#13347: Check doctest examples using QuotientRings, which do not fulfill the
assumptions made on the ideal
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Reporter: tfeulner | Owner: mvngu
Type: task | Status: new
Priority: major | Milestone: sage-6.4
Component: doctest coverage | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by saraedum:
Old description:
> The following files use quotient rings in their doctest examples, which
> contradict the assumption on the defining ideal:
>
> ASSUMPTION:
>
> ``I`` has a method ``I.reduce(x)`` returning the normal form
> of elements `x\in R`. In other words, it is required that
> ``I.reduce(x)==I.reduce(y)`` `\iff x-y \in I`, and
> ``x-I.reduce(x) in I``, for all `x,y\in R`.
>
> - sage/categories/pushout.py :
> - QuotientFunctor.__cmp__
> {{{
> sage: P.<x> = QQ[]
> sage: F =
> P.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
> sage: F == loads(dumps(F))
> True
> sage: P2.<x,y> = QQ[]
> sage: F ==
> P2.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
> False
> sage: P3.<x> = ZZ[]
> sage: F ==
> P3.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
> True
> }}}
>
> - sage/categories/rings.py :
> - Rings.quotient
> {{{
> sage: F.<x,y,z> = FreeAlgebra(QQ, 3)
> sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
> sage: Q = Rings().parent_class.quotient(F,I); Q
> }}}
> - Rings.quo
> {{{
> sage: MS = MatrixSpace(QQ,2)
> sage: MS.full_category_initialisation()
> sage: I = MS*MS.gens()*MS
> sage: MS.quo(I,names = ['a','b','c','d'])
> }}}
> - Rings.quotient_ring
> {{{
> sage: MS = MatrixSpace(QQ,2)
> sage: I = MS*MS.gens()*MS
> sage: MS.quotient_ring(I,names = ['a','b','c','d'])
> }}}
> - sage/structure/category_object.pyx :
> - CategoryObject.__temporarily_change_names
> {{{
> sage: MS = MatrixSpace(GF(5),2,2)
> sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
> sage: Q.<a,b,c,d> = MS.quo(I)
> }}}
>
> - sage/rings/quotient_ring_element.py :
> - QuotientRingElement
> {{{
> sage: R.<x> = PolynomialRing(ZZ)
> sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
> }}}
> - QuotientRingElement.__init__
> {{{
> sage: R.<x> = PolynomialRing(ZZ)
> sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
> }}}
> - QuotientRingElement._repr_
> {{{
> sage: S = SteenrodAlgebra(2)
> sage: I = S*[S.0+S.1]*S
> sage: Q = S.quo(I)
> }}}
>
> - sage/rings/morphism.pyx :
> - RingMap_lift
> {{{
> sage: MS = MatrixSpace(GF(5),2,2)
> sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
> sage: Q = MS.quo(I)
> }}}
> - sage/rings/ring.pyx:
> - Ring.ideal_monoid
> {{{
> sage: F.<x,y,z> = FreeAlgebra(ZZ, 3)
> sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
> sage: Q = sage.rings.ring.Ring.quotient(F,I)
> }}}
> - Ring.quotient
> {{{
> sage: R.<x> = PolynomialRing(ZZ)
> sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
> sage: S = R.quotient(I, 'a')
> }}}
> - Ring.quotient_ring
> {{{
> sage: R.<x> = PolynomialRing(ZZ)
> sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
> sage: S = R.quotient_ring(I, 'a')
> sage: S.gens()
> }}}
>
> These examples have to be modified, one possibility is that they use
> quotient rings which fulfill the assumption or the reduce function of the
> corresponding ideal class must be provided.
>
> See also ticket:13345 and https://groups.google.com/d/topic/sage-
> devel/s5y604ZPiQ8/discussion.
New description:
The following files use quotient rings in their doctest examples, which
contradict the assumption on the defining ideal:
ASSUMPTION:
`I` has a method `I.reduce(x)` returning the normal form
of elements `x\in R`. In other words, it is required that
`I.reduce(x)==I.reduce(y)` `\iff x-y \in I`, and
`x-I.reduce(x) in I`, for all `x,y\in R`.
- sage/categories/pushout.py :
- QuotientFunctor.__cmp__
{{{
sage: P.<x> = QQ[]
sage: F =
P.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
sage: F == loads(dumps(F))
True
sage: P2.<x,y> = QQ[]
sage: F ==
P2.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
False
sage: P3.<x> = ZZ[]
sage: F ==
P3.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0]
True
}}}
- sage/categories/rings.py :
- Rings.quotient
{{{
sage: F.<x,y,z> = FreeAlgebra(QQ, 3)
sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
sage: Q = Rings().parent_class.quotient(F,I); Q
}}}
- Rings.quo
{{{
sage: MS = MatrixSpace(QQ,2)
sage: MS.full_category_initialisation()
sage: I = MS*MS.gens()*MS
sage: MS.quo(I,names = ['a','b','c','d'])
}}}
- Rings.quotient_ring
{{{
sage: MS = MatrixSpace(QQ,2)
sage: I = MS*MS.gens()*MS
sage: MS.quotient_ring(I,names = ['a','b','c','d'])
}}}
- sage/structure/category_object.pyx :
- CategoryObject.__temporarily_change_names
{{{
sage: MS = MatrixSpace(GF(5),2,2)
sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
sage: Q.<a,b,c,d> = MS.quo(I)
}}}
- sage/rings/quotient_ring_element.py :
- QuotientRingElement
{{{
sage: R.<x> = PolynomialRing(ZZ)
sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
}}}
- QuotientRingElement.__init__
{{{
sage: R.<x> = PolynomialRing(ZZ)
sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
}}}
- QuotientRingElement._repr_
{{{
sage: S = SteenrodAlgebra(2)
sage: I = S*[S.0+S.1]*S
sage: Q = S.quo(I)
}}}
- sage/rings/morphism.pyx :
- RingMap_lift
{{{
sage: MS = MatrixSpace(GF(5),2,2)
sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
sage: Q = MS.quo(I)
}}}
- sage/rings/ring.pyx:
- Ring.ideal_monoid
{{{
sage: F.<x,y,z> = FreeAlgebra(ZZ, 3)
sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
sage: Q = sage.rings.ring.Ring.quotient(F,I)
}}}
- Ring.quotient
{{{
sage: R.<x> = PolynomialRing(ZZ)
sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
sage: S = R.quotient(I, 'a')
}}}
- Ring.quotient_ring
{{{
sage: R.<x> = PolynomialRing(ZZ)
sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
sage: S = R.quotient_ring(I, 'a')
sage: S.gens()
}}}
These examples have to be modified, one possibility is that they use
quotient rings which fulfill the assumption or the reduce function of the
corresponding ideal class must be provided.
See also ticket:13345 and https://groups.google.com/d/topic/sage-
devel/s5y604ZPiQ8/discussion.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/13347#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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