A new command, \numberbysection, which should appear only in
the preamble, places the equation, figure, table, and theorem counters
within the section counter and redefines \the<counter> to be
\thesection.\arabic{<counter>}. The change is inherited by all
theorem environments that are defined to be numbered with
theorem (however, be sure to create the theorem
environments before invoking \numberbysection).
In article style, \numberbysection is the natural way to
write a paper. In the report style, the user of
\numberbysection must provide explicit chapter numbers
when referencing equations, theorems, etc. This is no hardship
if you adopt the convention that references without chapter
numbers refer to the current chapter, since in most works
references tend to be to nearby items. If you do this you may
want to redefine \thechapter to be
\Roman{chapter}. Then (2.5.2) can refer to the second
item of equation (2.5) in the current chapter, while (II.5.2)
refers equation (5.2) in Chapter II.
An analogous command, \numberbysubsection, causes the
counters to be reset when subsections change. This option is
especially useful for a style of writing in which the work is
broken up into short subsections of one or two paragraphs, each
with its own heading. Try writing this way if you have
temporary writer's block. At its best the technique produces a
lively work that moves quickly from topic to topic. At its
worst it produces a rambling, ill-organized mish-mash.