OGr-k-2n+1.ipynb

Kernel: SageMath 10.3

%run '/home/user/Equivariant_Vector_Bundles_On_Homogeneous_Varieties__0-0-1/src/Initialize.ipynb'

Minimal_n = 2
Maximal_n = 10

Keys   = [ 'Base_Space' , 'Ist/Soll' , 'Tooltips', 'Numerically_Exceptional' , 'Cell_Coloring' , 'Cell_Bordering' ]
Data   = { Key : [] for Key in Keys }
Header = [ str(Node) for Node in [ 1 .. Maximal_n ] ]

for n in [ Minimal_n .. Maximal_n ] :
    for Key in Data.keys() :
        if Key in [ 'CellColoring' , 'CellBordering' ] : Value = ''
        else : Value = None
        Data[Key] += [ n * [ '?' ] + (Maximal_n-n) * [ Value ] ]

    for k in [ 1 .. n ] : #[ 1 .. n ] : #[ 1 .. CartanDegree ] :
        X = Orthogonal_Grassmannian( k , 2*n+1 )
        fw = X.Basis('fw')

        if k <= 3 : LC  = X.Tautological_Collection( Parts=[1,2] )
        else      : LC  = X.Tautological_Collection( Parts=[1] )
        LC += X.Spinor_Collection()

        Case = { Key : None for Key in Keys }
        # Base space
        Case['Base_Space'] = X.__str__( Output_Style='Short' )
        # Ist/Soll and Cell_Bordering
        Ist  = len(LC)
        Soll = X.K0().rank()
        Case['Ist/Soll'] = str(Ist)+ ' / '+str(Soll)
        if Ist == Soll : Case['Cell_Bordering'] = 'Maximal_Expected_Length'
        else           : Case['Cell_Bordering'] = ''
        # Tooltips
        Case['Tooltips'] = ', '.join([ str(Object) for Object in LC.Starting_Block() ]) + '   '
        # Numerically_Exceptional and Cell_Coloring
        if LC.Is_Numerically_Exceptional() :
            Case['Numerically_Exceptional'] = True
            Case['Cell_Coloring']           = 'Numerically_Exceptional'
        else :
            Case['Numerically_Exceptional'] = False
            Case['Cell_Coloring']           = 'Not_Exceptional'
        # Transfer single case into Data-Pool.
        for Key , Value in Case.items() :
            Data[Key][-1][k-1] = Value
        # Implement dataframe.
        Index = pd.Index( [Minimal_n .. n] , name='n:' )
        Columns = pd.Index( [1 .. Maximal_n] , name='k:')
        DF = {}
        for Key , Rows in Data.items() :
            DF.update({ Key : pd.DataFrame( Rows , index=Index , columns=Columns ) })
        S = DF['Ist/Soll'].style
        S = DF['Ist/Soll'].style\
            .set_caption("Working status for exceptional collections on homogeneous varieties belonging to the Cartan family B.")\
            .set_table_styles( [ { 'selector' : '' , 'props' :  'border-collapse: separate;' } ,
                                 { 'selector' : 'caption' , 'props' : 'caption-side: bottom; font-size:1.3em;' } ,
                                 { 'selector' : '.index_name' , 'props' : 'font-style: italic; color: darkgrey; font-weight:normal;' } ,
                                 { 'selector' : 'th:not(.index_name)' , 'props' : 'background-color: #FFA500; color: white;' } ,
                                 { 'selector' : 'th.col_heading' , 'props' : 'text-align: center;' } ,
                                 { 'selector' : 'td' , 'props' : 'text-align: center; font-weight:normal;' } ,
                                 { 'selector' : '.Maximal_Expected_Length' ,'props' : 'border: 2px dashed green;' } ,
                                 { 'selector' : '.Numerically_Exceptional' ,'props' : 'background-color: #e6ffe6;' } ,
                                 { 'selector' : '.Not_Exceptional' , 'props' : 'background-color: #f28080;' } ,
                                 { 'selector' : 'td:hover' , 'props' : 'background-color: #ffffb3;' }
                               ] ,
                               overwrite=False
                             )\
            .set_tooltips( DF['Tooltips'] ,
                           css_class='pd-tt' ,
                           props='visibility: hidden; position: absolute; z-index: 1; border: 1px solid #000066;'
                                 'background-color: white; color: #000066; font-size: 0.8em;'
                                 'transform: translate(0px, -24px); padding: 0.6em; border-radius: 0.5em;'
                         )\
            .set_td_classes( DF['Cell_Coloring'] )
        clear_output(wait=True)
        display(S)