#8992: Coercion of univariate quotient polynomial rings
-------------------------+--------------------------------------------------
Reporter: SimonKing | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-4.4.2
Component: coercion | Keywords: coercion quotient ring
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-------------------------+--------------------------------------------------
Consider the following setting:
{{{
sage: P.<x> = QQ[]
sage: Q1 = P.quo([(x^2+1)^2*(x^2-3)])
sage: Q2 = P.quo([(x^2+1)^2*(x^5+3)])
}}}
The gcd of the moduli is {{{(x^2+1)^2}}}, and so it should be true that
the pushout of Q1 and Q2 is the quotient ring with this gcd as modulus.
Currently, the pushout raises an error, but with #8800 one has:
{{{
sage: from sage.categories.pushout import pushout
sage: Q = pushout(Q1,Q2); Q
Univariate Quotient Polynomial Ring in xbar over Rational Field with
modulus x^4 + 2*x^2 + 1
}}}
However, there remain two bugs that are not covered in #8800 and that
prevent a proper coercion of Q1 and Q2.
First bug:
{{{
sage: Q.has_coerce_map_from(Q1)
False
sage: Q.has_coerce_map_from(Q2)
False
}}}
Second bug:
{{{
sage: Q(Q1.gen())
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (932, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (932, 0))
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/king/SAGE/sage-4.3.1/devel/<ipython console> in <module>()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_quotient_ring.pyc in
__call__(self, x)
272 return PolynomialQuotientRingElement(self,
self.__ring(x.lift()), check=False)
273 return PolynomialQuotientRingElement(
--> 274 self, self.__ring(x) , check=True)
275
276 def _is_valid_homomorphism_(self, codomain, im_gens):
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:6332)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3108)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3010)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_ring.pyc in
_element_constructor_(self, x, check, is_gen, construct, **kwds)
310 x = x.Polrev()
311
--> 312 return C(self, x, check, is_gen, construct=construct,
**kwds)
313
314 def is_integral_domain(self, proof = True):
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element_generic.pyc in
__init__(self, parent, x, check, is_gen, construct)
654
655 if check:
--> 656 x = [QQ(z) for z in x]
657
658 self.__list = list(x)
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:6332)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3108)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3010)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/rational.so in sage.rings.rational.Rational.__init__
(sage/rings/rational.c:5781)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/rational.so in
sage.rings.rational.Rational.__set_value (sage/rings/rational.c:7052)()
TypeError: Unable to coerce xbar (<class
'sage.rings.polynomial.polynomial_quotient_ring_element.PolynomialQuotientRingElement'>)
to Rational
sage: Q.gen()
xbar
}}}
It could be that the following is an additional bug, but perhaps it is
just a special case of the previous:
{{{
sage: Q(str(Q.gen()))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (932, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (932, 0))
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/king/SAGE/sage-4.3.1/devel/<ipython console> in <module>()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_quotient_ring.pyc in
__call__(self, x)
272 return PolynomialQuotientRingElement(self,
self.__ring(x.lift()), check=False)
273 return PolynomialQuotientRingElement(
--> 274 self, self.__ring(x) , check=True)
275
276 def _is_valid_homomorphism_(self, codomain, im_gens):
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:6332)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3108)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3010)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_ring.pyc in
_element_constructor_(self, x, check, is_gen, construct, **kwds)
297 R = self.base_ring()
298 p = Parser(Integer, R,
LookupNameMaker({self.variable_name(): self.gen()}, R))
--> 299 return self(p.parse(x))
300 except NameError:
301 raise TypeError,"Unable to coerce string"
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.parse
(sage/misc/parser.c:3481)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.parse
(sage/misc/parser.c:3345)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_eqn
(sage/misc/parser.c:5136)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_expr
(sage/misc/parser.c:5456)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_term
(sage/misc/parser.c:5681)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_factor
(sage/misc/parser.c:6044)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_power
(sage/misc/parser.c:6158)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_atom
(sage/misc/parser.c:6711)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.LookupNameMaker.__call__
(sage/misc/parser.c:7653)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__
(sage/structure/parent.c:6332)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3108)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(sage/structure/coerce_maps.c:3010)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/rational.so in sage.rings.rational.Rational.__init__
(sage/rings/rational.c:5781)()
/home/king/SAGE/sage-4.3.1/local/lib/python2.6/site-
packages/sage/rings/rational.so in
sage.rings.rational.Rational.__set_value (sage/rings/rational.c:6517)()
TypeError: unable to convert xbar to a rational
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8992>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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