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gh-35537: Fix Sphinx markup in some file <!-- Please provide a concise, informative and self-explanatory title. --> <!-- Don't put issue numbers in the title. Put it in the Description below. --> <!-- For example, instead of "Fixes #12345", use "Add a new method to multiply two integers" --> ### 📚 Description <!-- Describe your changes here in detail. --> Math equations should be marked in the math environment. Change the Sphinx markup in src/sage/categories/crystals.py <!-- Why is this change required? What problem does it solve? --> Fix some Sphinx markup as posted in Issue #35496 <!-- If this PR resolves an open issue, please link to it here. For example "Fixes #12345". --> Fixes #35496 <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x ]`. --> - [ ] The title is concise, informative, and self-explanatory. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - #12345: short description why this is a dependency - #34567: ... --> - #35536: branch is on top of this PR to fix a build issue in conda <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: #35537 Reported by: xuluze Reviewer(s):
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src/sage/categories/crystals.py

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@@ -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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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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- ``filename`` -- name of the output file, e.g., ``'filename.mp'``
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- ``thicklines`` -- (default: ``True``) for thicker edges
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- ``labels`` -- (default: False) to suppress labeling of the vertices
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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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- ``tallness`` -- (default: ``1.0``) Increasing makes the image taller
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without increasing the width
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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]`
1565-
such that `self = f_{i_1} ... f_{i_k} u`, where `i_1,...,i_k` are
1573+
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
1569-
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::
15721580
@@ -1603,11 +1611,11 @@ def to_highest_weight(self, index_set=None):
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def to_lowest_weight(self, index_set=None):
16041612
r"""
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Return the lowest weight element `u` and a list `[i_1,...,i_k]`
1606-
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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