Ticket #3660: trac_3660.patch

a/sage/combinat/crystals/crystals.py

@@ -10 +10 @@
-\begin{itemize}
-\item each edge has a label in $I$
-\item for each $i$ in $I$, each node $x$ has:
-
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-   Furthermore, when the exists,
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-This crystal actually models a representation of a Lie algebra if it
-satisfies some further local conditions due to Stembridge.
@@ -61 +66 @@
-syntax details may be subject to changes.
-
-TODO:
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-Most of the above features (except Littelmann/alcove paths) are in
-MuPAD-Combinat (see lib/COMBINAT/crystals.mu), which could provide
@@ -157 +166 @@
-        r"""
-        Runs sanity checks on the crystal:
-        \begin{itemize}
-
+  
-        consistent. For a ClassicalCrystal, this in particular checks
-        that the number of elements returned by the brute force
-        listing and the iterator __iter__ are consistent with the Weyl
-        dimension formula.
-
+  
-        \end{itemize}
-
-        EXAMPLES:
@@ -300 +309 @@
-        This requires dot2tex to be installed in sage-python.
-
-        Here some tips for installation:
- - Install graphviz >= 2.14
-- Make sure sage-python is >= 2.
--
+\begin{itemize}
+\item Install graphviz >= 2.1
+\item
-           (see the dot2tex web page for download links)
-           (note that the most recent version of pydot may not work.  Be sure to install the 0.9.10
-           version.)
-           Install each of them using the standard python install, but using sage-python:
-           
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-                    tar zxvf $package.tar.gz;\
-                    cd $package;\
-                    sudo $sagepython setup.py install;\
-                    cd ..;\
-                done
+           \end{verbatim}
-         
--
+\item
-           In short:
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-        You should be done!
-        To test, go to the dot2tex-2.7.0/examples directory, and type:
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-
-        EXAMPLES:
-            sage: C = CrystalOfLetters(['A', 5])
-            sage: C.latex() #optional requires dot2tex
+            ...
-        """
-
-        try:

a/sage/combinat/crystals/tensor_product.py

@@ -575 +575 @@
-        return repr(self.to_tableau())
-
-    def _latex_(self):
-
+r
-        EXAMPLES:
-            sage: T = CrystalOfTableaux(['A',3], shape = [2,2])
-            sage: t = T(rows=[[1,2],[3,4]])

a/sage/combinat/root_system/cartan_matrix.py

@@ +1 @@
+"""
+Cartan matrices
+"""
-#*****************************************************************************
-#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>, 
-#

a/sage/combinat/root_system/cartan_type.py

@@ +1 @@
+"""
+Cartan types
+"""
-#*****************************************************************************
-#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>, 
-#

a/sage/combinat/root_system/coxeter_matrix.py

@@ +1 @@
+"""
+Coxeter matrices
+"""
-#*****************************************************************************
-#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>, 
-#

a/sage/combinat/root_system/dynkin_diagram.py

@@ +1 @@
+"""
+Dynkin diagrams
+"""
-#*****************************************************************************
-#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>, 
-#

a/sage/combinat/root_system/root_system.py

@@ -682 +682 @@
-        """
-        Create the ambient lattice for the root system for E6, E7, E8.
-        Specify the Base, i.e., the simple roots w.r. to the canonical
-R^8
+$R^8$
-        
-        EXAMPLES:
-            sage: e = RootSystem(['E',6]).ambient_lattice()
@@ -864 +864 @@
-        """
-        Create the ambient lattice for the root system for F4.
-        Specify the Base, i.e., the simple roots w.r. to the canonical
-R^4
+$R^4$
-
-        EXAMPLES:
-            sage: e = RootSystem(['F',4]).ambient_lattice()

a/sage/combinat/root_system/weyl_characters.py

@@ -242 +242 @@
-
-    def __pow__(self, n):
-        """
-self^n
+$self^n$
-        
-chi^k
-S_k
+$chi^k$
+$S_k$
-
-        EXAMPLES:
-            sage: A2 = WeylCharacterRing(['A',2])
@@ -871 +871 @@
-    Here A3(x,y,z,w) can be understood as a representation of SL(4). The
-    weights x,y,z,w and x+t,y+t,z+t,w+t represent the same representation
-    of SL(4) - though not of GL(4) -- since A3(x+t,y+t,z+t,w+t) is the
-det^t
+$det^t$
-    SL(4), A3(1/4,1/4,1/4,-3/4) is the same as A3(1,1,1,0). The exterior
-    square representation SL(4) --> GL(6) admits an invariant symmetric
-    bilinear form, so is a representation SL(4) --> SO(6) that lifts to