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 : line 2393
• sage/categories/rings.py : lines 446, 482, 522
• sage/structure/category_object.pyx : line 473
• sage/rings/quotient_ring_element.py : lines 56, 98, 208
• sage/rings/morphism.pyx : line 465
• sage/rings/ring.pyx: lines 409, 708, 792

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?