Ticket #5794: trac_5794-reviewer-nt.patch

File trac_5794-reviewer-nt.patch, 5.9 KB (added by bump, 13 years ago)
  • sage/combinat/root_system/weyl_characters.py

    ReST fixes and improvements
    
    diff --git a/sage/combinat/root_system/weyl_characters.py b/sage/combinat/root_system/weyl_characters.py
    a b class WeylCharacter(AlgebraElement): 
    212212
    213213    def cartan_type(self):
    214214        """
    215         Returns the Cartan Type.
     215        Returns the Cartan type.
    216216
    217217        EXAMPLES::
    218218
    class WeylCharacter(AlgebraElement): 
    315315        rule is specified, we will try to specify one.
    316316       
    317317        INPUT:
    318        
    319        
    320         -  ``S`` - a Weyl character ring for a Lie subgroup or
     318
     319         - ``S`` - a Weyl character ring for a Lie subgroup or
    321320           subalgebra
    322        
    323         -  ``rule`` - a branching rule.
     321
     322         -  ``rule`` - a branching rule.
    324323       
    325324       
    326325        See branch_weyl_character? for more information about branching
    class WeylCharacter(AlgebraElement): 
    358357       
    359358            sage: B3 = WeylCharacterRing(['B',3])
    360359            sage: [B3(x).is_irreducible() for x in B3.fundamental_weights()]
    361              [True, True, True]
     360            [True, True, True]
    362361            sage: sum(B3(x) for x in B3.fundamental_weights()).is_irreducible()
    363              False
     362            False
    364363        """
    365364        h = self.hlist()
    366365        return len(h) is 1 and h[0][1] is 1
    class WeylCharacter(AlgebraElement): 
    370369        Returns the symmetric square of the character.
    371370
    372371        EXAMPLES::
    373        
     372
    374373            sage: A2 = WeylCharacterRing("A2",style="coroots")
    375374            sage: A2(1,0).symmetric_square()
    376              A2(2,0)
     375            A2(2,0)
    377376        """
    378 
    379377        cmlist = self.mlist()
    380378        mdict = {}
    381379        for j in range(len(cmlist)):
    class WeylCharacter(AlgebraElement): 
    400398       
    401399            sage: A2 = WeylCharacterRing("A2",style="coroots")
    402400            sage: A2(1,0).exterior_square()
    403              A2(0,1)
     401            A2(0,1)
    404402        """
    405403        cmlist = self.mlist()
    406404        mdict = {}
    class WeylCharacter(AlgebraElement): 
    422420        """
    423421        Returns:
    424422
    425         1 if the representation is real (orthogonal)
    426         -1 if the representation is quaternionic (symplectic)   
    427         0 if the representation is complex (not self dual)
     423         - `1` if the representation is real (orthogonal)
     424
     425         - `-1` if the representation is quaternionic (symplectic)
     426
     427         - `0` if the representation is complex (not self dual)
    428428
    429429        The Frobenius-Schur indicator of a character 'chi'
    430430        of a compact group G is the Haar integral over the
    def WeylCharacterRing(ct, base_ring=ZZ,  
    481481    character of a semisimple (or reductive) Lie group or algebra. They
    482482    form a ring, in which the addition and multiplication correspond to
    483483    direct sum and tensor product of representations.
    484    
    485     INPUT:
    486484
    487     - ``ct`` - The Cartan Type
    488    
    489     OPTIONAL ARGUMENTS:
     485    INPUT:
    490486
    491     - ``base_ring`` -  (default: `\ZZ`)
     487     - ``ct`` -- The Cartan Type
    492488
    493     - ``prefix`` (default an automatically generated prefix
    494       based on Cartan type)
     489    OPTIONAL ARGUMENTS:
    495490
    496     - ``cache`` -  (default False) setting cache = True is a substantial
    497       speedup at the expense of some memory.
    498    
    499     - ``style`` - (default "lattice") can be set style = "coroots"
    500     to obtain an alternative representation of the elements.
     491     - ``base_ring`` --  (default: `\ZZ`)
     492
     493     - ``prefix`` -- (default: an automatically generated prefix based on Cartan type)
     494
     495     - ``cache`` --  (default False) setting cache = True is a substantial
     496       speedup at the expense of some memory.
     497
     498     - ``style`` -- (default "lattice") can be set style = "coroots"
     499       to obtain an alternative representation of the elements.
    501500
    502501    If no prefix specified, one is generated based on the Cartan type.
    503502    It is good to name the ring after the prefix, since then it can
    def WeylCharacterRing(ct, base_ring=ZZ,  
    562561    ring represent characters of SL(r+1,CC), while in the default
    563562    style, they represent characters of GL(r+1,CC).
    564563
    565     EXAMPLES:
     564    EXAMPLES::
    566565
    567566        sage: A2 = WeylCharacterRing("A2")
    568567        sage: L = A2.space()
    class WeylCharacterRing_class(Algebra): 
    815814
    816815    def cartan_type(self):
    817816        """
    818         Returns the Cartan Type.
     817        Returns the Cartan type.
    819818
    820819        EXAMPLES::
    821820
    def branching_rule_from_plethysm(chi, ca 
    21382137    through SO(8). The branching rule in question will
    21392138    describe how representations of SO(8) composed with
    21402139    this homomorphism decompose into irreducible characters
    2141     of SL(3).
     2140    of SL(3)::
    21422141
    21432142        sage: A2 = WeylCharacterRing("A2")
    21442143        sage: A2 = WeylCharacterRing("A2", style="coroots")
    21452144        sage: ad = A2(1,1)
    21462145        sage: ad.degree()
    2147          8
     2146        8
    21482147        sage: ad.frobenius_schur_indicator()
    2149          1
     2148        1
    21502149
    2151     This confirms that ad has degree 8 and is orthogonal,
    2152     hence factors through SO(8)=D4.
     2150    This confirms that `ad` has degree 8 and is orthogonal,
     2151    hence factors through SO(8)=D4::
    21532152
    21542153        sage: br = branching_rule_from_plethysm(ad,"D4")
    21552154        sage: D4 = WeylCharacterRing("D4")
    21562155        sage: [D4(f).branch(A2,rule = br) for f in D4.fundamental_weights()]
    2157          [A2(1,1), A2(1,1) + A2(0,3) + A2(3,0), A2(1,1), A2(1,1)]
     2156        [A2(1,1), A2(1,1) + A2(0,3) + A2(3,0), A2(1,1), A2(1,1)]
    21582157    """
    21592158    ct = CartanType(cartan_type)
    21602159    if ct[0] not in ["A","B","C","D"]:
    class WeightRingElement(AlgebraElement): 
    23762375
    23772376    def cartan_type(self):
    23782377        """
    2379         Returns the Cartan Type.
     2378        Returns the Cartan type.
    23802379
    23812380        EXAMPLES::
    23822381
    class WeightRing(Algebra): 
    26192618
    26202619    def cartan_type(self):
    26212620        """
    2622         Returns the Cartan Type.
     2621        Returns the Cartan type.
    26232622
    26242623        EXAMPLES::
    26252624