def __init__(self):
"""
Initialize ``self``.
EXAMPLES::
sage: S = WeakReversePlanePartitions()
sage: TestSuite(S).run()
"""
Tableaux.__init__(self, category=Sets())
def __init__(self):
"""
Initialize ``self``.
EXAMPLES::
sage: S = WeakReversePlanePartitions()
sage: TestSuite(S).run()
"""
Tableaux.__init__(self, category=Sets())
def __contains__(self, x):
"""
Return ``True`` if ``t`` can be interpreted as a
:class:`SemistandardSuperTableau`.
TESTS::
sage: from sage.combinat.shifted_primed_tableau import PrimedEntry
sage: T = sage.combinat.super_tableau.SemistandardSuperTableaux_all()
sage: [[1,2],[2]] in T
True
sage: [[PrimedEntry('1p'),PrimedEntry(2)],[PrimedEntry(2)]] in T
True
sage: [] in T
True
sage: Tableau([[1]]) in T
True
sage: StandardSuperTableau([[1]]) in T
Traceback (most recent call last):
...
ValueError: the entries in a standard tableau must be in bijection
with 1',1,2',2,...,n
sage: [[1,2],[1]] in T
False
sage: [[1,1],[5]] in T
True
sage: [[1,3,2]] in T
False
"""
if isinstance(x, SemistandardSuperTableau):
return True
elif Tableaux.__contains__(self, x):
x = SemistandardSuperTableau._preprocess(x)
for row in x:
if any(row[c] > row[c+1] for c in range(len(row)-1)):
return False
if not all(row[c] < row[c+1]
for c in range(len(row)-1)
if (row[c].is_primed() or row[c+1].is_primed())):
return False
for row, next in zip(x, x[1:]):
if any(row[c] > next[c] for c in range(len(next))):
return False
if not all(row[c] < next[c]
for c in range(len(next))
if (row[c].is_unprimed() or next[c].is_unprimed())):
return False
return True
else:
return False
def __contains__(self, x):
"""
Return ``True`` if ``t`` can be interpreted as a
:class:`StandardSuperTableau`.
TESTS::
sage: from sage.combinat.shifted_primed_tableau import PrimedEntry
sage: T = sage.combinat.super_tableau.StandardSuperTableaux_all()
sage: [[0.5,1],[1.5]] in T
True
sage: [[PrimedEntry('1p'),PrimedEntry('2p')],[PrimedEntry(1)]] in T
True
sage: [] in T
True
sage: Tableau([['1p']]) in T
True
sage: StandardSuperTableau([['1p']]) in T
True
sage: [[1,2],[1]] in T
False
sage: [[1,1],[5]] in T
False
sage: [[1,3,2]] in T
False
"""
if isinstance(x, StandardSuperTableau):
return True
elif Tableaux.__contains__(self, x):
x = SemistandardSuperTableau._preprocess(x)
flattened_list = [i for row in x for i in row]
a = PrimedEntry('1p')
primed_list = []
for i in range(len(flattened_list)):
primed_list.append(a)
a = a.increase_half()
# return True
return sorted(flattened_list) == primed_list and (x or
(all(row[i]<row[i+1] for row in x for i in range(len(row)-1)) and
all(x[r][c]<x[r+1][c] for r in range(len(x)-1)
for c in range(len(x[r+1])))
))
else:
return False
def tex_from_array(array, with_lines=True):
r"""
Return a latex string for a two dimensional array of partition, composition or skew composition shape
INPUT:
- ``array`` -- a list of list
- ``with_lines`` -- a boolean (default: ``True``)
Whether to draw a line to separate the entries in the array.
Empty rows are allowed; however, such rows should be given as
``[None]`` rather than ``[]``.
The array is drawn using either the English or French convention
following :meth:`Tableaux.global_options``.
