Kuznetsov-Polishchuk-collection.ipynb

Kernel: SageMath 9.8

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

from IPython.display import clear_output , display , HTML
import pandas as pd

Cartan_Family = 'B'
n=4
k=3

G = Irreducible_Cartan_Group( Cartan_Family , n )
P = G.Maximal_Parabolic_Subgroup(k)
X = G/P
#sr = X.Basis('sr')
#fw = X.Basis('fw')
#ambt  = X.Basis('ambt')
print( 'X:' , X )
print( '(rk K_0(X) = '+str(X.K0().rank())+')' )
print()

Keys   = [ 'Output' , 'Coloring' , 'ToolTips' ]
Data   = { Key : [] for Key in Keys }

cUs_In_Previous_Blocks = []
cUs_In_Current_Block   = []
Previous_Coloring = -1
Rows = []
for Counter_Over_Collection , Counter_Over_Block , t , Highest_Weight , cE in X.Kuznetsov_Polishchuk_Collection() :
    if Counter_Over_Block == 1 :
        Coloring = (Previous_Coloring+1)%2
        cUs_In_Previous_Blocks += cUs_In_Current_Block
        cUs_In_Current_Block = []
    else                 :
        Coloring = Previous_Coloring

    cU = X.calU(Highest_Weight)
    if cU.Is_Exceptional() : Is_Exceptional = 'Yes.'
    else                   : Is_Exceptional = 'No.'
    cUs_In_Current_Block += [ cU ]
    if not False in [ Result for Result in cU.Is_SemiOrthogonal_To(cUs_In_Previous_Blocks) ] : SemiOrthogonal_Relations = 'Yes.'
    else                                                                                     : SemiOrthogonal_Relations = 'No.'

    Data['Output']   += [ [ str(t) , str(Counter_Over_Block) , str(cU) , str(Is_Exceptional) , str(SemiOrthogonal_Relations) ] ]
    Data['Coloring'] += [ 5*[str(Coloring)] ]
    Data['ToolTips'] += [ [ '' , '' , cE , '' , '' ] ]
Length = Counter_Over_Collection

# Implement dataframe.
Index = pd.Index( [ 1 .. Length ] , name='Numbering running over total collection:' )
Columns = pd.Index( [ 'Block index t' , 'Numbering running over current block' , 'cU(Lambda)' , 'Is cU(Lambda) exceptional?' , 'Is cU(Lambda) semi-orthogonal to those cU`s of the previous blocks?' ] , name='' )
DF = {}
for Key , Rows in Data.items() :
    DF.update({ Key : pd.DataFrame( Rows , index=Index , columns=Columns ) })
#DF = pd.DataFrame( Data['Rows'] , index=Index , columns=Columns )
S = DF['Output'].style
S = DF['Output'].style\
    .set_caption("Kuznetsov-Polishchuk collection on "+str( X.__str__( Output_Style='Short' ) )+".")\
    .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' : '.0' ,'props' : '' } ,
                         { 'selector' : '.1' , '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['Coloring'] )
display(S)

X: Smooth projective variety B4/P({1, 2, 4}).
(rk K_0(X) = 32)