#19889: improve coding style and documentation style in affine schemes
-------------------------------------+-------------------------------------
       Reporter:  bhutz              |        Owner:  rlmiller
           Type:  enhancement        |       Status:  needs_work
       Priority:  trivial            |    Milestone:  sage-7.0
      Component:  algebraic          |   Resolution:
  geometry                           |    Merged in:
       Keywords:                     |    Reviewers:  Ben Hutz
        Authors:  Rebecca Miller     |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  1a86718a61fec39cb0328770318cf7d82f110e2e
  u/rlmiller/ticket/19889            |     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------
Changes (by bhutz):

 * status:  needs_review => needs_work


Comment:

 There is a minor merge conflict with the latest beta.

 The docs do not build, so I wasn't able to look at them for formatting
 issues. However, I went through the changes are there are some specifics
 to fix:

 undo
 {{{
 -            if not isinstance(polys, (list, tuple)):
 +            if not isinstance(polys,(list, tuple)):
 }}}

 define - this occurs in two places
 {{{
 +        - Boolean - True if the two affine maps defined the same map.
 +        - Boolean - True if the two affine maps defined the same map.
 }}}


 map's
 {{{
 +        - ``P`` -- a point in the map domain.
 }}}

 extra space
 {{{
 +            sage: A.<x,y> =  AffineSpace(FractionField(R), 2)
 }}}

 new paragraph for 2nd sentence
 {{{
 +        Returns the multiplier of the point ``P`` of period ``n`` by the
 map.
 +        The map must be an endomorphism.
 }}}

 of the map instead of extension field
 {{{
 +            and codomain of extension field.
 }}}

 no period
 {{{
 +Scheme morphism for points on affine varieties.
 }}}

 undo
 {{{
 -        Returns the point `f^n(self)`
 +        Returns the point `f^n(point)`
 }}}

 'with this point in' instead of 'self if'
 {{{
 +        - ``f`` -- a :class:`SchemeMorphism_polynomial` with ``self`` if
 ``f.domain()``.
 }}}

 2nd sentence new paragraph
 {{{
 +        Returns the orbit of the point by `f`. If `n` is an integer it
 returns
 +        `[self,f(self), \ldots, f^{n}(self)]`.
 }}}

 missing space
 {{{
 +            sage: A.<x,y>=AffineSpace(QQ, 2)
 +            sage: H = Hom(A, A)
 +            sage: f = H([(x-2*y^2)/x,3*x*y])
 +            sage: A(9, 3).orbit(f, 3)
 }}}

 another special case to remove + associated code
 {{{
 -            add heights to integer.pyx and remove special case
 +            Add heights to integer.pyx and remove special case.
 }}}

 The 2nd sentence should be the 1st. The 1st sentence needs more info
 ('Since every...finite field, this pair always exists.')
 {{{
 +        Every point is preperiodic over a finite field.
 +
 +        This function returns the pair `[m, n]` where `m` is the
 +        preperiod and `n` is the period of the point by ``f``.
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/19889#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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