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adding a comment about chain_polynomial
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src/sage/combinat/posets/posets.py

Lines changed: 14 additions & 10 deletions
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@@ -1396,9 +1396,9 @@ def _latex_(self) -> str:
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return self.hasse_diagram()._latex_()
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def tikz(self, format=None, edge_labels=False, color_by_label=False,
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prog='dot', rankdir='up', standalone_config=None,
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usepackage=None, usetikzlibrary=None, macros=None,
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use_sage_preamble=None, **kwds):
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prog='dot', rankdir='up', standalone_config=None,
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usepackage=None, usetikzlibrary=None, macros=None,
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use_sage_preamble=None, **kwds):
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r"""
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Return a TikzPicture illustrating the poset.
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@@ -1460,10 +1460,10 @@ def tikz(self, format=None, edge_labels=False, color_by_label=False,
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"""
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G = self.hasse_diagram()
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return G.tikz(format=format, edge_labels=edge_labels,
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color_by_label=color_by_label, prog=prog, rankdir=rankdir,
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standalone_config=standalone_config, usepackage=usepackage,
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usetikzlibrary=usetikzlibrary, macros=macros,
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use_sage_preamble=use_sage_preamble, **kwds)
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color_by_label=color_by_label, prog=prog, rankdir=rankdir,
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standalone_config=standalone_config, usepackage=usepackage,
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usetikzlibrary=usetikzlibrary, macros=macros,
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use_sage_preamble=use_sage_preamble, **kwds)
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def _repr_(self) -> str:
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r"""
@@ -3596,8 +3596,8 @@ def dimension(self, certificate=False, *, solver=None, integrality_tolerance=1e-
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ALGORITHM:
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As explained [FT00]_, the dimension of a poset is equal to the (weak)
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chromatic number of a hypergraph. More precisely:
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As explained in [FT00]_, the dimension of a poset is equal to
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the (weak) chromatic number of a hypergraph. More precisely:
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Let `inc(P)` be the set of (ordered) pairs of incomparable elements
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of `P`, i.e. all `uv` and `vu` such that `u\not \leq_P v` and `v\not
@@ -7776,13 +7776,17 @@ def chain_polynomial(self):
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elements in the poset. List of coefficients of this polynomial
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is also called a *f-vector* of the poset.
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This is multiplicative with respect to ordinal sum.
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.. NOTE::
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This is not what has been called the chain polynomial
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in [St1986]_. The latter is identical with the order
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polynomial in SageMath (:meth:`order_polynomial`).
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.. SEEALSO:: :meth:`f_polynomial`, :meth:`order_polynomial`
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.. SEEALSO::
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:meth:`f_polynomial`, :meth:`order_polynomial`, :meth:`ordinal_sum`
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EXAMPLES::
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