Пример #1
0
    def __init__(self):
        """
        Initialize ``self``.

        EXAMPLES::

            sage: S = WeakReversePlanePartitions()
            sage: TestSuite(S).run()
        """
        Tableaux.__init__(self, category=Sets())
Пример #2
0
    def __init__(self):
        """
        Initialize ``self``.

        EXAMPLES::

            sage: S = WeakReversePlanePartitions()
            sage: TestSuite(S).run()
        """
        Tableaux.__init__(self, category=Sets())
Пример #3
0
    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
Пример #4
0
    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
Пример #5
0
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'))
Пример #6
0
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))
Пример #7
0
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'))
Пример #8
0
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))