Ticket #3660: trac_3660.patch

File trac_3660.patch, 10.0 KB (added by mhansen, 10 years ago)
  • sage/combinat/crystals/crystals.py

    # HG changeset patch
    # User Mike Hansen <mhansen@gmail.com>
    # Date 1216175127 18000
    # Node ID 7c8d2980218151168794e93ef2b01d77b2b39b7d
    # Parent  7c0da9c87d68b2d24de0846932cef50467c6f923
    imported patch doc_fixes-3660-mh.patch
    
    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/crystals/crystals.py
    a b  
    1010\begin{itemize}
    1111\item each edge has a label in $I$
    1212\item for each $i$ in $I$, each node $x$ has:
    13     - at most one $i$-successor $f_i(x)$
    14     - at most one $i$-predecessor $e_i(x)$
     13  \begin{itemize}
     14     \item at most one $i$-successor $f_i(x)$
     15     \item at most one $i$-predecessor $e_i(x)$
     16  \end{itemize}
    1517   Furthermore, when the exists,
    16     - $f_i(x)$.weight() = x.weight() - $\alpha_i$
    17     - $e_i(x)$.weight() = x.weight() + $\alpha_i$
     18   \begin{itemize}
     19     \item $f_i(x)$.weight() = x.weight() - $\alpha_i$
     20     \item $e_i(x)$.weight() = x.weight() + $\alpha_i$
     21   \end{itemize}
     22\end{itemize}
    1823
    1924This crystal actually models a representation of a Lie algebra if it
    2025satisfies some further local conditions due to Stembridge.
     
    6166syntax details may be subject to changes.
    6267
    6368TODO:
    64  - Vocabulary and conventions:
    65    - elements or vectors of a crystal?
    66    - For a classical crystal: connected / highest weight / irreducible
    67    - ...
    68  - More introductory doc explaining the mathematical background
    69  - Layout instructions for plot() for rank 2 types
    70  - Streamlining the latex output
    71  - Littelmann paths and/or alcove paths (this would give us the exceptional types)
    72  - RestrictionOfCrystal / DirectSumOfCrystals
    73  - Crystal.crystal_morphism
    74  - Affine crystals
     69\begin{itemize}
     70  \item Vocabulary and conventions:
     71  \begin{itemize}
     72    \item elements or vectors of a crystal?
     73    \item For a classical crystal: connected / highest weight / irreducible
     74    \item ...
     75  \end{itemize}
     76  \item More introductory doc explaining the mathematical background
     77  \item Layout instructions for plot() for rank 2 types
     78  \item Streamlining the latex output
     79  \item Littelmann paths and/or alcove paths (this would give us the exceptional types)
     80  \item RestrictionOfCrystal / DirectSumOfCrystals
     81  \item Crystal.crystal_morphism
     82  \item Affine crystals
     83\end{itemize}
    7584
    7685Most of the above features (except Littelmann/alcove paths) are in
    7786MuPAD-Combinat (see lib/COMBINAT/crystals.mu), which could provide
     
    157166        r"""
    158167        Runs sanity checks on the crystal:
    159168        \begin{itemize}
    160         \item Checks that count, list, and __iter__ are
     169          \item Checks that count, list, and __iter__ are
    161170        consistent. For a ClassicalCrystal, this in particular checks
    162171        that the number of elements returned by the brute force
    163172        listing and the iterator __iter__ are consistent with the Weyl
    164173        dimension formula.
    165         \item Should check Stembridge's rules, etc.
     174          \item Should check Stembridge's rules, etc.
    166175        \end{itemize}
    167176
    168177        EXAMPLES:
     
