#4276: [with patch, needs review] move number fields to new coercion, implement
embeddings
----------------------+-----------------------------------------------------
Reporter: robertwb | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.2
Component: coercion | Resolution:
Keywords: |
----------------------+-----------------------------------------------------
Comment (by ncalexan):
This code is good, it really is, but it's just not tested. I don't have
time right now to test it and I will be sans computer over the Christmas
break.
I have to give this a negative review because I do not believe the
embeddings work in anything more than the trivial situation: two absolute
fields, compatible embeddings into CC.
On the other hand, I have no reservations about the coercion part of this
patch. Are we willing to accept almost certainly broken new functionality
to have valuable infrastructure upgrades?
{{{
sage: L1 = NumberField(x^4 + 6*x^2 + 1, 'a', embedding=CC(5*I))
sage: NumberField(x^4 + 6*x^2 + 1, 'a', embedding=L1.gen())
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/ncalexan/.sage/temp/pv139196.reshsg.uci.edu/23733/_Users_ncalexan__sage_init_sage_0.py
in <module>()
----> 1
2
3
4
5
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.pyc in
NumberField(polynomial, name, check, names, cache, embedding)
371 K = NumberField_quadratic(polynomial, name, check,
embedding)
372 else:
--> 373 K = NumberField_absolute(polynomial, name, None, check,
embedding)
374
375 if cache:
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.pyc in __init__(self,
polynomial, name, latex_name, check, embedding)
3655 NumberField_generic.__init__(self, polynomial, name,
latex_name, check, embedding)
3656 self._element_class =
number_field_element.NumberFieldElement_absolute
-> 3657 self._zero_element = self(0)
3658 self._one_element = self(1)
3659
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:3665)()
277
278
--> 279
280
281
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent.so in
sage.structure.parent.Parent.convert_map_from
(sage/structure/parent.c:8640)()
1000
1001
-> 1002
1003
1004
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent.so in
sage.structure.parent.Parent.discover_convert_map_from
(sage/structure/parent.c:8771)()
1007
1008
-> 1009
1010
1011
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent.so in
sage.structure.parent.Parent.coerce_map_from
(sage/structure/parent.c:7653)()
876
877
--> 878
879
880
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent.so in
sage.structure.parent.Parent.discover_coerce_map_from
(sage/structure/parent.c:7956)()
921
922
--> 923
924
925
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent_old.so in
sage.structure.parent_old.Parent._coerce_map_from_
(sage/structure/parent_old.c:6291)()
576
577
--> 578
579
580
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.pyc in
_coerce_map_from_(self, R)
1531 """
1532 if R in [int, long, ZZ, QQ, self.base()]:
-> 1533 return self._generic_convert_map(R)
1534 from sage.rings.number_field.order import
is_NumberFieldOrder
1535 if is_NumberFieldOrder(R) and
R.number_field().has_coerce_map_from(self):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent_old.so in
sage.structure.parent_old.Parent._generic_convert_map
(sage/structure/parent_old.c:6841)()
594
595
--> 596
597
598
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent_old.so in
sage.structure.parent_old.Parent._generic_convert_map
(sage/structure/parent_old.c:6806)()
602
603
--> 604
605
606
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/parent.so in
sage.structure.parent.Parent._generic_convert_map
(sage/structure/parent.c:6875)()
747
748
--> 749
750
751
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap.__init__
(sage/structure/coerce_maps.c:1931)()
22
23
---> 24
25
26
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/categories/map.so in sage.categories.map.Map.__init__
(sage/categories/map.c:1768)()
39
40
---> 41
42
43
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/categories/homset.pyc in Hom(X, Y, cat)
151
152 ##_cache[key] = weakref.ref(H)
--> 153 _cache[(X, Y, cat)] = weakref.ref(H)
154
155 return H
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/number_field/number_field.pyc in __cmp__(self, other)
1645 else:
1646 return cmp(self.coerce_embedding()(self.gen()),
-> 1647 other.coerce_embedding()(other.gen()))
1648
1649 def _ideal_class_(self):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/real_lazy.so in
sage.rings.real_lazy.LazyBinop.__richcmp__ (sage/rings/real_lazy.c:7864)()
868
869 def __richcmp__(left, right, int op):
--> 870 return (<Element>left)._richcmp(right, op)
871
872 def __hash__(self):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.Element._richcmp (sage/structure/element.c:5167)()
530
531
--> 532
533
534
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.Element._richcmp_c_impl
(sage/structure/element.c:5398)()
577
578
--> 579
580
581
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/real_lazy.so in
sage.rings.real_lazy.LazyFieldElement._cmp_c_impl
(sage/rings/real_lazy.c:5454)()
508 except TypeError:
509 pass
--> 510 left, right = self.approx(), other.approx()
511 return cmp(left, right)
512
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/real_lazy.so in
sage.rings.real_lazy.LazyFieldElement.approx
(sage/rings/real_lazy.c:5886)()
567 Complex Interval Field with 53 bits of precision
568 """
--> 569 return self.eval(self._parent.interval_field())
570
571 def _real_double_(self, R):
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/real_lazy.so in sage.rings.real_lazy.LazyBinop.eval
(sage/rings/real_lazy.c:7433)()
825 '68'
826 """
--> 827 left = self._left.eval(R)
828 right = self._right.eval(R)
829 if self._op is add:
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/real_lazy.so in sage.rings.real_lazy.LazyBinop.eval
(sage/rings/real_lazy.c:7445)()
826 """
827 left = self._left.eval(R)
--> 828 right = self._right.eval(R)
829 if self._op is add:
830 return left + right
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/rings/real_lazy.so in
sage.rings.real_lazy.LazyAlgebraic.eval (sage/rings/real_lazy.c:10512)()
1292 roots = self._poly.roots(ring = AA if
isinstance(self._parent, RealLazyField_class) else QQbar)
1293 best_root = roots[0][0]
-> 1294 min_dist = abs(self._root_approx - best_root)
1295 for r, e in roots[1:]:
1296 dist = abs(self._root_approx - r)
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.ModuleElement.__sub__
(sage/structure/element.c:6075)()
680
681
--> 682
683
684
/Users/ncalexan/sage-3.2.1.alpha1/local/lib/python2.5/site-
packages/sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:5808)()
695
696
--> 697
698
699
TypeError: unsupported operand parent(s) for '-': 'Number Field in a with
defining polynomial x^4 + 6*x^2 + 1' and 'Algebraic Field'
sage: NumberField(x^4 + 6*x^2 + 1, 'a').extension(x^4 + 111, embeding=2.5)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/ncalexan/.sage/temp/pv139196.reshsg.uci.edu/23733/_Users_ncalexan__sage_init_sage_0.py
in <module>()
----> 1
2
3
4
5
TypeError: extension() got an unexpected keyword argument 'embeding'
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4276#comment:18>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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