REF: Use Styler implementation for DataFrame.to_latex (#47970)

* Base implementation

* Base implementation

* test fix up

* test fix up

* test fix up

* doc change

* doc change

* doc change

* mypy fixes

* ivanov doc comment

* ivanov doc comment

* rhshadrach reduction

* change text  from 1.5.0 to 2.0.0

* remove argument col_space and add whatsnew

* mroeschke requests

* mroeschke requests

* pylint fix

* Whats new text improvements and description added

* Update doc/source/whatsnew/v2.0.0.rst

Co-authored-by: Matthew Roeschke <10647082+mroeschke@users.noreply.github.com>

* Update doc/source/whatsnew/v2.0.0.rst

* remove trailing whitespace

* remove trailing whitespace

* Whats new linting fixes

* mroeschke requests

Co-authored-by: JHM Darbyshire (iMac) <attack68@users.noreply.github.com>
Co-authored-by: Matthew Roeschke <10647082+mroeschke@users.noreply.github.com>

doc/source/whatsnew/v2.0.0.rst

@@ -454,6 +454,37 @@ Now, the axes return an empty :class:`RangeIndex`.
    pd.Series().index
    pd.DataFrame().axes
 
+.. _whatsnew_200.api_breaking.to_latex:
+
+DataFrame to LaTeX has a new render engine
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The existing :meth:`DataFrame.to_latex` has been restructured to utilise the
+extended implementation previously available under :meth:`.Styler.to_latex`.
+The arguments signature is similar, albeit ``col_space`` has been removed since
+it is ignored by LaTeX engines. This render engine also requires ``jinja2`` as a
+dependency which needs to be installed, since rendering is based upon jinja2 templates.
+
+The pandas options below are no longer used and will be removed in future releases.
+The alternative options giving similar functionality are indicated below:
+
+- ``display.latex.escape``: replaced with ``styler.format.escape``,
+- ``display.latex.longtable``: replaced with ``styler.latex.environment``,
+- ``display.latex.multicolumn``, ``display.latex.multicolumn_format`` and
+  ``display.latex.multirow``: replaced with ``styler.sparse.rows``,
+  ``styler.sparse.columns``, ``styler.latex.multirow_align`` and
+  ``styler.latex.multicol_align``,
+- ``display.latex.repr``: replaced with ``styler.render.repr``,
+- ``display.max_rows`` and ``display.max_columns``: replace with
+  ``styler.render.max_rows``, ``styler.render.max_columns`` and
+  ``styler.render.max_elements``.
+
+Note that the behaviour of ``_repr_latex_`` is also changed. Previously
+setting ``display.latex.repr`` would generate LaTeX only when using nbconvert for a
+JupyterNotebook, and not when the user is running the notebook. Now the
+``styler.render.repr`` option allows control of the specific output
+within JupyterNotebooks for operations (not just on nbconvert). See :issue:`39911`.
+
 .. _whatsnew_200.api_breaking.deps:
 
 Increased minimum versions for dependencies
@@ -619,6 +650,7 @@ Removal of prior version deprecations/changes
 - Removed deprecated :meth:`.Styler.set_na_rep` and :meth:`.Styler.set_precision` (:issue:`49397`)
 - Removed deprecated :meth:`.Styler.where` (:issue:`49397`)
 - Removed deprecated :meth:`.Styler.render` (:issue:`49397`)
+- Removed deprecated argument ``col_space`` in :meth:`DataFrame.to_latex` (:issue:`47970`)
 - Removed deprecated argument ``null_color`` in :meth:`.Styler.highlight_null` (:issue:`49397`)
 - Removed deprecated argument ``check_less_precise`` in :meth:`.testing.assert_frame_equal`, :meth:`.testing.assert_extension_array_equal`, :meth:`.testing.assert_series_equal`,  :meth:`.testing.assert_index_equal` (:issue:`30562`)
 - Removed deprecated ``null_counts`` argument in :meth:`DataFrame.info`. Use ``show_counts`` instead (:issue:`37999`)
@@ -793,6 +825,7 @@ Removal of prior version deprecations/changes
 - Changed behavior of comparison of ``NaT`` with a ``datetime.date`` object; these now raise on inequality comparisons (:issue:`39196`)
 - Enforced deprecation of silently dropping columns that raised a ``TypeError`` in :class:`Series.transform` and :class:`DataFrame.transform` when used with a list or dictionary (:issue:`43740`)
 - Changed behavior of :meth:`DataFrame.apply` with list-like so that any partial failure will raise an error (:issue:`43740`)
+- Changed behaviour of :meth:`DataFrame.to_latex` to now use the Styler implementation via :meth:`.Styler.to_latex` (:issue:`47970`)
 - Changed behavior of :meth:`Series.__setitem__` with an integer key and a :class:`Float64Index` when the key is not present in the index; previously we treated the key as positional (behaving like ``series.iloc[key] = val``), now we treat it is a label (behaving like ``series.loc[key] = val``), consistent with :meth:`Series.__getitem__`` behavior (:issue:`33469`)
 - Removed ``na_sentinel`` argument from :func:`factorize`, :meth:`.Index.factorize`, and :meth:`.ExtensionArray.factorize` (:issue:`47157`)
 - Changed behavior of :meth:`Series.diff` and :meth:`DataFrame.diff` with :class:`ExtensionDtype` dtypes whose arrays do not implement ``diff``, these now raise ``TypeError`` rather than casting to numpy (:issue:`31025`)