    300309        This requires dot2tex to be installed in sage-python.
    301310
    302311        Here some tips for installation:
    303          - Install graphviz >= 2.14
    304          - Make sure sage-python is >= 2.4
    305          - Download pyparsing-1.4.11.tar.gz pydot-0.9.10.tar.gz dot2tex-2.7.0.tar.gz
     312        \begin{itemize}
     313         \item Install graphviz >= 2.14
     314         \item Download pyparsing-1.4.11.tar.gz pydot-0.9.10.tar.gz dot2tex-2.7.0.tar.gz
    306315           (see the dot2tex web page for download links)
    307316           (note that the most recent version of pydot may not work.  Be sure to install the 0.9.10
    308317           version.)
    309318           Install each of them using the standard python install, but using sage-python:
    310319           
    311                 sagedir=/opt/sage-2.10-opteron-ubuntu64-x86_64-Linux/  # FIX ACCORDING TO YOUR SAGE INSTALL
    312                 sagepython=$sagedir/local/bin/sage-python
    313             for package in pyparsing-1.4.11 pydot-0.9.10 dot2tex-2.7.0; do\  # Use downloaded version nums
     320           \begin{verbatim}
     321            # FIX ACCORDING TO YOUR SAGE INSTALL
     322            export sagedir=/opt/sage/
     323            export sagepython=$sagedir/local/bin/sage-python
     324
     325            # Use downloaded version nums
     326            for package in pyparsing-1.4.11 pydot-0.9.10 dot2tex-2.7.0; do\ 
    314327                    tar zxvf $package.tar.gz;\
    315328                    cd $package;\
    316329                    sudo $sagepython setup.py install;\
    317330                    cd ..;\
    318331                done
     332           \end{verbatim}
    319333         
    320          - Install pgf-2.00 inside your latex tree
     334         \item Install pgf-2.00 inside your latex tree
    321335           In short:
    322             - untaring in /usr/share/texmf/tex/generic
    323             - clean out remaining pgf files from older version
    324             - run texhash
     336           \begin{itemize}
     337             \item untaring in /usr/share/texmf/tex/generic
     338             \item clean out remaining pgf files from older version
     339             \item run texhash
     340           \end{itemize}
     341        \end{itemize}
    325342
    326343        You should be done!
    327344        To test, go to the dot2tex-2.7.0/examples directory, and type:
    328345
    329             $sagedir//local/bin/dot2tex balls.dot > balls.tex
    330                 pdflatex balls.tex
    331                 open balls.pdf # your favorite viewer here
     346        \begin{verbatim}
     347        $sagedir//local/bin/dot2tex balls.dot > balls.tex
     348        pdflatex balls.tex
     349        open balls.pdf \#your favorite viewer here
     350        \end{verbatim}
    332351
    333352        EXAMPLES:
    334353            sage: C = CrystalOfLetters(['A', 5])
    335354            sage: C.latex() #optional requires dot2tex
     355            ...
    336356        """
    337357
    338358        try:
  • sage/combinat/crystals/tensor_product.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/crystals/tensor_product.py
    a b  
    575575        return repr(self.to_tableau())
    576576
    577577    def _latex_(self):
    578         """
     578        r"""
    579579        EXAMPLES:
    580580            sage: T = CrystalOfTableaux(['A',3], shape = [2,2])
    581581            sage: t = T(rows=[[1,2],[3,4]])
  • sage/combinat/root_system/cartan_matrix.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/root_system/cartan_matrix.py
    a b  
     1"""
     2Cartan matrices
     3"""
    14#*****************************************************************************
    25#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>,
    36#
  • sage/combinat/root_system/cartan_type.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/root_system/cartan_type.py
    a b  
     1"""
     2Cartan types
     3"""
    14#*****************************************************************************
    25#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>,
    36#
  • sage/combinat/root_system/coxeter_matrix.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/root_system/coxeter_matrix.py
    a b  
     1"""
     2Coxeter matrices
     3"""
    14#*****************************************************************************
    25#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>,
    36#
  • sage/combinat/root_system/dynkin_diagram.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/root_system/dynkin_diagram.py
    a b  
     1"""
     2Dynkin diagrams
     3"""
    14#*****************************************************************************
    25#       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>,
    36#
  • sage/combinat/root_system/root_system.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/root_system/root_system.py
    a b  
    682682        """
    683683        Create the ambient lattice for the root system for E6, E7, E8.
    684684        Specify the Base, i.e., the simple roots w.r. to the canonical
    685         basis for R^8.
     685        basis for $R^8$.
    686686       
    687687        EXAMPLES:
    688688            sage: e = RootSystem(['E',6]).ambient_lattice()
     
    864864        """
    865865        Create the ambient lattice for the root system for F4.
    866866        Specify the Base, i.e., the simple roots w.r. to the canonical
    867         basis for R^4.
     867        basis for $R^4$.
    868868
    869869        EXAMPLES:
    870870            sage: e = RootSystem(['F',4]).ambient_lattice()
  • sage/combinat/root_system/weyl_characters.py

    diff -r 7c0da9c87d68 -r 7c8d29802181 sage/combinat/root_system/weyl_characters.py
    a b  
    242242
    243243    def __pow__(self, n):
    244244        """
    245         Returns self^n.
     245        Returns $self^n$.
    246246       
    247         The coefficients in chi^k are the degrees of those irreducible representations
    248         of the symmetric group S_k corresponding to partitions of length <=3.
     247        The coefficients in $chi^k$ are the degrees of those irreducible representations
     248        of the symmetric group $S_k$ corresponding to partitions of length <=3.
    249249
    250250        EXAMPLES:
    251251            sage: A2 = WeylCharacterRing(['A',2])
     
    871871    Here A3(x,y,z,w) can be understood as a representation of SL(4). The
    872872    weights x,y,z,w and x+t,y+t,z+t,w+t represent the same representation
    873873    of SL(4) - though not of GL(4) -- since A3(x+t,y+t,z+t,w+t) is the
    874     same as A3(x,y,z,w) tensored with det^t. So as a representation of
     874    same as A3(x,y,z,w) tensored with $det^t$. So as a representation of
    875875    SL(4), A3(1/4,1/4,1/4,-3/4) is the same as A3(1,1,1,0). The exterior
    876876    square representation SL(4) --> GL(6) admits an invariant symmetric
    877877    bilinear form, so is a representation SL(4) --> SO(6) that lifts to