@@ -919,7 +919,7 @@ def digraph(self, subset=None, index_set=None):
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def latex_file (self , filename ):
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r"""
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- Export a file, suitable for pdflatex, to ' filename' .
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+ Export a file, suitable for pdflatex, to `` filename`` .
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This requires
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a proper installation of ``dot2tex`` in sage-python. For more
@@ -954,7 +954,7 @@ def latex_file(self, filename):
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def _latex_ (self , ** options ):
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r"""
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Returns the crystal graph as a latex string. This can be exported
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- to a file with self.latex_file('filename').
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+ to a file with `` self.latex_file('filename')`` .
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EXAMPLES::
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@@ -977,15 +977,9 @@ def _latex_(self, **options):
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def metapost (self , filename , thicklines = False , labels = True , scaling_factor = 1.0 , tallness = 1.0 ):
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r"""
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- Use C.metapost("filename.mp",[options]), where options can be:
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+ Export a file, suitable for MetaPost, to ``filename``.
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- thicklines = True (for thicker edges) labels = False (to suppress
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- labeling of the vertices) scaling_factor=value, where value is a
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- floating point number, 1.0 by default. Increasing or decreasing the
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- scaling factor changes the size of the image. tallness=1.0.
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- Increasing makes the image taller without increasing the width.
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-
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- Root operators e(1) or f(1) move along red lines, e(2) or f(2)
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+ Root operators `e(1)` or `f(1)` move along red lines, `e(2)` or `f(2)`
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along green. The highest weight is in the lower left. Vertices with
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the same weight are kept close together. The concise labels on the
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nodes are strings introduced by Berenstein and Zelevinsky and
@@ -994,20 +988,34 @@ def metapost(self, filename, thicklines=False, labels=True, scaling_factor=1.0,
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For Cartan types B2 or C2, the pattern has the form
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- a2 a3 a4 a1
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+ `a_2 a_3 a_4 a_1`
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- where c\*a2 = a3 = 2\*a4 =0 and a1=0 , with c=2 for B2, c=1 for C2.
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- Applying e(2) a1 times, e(1) a2 times, e(2) a3 times, e(1) a4 times
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+ where `c*a_2 = a_3 = 2*a_4 = 0` and `a_1=0` , with ` c=2` for B2, ` c=1` for C2.
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+ Applying ` e(2)` `a_1` times, ` e(1)` `a_2` times, ` e(2)` `a_3` times, ` e(1)` `a_4` times
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returns to the highest weight. (Observe that Littelmann writes the
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- roots in opposite of the usual order, so our e(1) is his e(2) for
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+ roots in opposite of the usual order, so our ` e(1)` is his ` e(2)` for
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these Cartan types.) For type A2, the pattern has the form
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- a3 a2 a1
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+ `a_3 a_2 a_1`
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- where applying e(1) a1 times, e(2) a2 times then e(3) a1 times
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+ where applying ` e(1)` `a_3` times, ` e(2)` `a_2` times then `e(1)` `a_1` times
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returns to the highest weight. These data determine the vertex and
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may be translated into a Gelfand-Tsetlin pattern or tableau.
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+ INPUT:
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+
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+ - ``filename`` -- name of the output file, e.g., ``'filename.mp'``
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+
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+ - ``thicklines`` -- (default: ``True``) for thicker edges
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+
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+ - ``labels`` -- (default: False) to suppress labeling of the vertices
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+
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+ - ``scaling_factor`` -- (default: ``1.0``) Increasing or decreasing the
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+ scaling factor changes the size of the image
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+
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+ - ``tallness`` -- (default: ``1.0``) Increasing makes the image taller
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+ without increasing the width
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+
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EXAMPLES::
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sage: C = crystals.Letters(['A', 2])
@@ -1450,7 +1458,7 @@ def Phi(self):
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def f_string (self , list ):
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r"""
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- Applies `f_{i_r} \cdots f_{i_1}` to self for ``list`` as
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+ Applies `f_{i_r} \cdots f_{i_1}` to `` self`` for ``list`` as
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`[i_1, ..., i_r]`
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EXAMPLES::
@@ -1470,7 +1478,7 @@ def f_string(self, list):
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def e_string (self , list ):
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r"""
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- Applies `e_{i_r} \cdots e_{i_1}` to self for ``list`` as
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+ Applies `e_{i_r} \cdots e_{i_1}` to `` self`` for ``list`` as
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`[i_1, ..., i_r]`
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EXAMPLES::
@@ -1562,11 +1570,11 @@ def is_lowest_weight(self, index_set=None):
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def to_highest_weight (self , index_set = None ):
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r"""
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Return the highest weight element `u` and a list `[i_1,...,i_k]`
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- such that `self = f_{i_1} ... f_{i_k} u`, where `i_1,...,i_k` are
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+ such that `` self`` ` = f_{i_1} ... f_{i_k} u`, where `i_1,...,i_k` are
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elements in ``index_set``.
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- By default the index set is assumed to be
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- the full index set of self.
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+ By default the ``index_set`` is assumed to be
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+ the full index set of `` self`` .
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EXAMPLES::
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@@ -1603,11 +1611,11 @@ def to_highest_weight(self, index_set=None):
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def to_lowest_weight (self , index_set = None ):
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r"""
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Return the lowest weight element `u` and a list `[i_1,...,i_k]`
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- such that `self = e_{i_1} ... e_{i_k} u`, where `i_1,...,i_k` are
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+ such that `` self`` ` = e_{i_1} ... e_{i_k} u`, where `i_1,...,i_k` are
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elements in ``index_set``.
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- By default the index set is assumed to be the full index
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- set of self.
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+ By default the ``index_set`` is assumed to be the full index
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+ set of `` self`` .
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EXAMPLES::
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