def _latex_(self):
r"""
EXAMPLES::
sage: T = CrystalOfTableaux(['A',3], shape = [4,2])
sage: t = T(rows=[[1,1,2,3],[2,3]])
sage: latex(t) # indirect doctest
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{1-4}
\lr{1}&\lr{1}&\lr{2}&\lr{3}\\\cline{1-4}
\lr{2}&\lr{3}\\\cline{1-2}
\end{array}$}
}
"""
from sage.combinat.output import tex_from_array
# Modified version of to_tableau() to have the entrys be letters
# rather than their values
if self._list == []:
return "{\\emptyset}"
tab = [[self[0]]]
for i in range(1, len(self)):
if self[i - 1] < self[i] or (self[i - 1].value != 0
and self[i - 1] == self[i]):
tab.append([self[i]])
else:
l = len(tab) - 1
tab[l].append(self[i])
for x in tab:
x.reverse()
T = Tableau(tab).conjugate()
return tex_from_array([[letter._latex_() for letter in row]
for row in T])
def _latex_(self):
r"""
EXAMPLES::
sage: T = CrystalOfTableaux(['A',3], shape = [4,2])
sage: t = T(rows=[[1,1,2,3],[2,3]])
sage: latex(t) # indirect doctest
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\cline{1-4}
\lr{1}&\lr{1}&\lr{2}&\lr{3}\\\cline{1-4}
\lr{2}&\lr{3}\\\cline{1-2}
\end{array}$}
}
"""
from sage.combinat.output import tex_from_array
# Modified version of to_tableau() to have the entrys be letters
# rather than their values
if self._list == []:
return "{\\emptyset}"
tab = [ [self[0]] ]
for i in range(1,len(self)):
if self[i-1] < self[i] or (self[i-1].value != 0 and self[i-1] == self[i]):
tab.append([self[i]])
else:
l = len(tab)-1
tab[l].append(self[i])
for x in tab:
x.reverse()
T = Tableau(tab).conjugate()
return tex_from_array([[letter._latex_() for letter in row] for row in T])
def _latex_(self):
"""
Return a latex representation of ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['A', 4, 1], 2, 3)
sage: latex(KRT([3,2,4,2,4,3])) # indirect doctest
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{2}&\lr{2}&\lr{3}\\\cline{1-3}
\lr{3}&\lr{4}&\lr{4}\\\cline{1-3}
\end{array}$}
}
"""
from sage.combinat.output import tex_from_array
return tex_from_array(self.to_array())
def _latex_(self):
"""
Return a latex representation of ``self``.
EXAMPLES::
sage: KRT = KirillovReshetikhinTableaux(['A', 4, 1], 2, 3)
sage: latex(KRT([3,2,4,2,4,3])) # indirect doctest
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{2}&\lr{2}&\lr{3}\\\cline{1-3}
\lr{3}&\lr{4}&\lr{4}\\\cline{1-3}
\end{array}$}
}
"""
from sage.combinat.output import tex_from_array
return tex_from_array(self.to_array())
def _latex_(self):
r"""
Return latex code for ``self``.
EXAMPLES::
sage: B = crystals.Tableaux(['Q',3], shape=[3,2,1])
sage: t = B.an_element()
sage: latex(t)
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{3}c}\cline{1-3}
\lr{3}&\lr{3}&\lr{3}\\\cline{1-3}
&\lr{2}&\lr{2}\\\cline{2-3}
&&\lr{1}\\\cline{3-3}
\end{array}$}
}
"""
from sage.combinat.output import tex_from_array
return tex_from_array([[None] * i + list(reversed(row))
for i, row in enumerate(self.rows())])
def _latex_(self):
"""
LaTeX output as a young diagram.
