Ticket #8800: referee.patch

File referee.patch, 3.1 KB (added by lftabera, 10 years ago)
  • sage/categories/pushout.py

    # HG changeset patch
    # User Luis Felipe Tabera Alonso <lftabera@yahoo.es>
    # Parent 1c08d131a36f9c3e6a341373a4f257d56916adbe
    #8800: doctest coverage of sage/categories/functor and sage/categories/pushout;
    
    diff -r 1c08d131a36f sage/categories/pushout.py
    a b  
    26862686        """
    26872687        Mathematically, Algebraic Closure subsumes Algebraic Extension.
    26882688        However, it seems that people do want to work with algebraic
    2689         extensions of ``RR``. Therefore, we dont merge with algebraic extension.
     2689        extensions of ``RR``. Therefore, we do not merge with algebraic extension.
    26902690
    26912691        TEST::
    26922692
     
    28512851def pushout(R, S):
    28522852    r"""
    28532853    Given a pair of Objects R and S, try and construct a
    2854     reasonable object $Y$ and return maps such that
     2854    reasonable object Y and return maps such that
    28552855    canonically $R \leftarrow Y \rightarrow S$.
    28562856   
    28572857    ALGORITHM:
    28582858   
    28592859    This incorporates the idea of functors discussed Sage Days 4.
    2860     Every object $R$ can be viewed as an initial object and
     2860    Every object R can be viewed as an initial object and
    28612861    a series of functors (e.g. polynomial, quotient, extension,
    28622862    completion, vector/matrix, etc.). Call the series of
    28632863    increasingly-simple rings (with the associated functors)
    2864     the "tower" of $R$. The \code{construction} method is used to
     2864    the "tower" of R. The construction method is used to
    28652865    create the tower.
    28662866
    2867     Given two objects $R$ and $S$, try and find a common initial
    2868     object $Z$. If the towers of $R$ and $S$ meet, let $Z$ be their
     2867    Given two objects R and S, try and find a common initial
     2868    object Z. If the towers of R and S meet, let Z be their
    28692869    join. Otherwise, see if the top of one coerces naturally into
    28702870    the other.
    28712871
    2872     Now we have an initial object and two \emph{ordered} lists of
     2872    Now we have an initial object and two ordered lists of
    28732873    functors to apply. We wish to merge these in an unambiguous order,
    28742874    popping elements off the top of one or the other tower as we
    2875     apply them to $Z$.
     2875    apply them to Z.
    28762876
    28772877    - If the functors are distinct types, there is an absolute ordering
    28782878      given by the rank attribute. Use this.
     
    28812881
    28822882      - If the tops are equal, we (try to) merge them.
    28832883
    2884       - If \emph{exactly} one occurs lower in the other tower
     2884      - If exactly one occurs lower in the other tower
    28852885        we may unambiguously apply the other (hoping for a later merge).
    28862886
    28872887      - If the tops commute, we can apply either first.
     
    28902890             
    28912891    EXAMPLES:
    28922892   
    2893     Here our "towers" are $R = Complete_7(Frac(\ZZ)$ and $Frac(Poly_x(\ZZ))$,
    2894     which give us $Frac(Poly_x(Complete_7(Frac(\ZZ)))$::
     2893    Here our "towers" are $R = Complete_7(Frac(\ZZ))$ and $Frac(Poly_x(\ZZ))$,
     2894    which give us $Frac(Poly_x(Complete_7(Frac(\ZZ))))$::
    28952895
    28962896        sage: from sage.categories.pushout import pushout
    28972897        sage: pushout(Qp(7), Frac(ZZ['x']))