NotebookWrite[notebook, data] writes data into a notebook at the current selection, setting the current selection to be just after the data written. NotebookWrite[notebook, ...
OpenAppend["file"] opens a file to append output to it, and returns an OutputStream object.
OverscriptBox[x, y] is the low-level box representation for OverscriptBox[x, y] in notebook expressions.
SetOptions[s, name_1 -> value_1, name_2 -> value_2, ...] sets the specified default options for a symbol s. SetOptions[stream, ...] or SetOptions["name", ...] sets options ...
x_y^z is the low-level box representation for x_y^z in notebook expressions.
Flatten
(Built-in Mathematica Symbol) Flatten[list] flattens out nested lists. Flatten[list, n] flattens to level n. Flatten[list, n, h] flattens subexpressions with head h. Flatten[list, {{s_11, s_12, ...}, ...
End Subexpression moves the cursor from a subexpression to the expression at the n\[Null]^th level.
FractionBox[x, y] is a low-level formatting construct that represents x/y in notebook expressions.
Operate
(Built-in Mathematica Symbol) Operate[p, f[x, y]] gives p[f][x, y]. Operate[p, expr, n] applies p at level n in the head of expr.
RadicalBox[x, n] is a low-level box construct that represents the displayed object Power[x, (n)^-1] in notebook expressions.