EXAMPLES::
sage: P = Partition([2, 1])
sage: print P._latex_young_diagram()
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{2}c}\cline{1-2}
\lr{\phantom{x}}&\lr{\phantom{x}}\\\cline{1-2}
\lr{\phantom{x}}\\\cline{1-1}
\end{array}$}
}
"""
if len(self._list) == 0:
return "{\\emptyset}"
from sage.combinat.output import tex_from_array
return tex_from_array([ ["\\phantom{x}"]*row_size for row_size in self._list ])
def _latex_(self):
"""
LaTeX output as a young diagram.
EXAMPLES::
sage: P = Partition([2, 1])
sage: print P._latex_young_diagram()
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{2}c}\cline{1-2}
\lr{\phantom{x}}&\lr{\phantom{x}}\\\cline{1-2}
\lr{\phantom{x}}\\\cline{1-1}
\end{array}$}
}
"""
if len(self._list) == 0:
return "{\\emptyset}"
from sage.combinat.output import tex_from_array
return tex_from_array([ ["\\phantom{x}"]*row_size for row_size in self._list ])
def latex_dual(elt):
r"""
Return a latex representation of a type `A_n` crystal tableau ``elt``
expressed in terms of dual letters.
The dual letter of `k` is expressed as `\overline{n+2-k}`.
EXAMPLES::
sage: from sage.combinat.crystals.kac_modules import latex_dual
sage: T = crystals.Tableaux(['A',2], shape=[2,1])
sage: print(latex_dual(T[0]))
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{2}c}\cline{1-2}
\lr{\overline{3}}&\lr{\overline{3}}\\\cline{1-2}
\lr{\overline{2}}\\\cline{1-1}
\end{array}$}
}
"""
M = elt.parent().cartan_type().rank() + 2
from sage.combinat.tableau import Tableau
from sage.combinat.output import tex_from_array
# Modified version of to_tableau() to have the entries be letters
# rather than their values
if not elt:
return "{\\emptyset}"
tab = [["\\overline{{{}}}".format(M - elt[0].value)]]
for i in range(1, len(elt)):
if elt[i - 1] < elt[i] or (elt[i - 1].value != 0
and elt[i - 1] == elt[i]):
tab.append(["\\overline{{{}}}".format(M - elt[i].value)])
else:
l = len(tab) - 1
tab[l].append("\\overline{{{}}}".format(M - elt[i].value))
for x in tab:
x.reverse()
T = Tableau(tab).conjugate()
return tex_from_array([list(row) for row in T])
def latex_dual(elt):
r"""
Return a latex representation of a type `A_n` crystal tableau ``elt``
expressed in terms of dual letters.
The dual letter of `k` is expressed as `\overline{n+2-k}`.
EXAMPLES::
sage: from sage.combinat.crystals.kac_modules import latex_dual
sage: T = crystals.Tableaux(['A',2], shape=[2,1])
sage: print(latex_dual(T[0]))
{\def\lr#1{\multicolumn{1}{|@{\hspace{.6ex}}c@{\hspace{.6ex}}|}{\raisebox{-.3ex}{$#1$}}}
\raisebox{-.6ex}{$\begin{array}[b]{*{2}c}\cline{1-2}
\lr{\overline{3}}&\lr{\overline{3}}\\\cline{1-2}
\lr{\overline{2}}\\\cline{1-1}
\end{array}$}
}
"""
M = elt.parent().cartan_type().rank() + 2
from sage.combinat.output import tex_from_array
# Modified version of to_tableau() to have the entries be letters
# rather than their values
if not elt:
return "{\\emptyset}"
tab = [ ["\\overline{{{}}}".format(M-elt[0].value)] ]
for i in range(1, len(elt)):
if elt[i-1] < elt[i] or (elt[i-1].value != 0 and elt[i-1] == elt[i]):
tab.append(["\\overline{{{}}}".format(M-elt[i].value)])
else:
l = len(tab)-1
tab[l].append("\\overline{{{}}}".format(M-elt[i].value))
for x in tab:
x.reverse()
from sage.combinat.tableau import Tableau
T = Tableau(tab).conjugate()
from sage.combinat.output import tex_from_array
return tex_from_array([list(row) for row in T])