Dear sage-devel,
I have recently come across a bug which is perhaps best summarised in
the following code (I've removed a big chunk of the backtrace to make
it easier to read; the full backtrace is available at the end of this
message):
--- BEGIN ---
sage: k.<a> = GF(5^2, 'a')
sage: EllipticCurve(k, [1,1]).formal_group().group_law(prec = 7)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/hlaw/src/<ipython console> in <module>()
/Users/hlaw/sage/local/lib/python2.5/site-packages/sage/schemes/
elliptic_curves/formal_group.py in group_law(self, prec)
440 lam3 = lam2*lam
441 t3 = -t1 - t2 - \
--> 442 (a1*lam + a3*lam2 + a2*nu + 2*a4*lam*nu +
3*a6*lam2*nu)/ \
443 (1 + a2*lam + a4*lam2 + a6*lam3)
444 inv = self.inverse(prec)
[snip]
/Users/hlaw/src/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.valuation (sage/
rings/polynomial/polynomial_element.c:22641)()
TypeError: The polynomial, p, must have the same parent as self.
--- END ---
(Note that the polynomial referred to in the TypeError is a red
herring: it's an optional parameter to the valuation() method that
is not being used in this case.) So the bug is being triggered in the
Polynomial.valuation() method, but from what I've determined so far,
it occurs because the polynomial whose valuation is being calculated
is "corrupted" in the following sense. If p is the polynomial
triggering the error, then:
p.coeffs() is [0, 0, 0, 0, 0, 0, 0]
p.degree() is 6
p.is_zero() is False
Moreover, the error only occurs at certain precisions. For example:
sage: def run_test(field, prec_bound=20):
E = EllipticCurve(field, [1,1])
FG = E.formal_group()
error_precisions = []
for precision in range(2, prec_bound):
try:
gl = FG.group_law(precision)
except TypeError:
error_precisions.append(precision)
return error_precisions
sage: run_test(GF(5^2, 'a'), 30)
[5, 6, 7, 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29]
I have tried randomly changing the elliptic curve and the field
degree, but run_test() returned exactly the same list each time.
Changing the base field modifies the list a bit:
sage: run_test(GF(7^2, 'a'), 30)
[5, 6, 7, 9, 11, 13, 15, 17, 18, 19, 20, 21, 23, 25, 27, 29]
So 14 and 26 are now gone, but 18 and 20 have been introduced.
And finally, no errors occur at all if we use a prime finite field
instead of a non-prime one:
sage: run_test(GF(5), 30); run_test(GF(7), 30)
[]
[]
The same basic bug occurs on the following machines:
Sage 3.0.3 (upgraded from 2.11), Ubuntu Linux 8.04, x86
Sage 2.11, Ubuntu Linux 8.04, x86
Sage 3.04, Mac OS X 10.5.3, x86
The examples in this message were all calculated on the MacOSX
machine.
Also, I'd like to be put on the CC list of the ticket, if/when a
ticket is created for this bug.
Thanks in advance,
Hamish.
Full backtrace:
sage: k.<a> = GF(5^2, 'a')
sage: EllipticCurve(k, [1,1]).formal_group().group_law(prec = 7)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/hlaw/src/<ipython console> in <module>()
/Users/hlaw/sage/local/lib/python2.5/site-packages/sage/schemes/
elliptic_curves/formal_group.py in group_law(self, prec)
440 lam3 = lam2*lam
441 t3 = -t1 - t2 - \
--> 442 (a1*lam + a3*lam2 + a2*nu + 2*a4*lam*nu +
3*a6*lam2*nu)/ \
443 (1 + a2*lam + a4*lam2 + a6*lam3)
444 inv = self.inverse(prec)
/Users/hlaw/src/element.pyx in
sage.structure.element.RingElement.__mul__ (sage/structure/element.c:
8797)()
/Users/hlaw/src/coerce.pxi in sage.structure.element._mul_c (sage/
structure/element.c:16614)()
/Users/hlaw/src/power_series_poly.pyx in
sage.rings.power_series_poly.PowerSeries_poly._mul_c_impl (sage/rings/
power_series_poly.c:3161)()
/Users/hlaw/src/element.pyx in
sage.structure.element.RingElement.__mul__ (sage/structure/element.c:
8797)()
/Users/hlaw/src/coerce.pxi in sage.structure.element._mul_c (sage/
structure/element.c:16614)()
/Users/hlaw/src/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial._mul_c_impl (sage/
rings/polynomial/polynomial_element.c:7260)()
/Users/hlaw/src/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial._mul_karatsuba
(sage/rings/polynomial/polynomial_element.c:10735)()
/Users/hlaw/src/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.do_karatsuba (sage/rings/
polynomial/polynomial_element.c:25040)()
/Users/hlaw/src/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.do_karatsuba (sage/rings/
polynomial/polynomial_element.c:24742)()
/Users/hlaw/src/element.pyx in
sage.structure.element.RingElement.__mul__ (sage/structure/element.c:
8797)()
/Users/hlaw/src/coerce.pxi in sage.structure.element._mul_c (sage/
structure/element.c:16614)()
/Users/hlaw/src/power_series_poly.pyx in
sage.rings.power_series_poly.PowerSeries_poly._mul_c_impl (sage/rings/
power_series_poly.c:3145)()
/Users/hlaw/src/power_series_ring_element.pyx in
sage.rings.power_series_ring_element.PowerSeries._mul_prec (sage/rings/
power_series_ring_element.c:5554)()
/Users/hlaw/src/power_series_poly.pyx in
sage.rings.power_series_poly.PowerSeries_poly.valuation (sage/rings/
power_series_poly.c:2050)()
/Users/hlaw/src/polynomial_element.pyx in
sage.rings.polynomial.polynomial_element.Polynomial.valuation (sage/
rings/polynomial/polynomial_element.c:22641)()
TypeError: The polynomial, p, must have the same parent as self.
--
Hamish Ivey-Law
PhD student,
Institut de Mathématiques de Luminy, Université de la Méditerranée,
and
School of Mathematics and Statistics, University of Sydney.
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