a reasonable cutoff point. (This is field
specific, but
1093 # seems to be quite large for Q[x].)
-> 1094 if (R.is_field() and R.is_exact() and algorithm is None)
or (algorithm == "hessenberg"):
1095 try:
1096 c = self.charpoly('x', algorithm="hessenberg")[0]
/opt/sagemath/sage-4.5.3/local/lib/python2.6/site-
packages/sage/rings/quotient_ring.pyc in is_field(self, proof)
420 """
421 if proof:
--> 422 return self.defining_ideal().is_maximal()
423 else:
424 try:
/opt/sagemath/sage-4.5.3/local/lib/python2.6/site-
packages/sage/rings/ideal.pyc in is_maximal(self)
559 NotImplementedError
560 """
--> 561 raise NotImplementedError
562
563 def is_primary(self, P=None):
NotImplementedError:
}}}
A simple (maybe dirty) solution might be to add a `try` at the beginning
of the method and an `except` that use a basic division-free formula in
case of error.
I am not an algebraist, so i prefer not to fix this bug by myself.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10063>
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