gh-38848: Adding a tikz method to FinitePoset class
    
We add a `tikz` method to the class `FinitePoset` returning a
`TikzPicture` instance from `sage.misc.latex_standalone`  module.

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

It uses the tikz method for graphs added in #38798 and the follow-up
small fix made in #38847.
    
URL: #38848
Reported by: Sébastien Labbé
Reviewer(s): Frédéric Chapoton, Travis Scrimshaw

Author: Release Manager

src/sage/combinat/posets/posets.py

@@ -1396,6 +1396,76 @@ def _latex_(self):
         """
         return self.hasse_diagram()._latex_()
 
+    def tikz(self, format=None, edge_labels=False, color_by_label=False,
+            prog='dot', rankdir='up', standalone_config=None,
+            usepackage=None, usetikzlibrary=None, macros=None,
+            use_sage_preamble=None, **kwds):
+        r"""
+        Return a TikzPicture illustrating the poset.
+
+        If ``graphviz`` and ``dot2tex`` are available, it uses these packages for
+        placements of vertices and edges.
+
+        INPUT:
+
+        - ``format`` -- string (default: ``None``), ``'dot2tex'`` or
+          ``'tkz_graph'``. If ``None``, it is set to ``'dot2tex'`` if
+          dot2tex is present, otherwise it is set to ``'tkz_graph'``.
+        - ``edge_labels`` -- bool (default: ``False``)
+        - ``color_by_label`` -- boolean or dictionary or function (default:
+          ``False``); whether to color each edge with a different color
+          according to its label; the colors are chosen along a rainbow, unless
+          they are specified by a function or dictionary mapping labels to
+          colors;
+
+        When using format ``'dot2tex'``, the following inputs are considered:
+
+        - ``prog`` -- string (default: ``'dot'``) the program used for the
+          layout corresponding to one of the software of the graphviz
+          suite: 'dot', 'neato', 'twopi', 'circo' or 'fdp'.
+        - ``rankdir`` -- string (default: ``'up'``), direction of graph layout
+          when prog is ``'dot'``, possible values are  ``'down'``,
+          ``'up'``, ``'right'`` and ``'left'``.
+
+        Additional keywords arguments are forwarded to
+        :meth:`sage.graphs.graph_latex.GraphLatex.set_option`.
+
+        The following inputs define the preamble of the latex standalone
+        document class file containing the tikzpicture:
+
+        - ``standalone_config`` -- list of strings (default: ``["border=4mm"]``);
+          latex document class standalone configuration options
+        - ``usepackage`` -- list of strings (default: ``[]``); latex
+          packages
+        - ``usetikzlibrary`` -- list of strings (default: ``[]``); tikz
+          libraries to use
+        - ``macros`` -- list of strings (default: ``[]``); list of
+          newcommands needed for the picture
+        - ``use_sage_preamble`` -- bool (default: ``None``), if ``None``
+          it is set to ``True`` if and only if format is ``'tkz_graph'``
+
+        OUTPUT:
+
+        An instance of :mod:`sage.misc.latex_standalone.TikzPicture`.
+
+        .. NOTE::
+
+            Prerequisite: dot2tex optional Sage package and graphviz must be
+            installed when using format ``'dot2tex'``.
+
+        EXAMPLES::
+
+            sage: P = Poset(([1,2], [[1,2]]), cover_relations=True)
+            sage: tikz = P.tikz()                   # optional - dot2tex graphviz        # long time
+            sage: _ = tikz.pdf(view=False)          # optional - dot2tex graphviz latex  # long time
+        """
+        G = self.hasse_diagram()
+        return G.tikz(format=format, edge_labels=edge_labels,
+            color_by_label=color_by_label, prog=prog, rankdir=rankdir,
+            standalone_config=standalone_config, usepackage=usepackage,
+            usetikzlibrary=usetikzlibrary, macros=macros,
+            use_sage_preamble=use_sage_preamble, **kwds)
+
     def _repr_(self):
         r"""
         Return a string representation of the poset.