.. SEEALSO:: :meth:`tex_from_array_tuple`
EXAMPLES::
sage: from sage.combinat.output import tex_from_array
sage: print tex_from_array([[1,2,3],[4,5]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\lr{4}&\lr{5}\\\cline{1-2}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\\
\lr{1}&\lr{2}&\lr{3}\\
\lr{4}&\lr{5}\\
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-4}
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\\cline{1-4}
\lr{8}\\\cline{1-1}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\
\lr{1}&\lr{2}&\lr{3}\\
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\
\lr{8}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{3-3}
&&\lr{3}\\\cline{2-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{1-4}
\lr{8}\\\cline{1-1}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{3-3}
&&\lr{3}\\\cline{2-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{2-4}
&\lr{8}\\\cline{2-2}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\
&&\lr{3}\\
&\lr{5}&\lr{6}&\lr{7}\\
\lr{8}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\
&&\lr{3}\\
&\lr{5}&\lr{6}&\lr{7}\\
&\lr{8}\\
\end{array}$}
}
sage: Tableaux.global_options(convention="french")
sage: print tex_from_array([[1,2,3],[4,5]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\cline{1-2}
\lr{4}&\lr{5}\\\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\\
\lr{4}&\lr{5}\\
\lr{1}&\lr{2}&\lr{3}\\
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\cline{1-1}
\lr{8}\\\cline{1-4}
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\\cline{1-4}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\\
\lr{8}\\
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\
\lr{1}&\lr{2}&\lr{3}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\cline{1-1}
\lr{8}\\\cline{1-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{2-4}
&&\lr{3}\\\cline{3-3}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\cline{2-2}
&\lr{8}\\\cline{2-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{2-4}
&&\lr{3}\\\cline{3-3}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\\
\lr{8}\\
&\lr{5}&\lr{6}&\lr{7}\\
&&\lr{3}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\\
&\lr{8}\\
&\lr{5}&\lr{6}&\lr{7}\\
&&\lr{3}\\
\end{array}$}
}
sage: Tableaux.global_options.reset()
"""
lr=lr_macro.substitute(bar='|' if with_lines else '')
if Tableaux.global_options("convention")=='english':
return '{%s\n%s\n}' % (lr, tex_from_skew_array(array, with_lines))
else:
return '{%s\n%s\n}' % (lr, tex_from_skew_array(array[::-1], with_lines, align='t'))
def tex_from_array_tuple(a_tuple, with_lines=True):
r"""
Return a latex string for a tuple of two dimensional array of partition,
composition or skew composition shape.
INPUT:
- ``a_tuple`` -- a tuple of lists of lists
- ``with_lines`` -- a boolean (default: ``True``)
Whether to draw lines to separate the entries in the components of ``a_tuple``.
.. SEEALSO:: :meth:`tex_from_array` for the description of each array
EXAMPLES::
sage: from sage.combinat.output import tex_from_array_tuple
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\lr{4}&\lr{5}\\\cline{1-2}
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{2-3}
&\lr{6}&\lr{7}\\\cline{2-3}
&\lr{8}\\\cline{1-2}
\lr{9}\\\cline{1-1}
\end{array}$}
}
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\\
\lr{1}&\lr{2}&\lr{3}\\
\lr{4}&\lr{5}\\
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\\
&\lr{6}&\lr{7}\\
&\lr{8}\\
\lr{9}\\
\end{array}$}
}
sage: Tableaux.global_options(convention="french")
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\cline{1-2}
\lr{4}&\lr{5}\\\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\cline{1-1}
\lr{9}\\\cline{1-2}
&\lr{8}\\\cline{2-3}
&\lr{6}&\lr{7}\\\cline{2-3}
\end{array}$}
}
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\\
\lr{4}&\lr{5}\\
\lr{1}&\lr{2}&\lr{3}\\
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\\
\lr{9}\\
&\lr{8}\\
&\lr{6}&\lr{7}\\
\end{array}$}
}
"""
lr=lr_macro.substitute(bar='|' if with_lines else '')
if Tableaux.global_options("convention")=='english':
return '{%s\n%s\n}' % (lr, ','.join(
r'\emptyset' if comp==[] else tex_from_skew_array(comp, with_lines) for comp in a_tuple))
else:
return '{%s\n%s\n}' % (lr, ','.join(
r'\emptyset' if comp==[] else tex_from_skew_array(comp[::-1], with_lines, align='t') for comp in a_tuple))
def tex_from_array(array, with_lines=True):
r"""
Return a latex string for a two dimensional array of partition, composition or skew composition shape
INPUT:
- ``array`` -- a list of list
- ``with_lines`` -- a boolean (default: ``True``)
Whether to draw a line to separate the entries in the array.
Empty rows are allowed; however, such rows should be given as
``[None]`` rather than ``[]``.
The array is drawn using either the English or French convention
following :meth:`Tableaux.global_options``.
