Coverage for local/lib/python2.7/site-packages/sage/combinat/output.py : 100%

""" 

Output functions 

These are the output functions for latexing partitions and tableaux. 

AUTHORS: 

- Mike Hansen (?): initial version 

- Andrew Mathas (2013-02-14): Added support for displaying conventions and 

lines, and tableaux of skew partition, composition, and 

skew/composition/partition/tableaux tuple shape. 

""" 

from __future__ import absolute_import, print_function 

from six.moves import range 

from string import Template 

from sage.combinat.tableau import Tableaux 

# The tex macro used to latex individual cells in an array (as a template). 

# When using bar should be replaced by '|' or ''. 

lr_macro = Template(r'\def\lr#1{\multicolumn{1}{$bar@{\hspace{.6ex}}c@{\hspace{.6ex}}$bar}{\raisebox{-.3ex}{$$#1$$}}}') 

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.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.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.options._reset() 

""" 

lr=lr_macro.substitute(bar='|' if with_lines else '') 

if Tableaux.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.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.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_skew_array(array, with_lines=False, align='b'): 

r""" 

This function creates latex code for a "skew composition" ``array``. 

That is, for a two dimensional array in which each row can begin with 

an arbitrary number ``None``'s and the remaining entries could, in 

principe, be anything but probably should be strings or integers of similar 

width. A row consisting completely of ``None``'s is allowed. 

INPUT: 

- ``array`` -- The array 

- ``with_lines`` -- (Default: ``False``) If ``True`` lines are drawn, if 

``False`` they are not 

- ``align`` -- (Default: ``'b'``) Determines the alignment on the latex 

array environments 

EXAMPLES:: 

sage: array=[[None, 2,3,4],[None,None],[5,6,7,8]] 

sage: print(sage.combinat.output.tex_from_skew_array(array)) 

\raisebox{-.6ex}{$\begin{array}[b]{*{4}c}\\ 

&\lr{2}&\lr{3}&\lr{4}\\ 

&\\ 

\lr{5}&\lr{6}&\lr{7}&\lr{8}\\ 

\end{array}$} 

""" 

# first identify where the None's appear in ``array`` and define a 

# function end_line which puts in the required \cline's. 

if with_lines: 

# last position of None in each row 

nones=[1 if not None in row else 1+len(row)-row[::-1].index(None) for row in array] 

def end_line(r): 

# in a slightly unpythonic way, we label the lines as 0, 1, ..., len(array) 

if r==0: 

return r'\cline{%s-%s}'%(nones[0],len(array[0])) 

elif r==len(array): 

start=nones[r-1] 

finish=len(array[r-1]) 

else: 

start=min(nones[r], nones[r-1]) 

finish=max(len(array[r]), len(array[r-1])) 

return r'\\' if start>finish else r'\\\cline{%s-%s}'%(start, finish) 

else: 

end_line=lambda r: r'\\' 

# now we draw the array 

tex=r'\raisebox{-.6ex}{$\begin{array}[%s]{*{%s}c}'%(align,max(map(len,array))) 

tex+=end_line(0)+'\n' 

for r in range(len(array)): 

tex+='&'.join('' if c is None else r'\lr{%s}'%c for c in array[r]) 

tex+=end_line(r+1)+'\n' 

return tex+r'\end{array}$}'