Check doctest examples using QuotientRings, which do not fulfill the assumptions made on the ideal

[tfeulner]

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.

[mstreng]

Wow, that's a long list of faulty quotient rings in the documentation! Can you add the examples themselves, as line numbers tend to change a lot as Sage evolves?