.. SEEALSO:: :meth:`tex_from_array_tuple`
EXAMPLES::
sage: from sage.combinat.output import tex_from_array
sage: print tex_from_array([[1,2,3],[4,5]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\lr{4}&\lr{5}\\\cline{1-2}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\\
\lr{1}&\lr{2}&\lr{3}\\
\lr{4}&\lr{5}\\
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-4}
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\\cline{1-4}
\lr{8}\\\cline{1-1}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\
\lr{1}&\lr{2}&\lr{3}\\
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\
\lr{8}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{3-3}
&&\lr{3}\\\cline{2-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{1-4}
\lr{8}\\\cline{1-1}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{3-3}
&&\lr{3}\\\cline{2-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{2-4}
&\lr{8}\\\cline{2-2}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\
&&\lr{3}\\
&\lr{5}&\lr{6}&\lr{7}\\
\lr{8}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\
&&\lr{3}\\
&\lr{5}&\lr{6}&\lr{7}\\
&\lr{8}\\
\end{array}$}
}
sage: Tableaux.global_options(convention="french")
sage: print tex_from_array([[1,2,3],[4,5]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\cline{1-2}
\lr{4}&\lr{5}\\\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\\
\lr{4}&\lr{5}\\
\lr{1}&\lr{2}&\lr{3}\\
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\cline{1-1}
\lr{8}\\\cline{1-4}
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\\cline{1-4}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\end{array}$}
}
sage: print tex_from_array([[1,2,3],[4,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\\
\lr{8}\\
\lr{4}&\lr{5}&\lr{6}&\lr{7}\\
\lr{1}&\lr{2}&\lr{3}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\cline{1-1}
\lr{8}\\\cline{1-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{2-4}
&&\lr{3}\\\cline{3-3}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\cline{2-2}
&\lr{8}\\\cline{2-4}
&\lr{5}&\lr{6}&\lr{7}\\\cline{2-4}
&&\lr{3}\\\cline{3-3}
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\\
\lr{8}\\
&\lr{5}&\lr{6}&\lr{7}\\
&&\lr{3}\\
\end{array}$}
}
sage: print tex_from_array([[None,None,3],[None,5,6,7],[None,8]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{4}c}\\
&\lr{8}\\
&\lr{5}&\lr{6}&\lr{7}\\
&&\lr{3}\\
\end{array}$}
}
sage: Tableaux.global_options.reset()
"""
lr=lr_macro.substitute(bar='|' if with_lines else '')
if Tableaux.global_options("convention") == "English":
return '{%s\n%s\n}' % (lr, tex_from_skew_array(array, with_lines))
else:
return '{%s\n%s\n}' % (lr, tex_from_skew_array(array[::-1], with_lines, align='t'))
def tex_from_array_tuple(a_tuple, with_lines=True):
r"""
Return a latex string for a tuple of two dimensional array of partition,
composition or skew composition shape.
INPUT:
- ``a_tuple`` -- a tuple of lists of lists
- ``with_lines`` -- a boolean (default: ``True``)
Whether to draw lines to separate the entries in the components of ``a_tuple``.
.. SEEALSO:: :meth:`tex_from_array` for the description of each array
EXAMPLES::
sage: from sage.combinat.output import tex_from_array_tuple
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\lr{4}&\lr{5}\\\cline{1-2}
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{2-3}
&\lr{6}&\lr{7}\\\cline{2-3}
&\lr{8}\\\cline{1-2}
\lr{9}\\\cline{1-1}
\end{array}$}
}
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\\
\lr{1}&\lr{2}&\lr{3}\\
\lr{4}&\lr{5}\\
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\\
&\lr{6}&\lr{7}\\
&\lr{8}\\
\lr{9}\\
\end{array}$}
}
sage: Tableaux.global_options(convention="french")
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]])
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\cline{1-2}
\lr{4}&\lr{5}\\\cline{1-3}
\lr{1}&\lr{2}&\lr{3}\\\cline{1-3}
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\cline{1-1}
\lr{9}\\\cline{1-2}
&\lr{8}\\\cline{2-3}
&\lr{6}&\lr{7}\\\cline{2-3}
\end{array}$}
}
sage: print tex_from_array_tuple([[[1,2,3],[4,5]],[],[[None,6,7],[None,8],[9]]], with_lines=False)
{\def\lr#1{\multicolumn{1}{@{\hspace{.6ex}}c@{\hspace{.6ex}}}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\\
\lr{4}&\lr{5}\\
\lr{1}&\lr{2}&\lr{3}\\
\end{array}$},\emptyset,\raisebox{-.6ex}{$\begin{array}[t]{*{3}c}\\
\lr{9}\\
&\lr{8}\\
&\lr{6}&\lr{7}\\
\end{array}$}
}
"""
lr=lr_macro.substitute(bar='|' if with_lines else '')
if Tableaux.global_options("convention") == "English":
return '{%s\n%s\n}' % (lr, ','.join(
r'\emptyset' if comp==[] else tex_from_skew_array(comp, with_lines) for comp in a_tuple))
else:
return '{%s\n%s\n}' % (lr, ','.join(
r'\emptyset' if comp==[] else tex_from_skew_array(comp[::-1], with_lines, align='t') for comp in a_tuple))