Environment to perform calculations of equivariant vector bundles on homogeneous varieties
License: GPL3
ubuntu2204
Kernel: SageMath 9.8
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Base space: OGr(4;11)
rk K0(X): 80
Fano index: 6
Objects of starting block:
Number of objects: 74
LC has maximal expected length? False
Grid of LC:
Is LC numerially exceptional? True
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len(Universe): 50
Object length: 2
-> Total number of candidates: 1225
Current object: 1120
New object to test: VB(Lambda[1] + 4*Lambda[2] - Lambda[4] + 2*Lambda[5]) + VB(4*Lambda[1] + 4*Lambda[2] - Lambda[4] + 2*Lambda[5])
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KeyboardInterrupt Traceback (most recent call last)
Cell In [20], line 34
31 print( 'New object to test: '+str(New_Object) )
33 String = ''
---> 34 for Column , Rows in LC.Test_For_Numerically_Exceptional_Proper_Extension( New_Object=New_Object , Test_If_Self_Is_Exceptional=False ) :
35 if Integer(0) < len(Rows) :
36 print( 'In the column='+str(Column)+': '+str(Rows) )
File /tmp/ipykernel_25707/80901849.py:531
, in Lefschetz_Collection.Test_For_Numerically_Exceptional_Proper_Extension(self, New_Object, Relevant_Columns, Test_If_Self_Is_Exceptional)
528 Test_Numerically=True
530 assert isinstance( New_Object , Equivariant_Vector_Bundle ) , 'The input for `New_Object` need to be an equivariant vector bundle.'
--> 531 New_Orbit = New_Object.Maximal_Numerically_Exceptional_Orbit()
533 if Relevant_Columns == None : Relevant_Columns = set(range(self.Width()+Integer(1)))
534 assert isinstance( Relevant_Columns , set ) , 'If the input for `Relevant_Columns` is not None, then it need to be a set.'
File /tmp/ipykernel_25707/3214646350.py:287
, in Equivariant_Vector_Bundle.Maximal_Numerically_Exceptional_Orbit(self, Twist)
284 assert Twist.Is_Line_Bundle() , ValueError('The input for ``Twist`` need to be a line bundle.')
286 Orbit_Length = Integer(0)
--> 287 if self.Is_Numerically_Exceptional() :
288 Orbit_Length = Integer(1)
289 Moving_Object = self
File /tmp/ipykernel_25707/3214646350.py:231
, in Equivariant_Vector_Bundle.Is_Numerically_Exceptional(self)
229 def Is_Numerically_Exceptional ( self ) -> bool :
230 """Tests if ``self`` is numerically exceptional, i.e. Euler_Sum(self,self) = kk."""
--> 231 return self.Is_Exceptional( Test_Numerically=True )
File /tmp/ipykernel_25707/3214646350.py:222
, in Equivariant_Vector_Bundle.Is_Exceptional(self, Test_Numerically)
219 else : return False
221 elif Test_Numerically == True :
--> 222 if self.Euler_Sum(self) == WCR(Integer(1)) : return True
223 else : return False
225 else :
File /tmp/ipykernel_25707/3214646350.py:157
, in Equivariant_Vector_Bundle.Euler_Sum(self, other)
155 """Returns sum_{ p } (-1)^p EXT^p(``self``,``other``)."""
156 WCR = self.Base_Space().Parent_Group().Weyl_Character_Ring()
--> 157 Result = sum([ (-Integer(1))**Degree * Weyl_Character for Degree , Weyl_Character in self.EXT(other).items() ])
158 if Result == Integer(0) : return WCR(Integer(0))
159 else : return Result
File /tmp/ipykernel_25707/3214646350.py:175
, in Equivariant_Vector_Bundle.EXT(self, other, *p)
172 elif isinstance( other , Extension_Of_Equivariant_Vector_Bundles ) : E2 = other.SemiSimplification()
173 else : raise TypeError( 'The input for ``other`` must be an equivariant vector bundle over an irreducible homogeneous variety or' + 'an equivariant extension of those ones.')
--> 175 return ( E1.Dual() * E2 ).Cohomology( *p )
File /tmp/ipykernel_25707/1189217894.py:98
, in Direct_Sum_Of_Equivariant_Vector_Bundles.__mul__(self, other)
96 for Weyl_Character_HW , Weyl_Character_Multiplicity in Multiplicity_1 * Multiplicity_2 :
97 for VB , Mult in ( Vector_Bundle_1 * Vector_Bundle_2 ).SemiSimplification().Summands() :
---> 98 Product += self.__class__( Base_Space=self.Base_Space() , Summands=[ ( VB , Mult * Weyl_Character_Multiplicity * WCR(Weyl_Character_HW) ) ] )
100 if isinstance( Product , self.__class__ ) : Product.Tidy_Up()
101 return Product
File /tmp/ipykernel_25707/3214646350.py:7
, in Equivariant_Vector_Bundle.__add__(self, other)
5 if isinstance( other , ( Irreducible_Equivariant_Vector_Bundle , Direct_Sum_Of_Equivariant_Vector_Bundles , Extension_Of_Equivariant_Vector_Bundles ) ) :
6 New_Constituent_Parts = self.Constituent_Parts() + other.Constituent_Parts()
----> 7 Sum = Direct_Sum_Of_Equivariant_Vector_Bundles( Base_Space=self.Base_Space() , Summands=New_Constituent_Parts )
8 Sum.Tidy_Up()
10 if Sum.Is_Irreducible() : return Sum[Integer(0)]
File /tmp/ipykernel_25707/1189217894.py:51
, in Direct_Sum_Of_Equivariant_Vector_Bundles.__init__(self, Base_Space, Summands)
47 assert Mult in WCR , ValueError('The multiplicity of the '+str(Summand_Counter)+'-th summnad is not an element of the Weyl character ring ``'+str(WCR)+'``.')
49 self._Summands += [ ( VB , Mult ) ]
---> 51 self.Tidy_Up()
File /tmp/ipykernel_25707/1189217894.py:404
, in Direct_Sum_Of_Equivariant_Vector_Bundles.Tidy_Up(self)
402 Summand_Is_Implemented_After_Tidying_Up = False
403 for Summand_Counter_2 , ( Vector_Bundle_2 , Multiplicity_2 ) in enumerate( Summands ) :
--> 404 if Vector_Bundle_1 == Vector_Bundle_2 :
405 Summands[Summand_Counter_2] = ( Vector_Bundle_2 , Multiplicity_2+Multiplicity_1 )
406 Summand_Is_Implemented_After_Tidying_Up = True
File /tmp/ipykernel_25707/2070952829.py:6
, in Algebraic_Structure.__eq__(self, other)
4 """Tests if two objects of the same class and if they coincide."""
5 if isinstance( other , self.__class__ ) :
----> 6 if self.__repr__() == other.__repr__() : return True
7 else : return False
8 else : return False
File /tmp/ipykernel_25707/3978931721.py:102
, in Irreducible_Equivariant_Vector_Bundle.__repr__(self)
98 Summands = [ ( self , -WCR(Integer(1)) ) ]
99 return Direct_Sum_Of_Equivariant_Vector_Bundles( Base_Space=Base_Space , Summands=Summands )
--> 102 def __repr__ ( self ) :
103 """Returns all attributes which are necessary to initialize the object."""
104 return self.Base_Space() , self.Highest_Weight()
File src/cysignals/signals.pyx:310
, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
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