#5451: Bug in addition of rational functions over a finite field
---------------------+------------------------------------------------------
Reporter: cremona | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: algebra | Keywords: rational function addition
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Alex Lara reported on sage-support on 20090307:
{{{
I recently upgrade sage from 3.2.3 to 3.3. I'm also have sage 3.1.1
The thing is that the following commands give different results:
F.<theta>=FiniteField(9)
A.<t> = PolynomialRing(F)
K.<t> = FractionField(A)
f= 2/(t^2+2*t); g =t^9/(t^18 + t^10 + t^2);f+g
In 3.1.1 gives the right answer (I guess) but in 3.2.3 give an error:
ZeroDivisionError Traceback (most recent call
last)
...
ZeroDivisionError: division by zero in finite field.
}}}
In more detail that traceback is
{{{
ZeroDivisionError Traceback (most recent call
last)
/home/john/.sage/temp/ubuntu/30503/_home_john__sage_init_sage_0.py in
<module>()
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.ModuleElement.__add__
(sage/structure/element.c:5746)()
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/rings/fraction_field_element.so in
sage.rings.fraction_field_element.FractionFieldElement._add_
(sage/rings/fraction_field_element.c:3975)()
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.PrincipalIdealDomainElement.gcd
(sage/structure/element.c:11697)()
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/rings/polynomial/polynomial_element_generic.pyc in
_gcd(self, other)
558 Return the GCD of self and other, as a monic polynomial.
559 """
--> 560 g = EuclideanDomainElement._gcd(self, other)
561 c = g.leading_coefficient()
562 if c.is_unit():
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.EuclideanDomainElement._gcd
(sage/structure/element.c:11939)()
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/rings/polynomial/polynomial_element_generic.pyc in
quo_rem(self, other)
542 Q = P.zero_element()
543 while R.degree() >= B.degree():
--> 544 aaa = R.leading_coefficient()/B.leading_coefficient()
545 diff_deg=R.degree()-B.degree()
546 Q += P(aaa).shift(diff_deg)
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__div__
(sage/structure/element.c:9099)()
/home/john/sage-3.4.alpha0/local/lib/python2.5/site-
packages/sage/rings/finite_field_givaro.so in
sage.rings.finite_field_givaro.FiniteField_givaroElement._div_
(sage/rings/finite_field_givaro.cpp:9661)()
ZeroDivisionError: division by zero in finite field.
}}}
which shows that somewhere in a gcd computation, a leading coefficient of
0 is being returned.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5451>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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