Environment to perform calculations of equivariant vector bundles on homogeneous varieties
License: GPL3
ubuntu2204
Kernel: SageMath 9.8
In [1]:
In [6]:
Out[6]:
Base space: OGr(3;23)
rk K0(X): 1320
Fano index: 19
Objects of starting block:
Number of objects: 1282
LC has maximal expected length? False
Is LC numerially exceptional? True
In [0]:
In [3]:
Out[3]:
Counter: 1
New object which is tested: VB(8*Lambda[1] + 4*Lambda[2])
Counter: 2
New object which is tested: VB(7*Lambda[1] + 5*Lambda[2])
Counter: 3
New object which is tested: VB(6*Lambda[1] + 6*Lambda[2])
Counter: 4
New object which is tested: VB(8*Lambda[1] + 5*Lambda[2])
Counter: 5
New object which is tested: VB(7*Lambda[1] + 6*Lambda[2])
Counter: 6
New object which is tested: VB(8*Lambda[1] + 6*Lambda[2])
Counter: 7
New object which is tested: VB(7*Lambda[1] + 7*Lambda[2])
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Cell In [3], line 16
13 print( 'Counter: '+str(Counter) )
14 print( 'New object which is tested: '+str(New_Object) )
---> 16 for Column , Rows in LC.Test_For_Numerically_Exceptional_Proper_Extension( New_Object=New_Object , Relevant_Columns=set([Integer(11)]), Test_If_Self_Is_Exceptional=False ) :
17 if Integer(0) < len(Rows) :
18 print( 'In the column='+str(Column)+': '+str(Rows) )
File /tmp/ipykernel_518/80901849.py:559
, in Lefschetz_Collection.Test_For_Numerically_Exceptional_Proper_Extension(self, New_Object, Relevant_Columns, Test_If_Self_Is_Exceptional)
555 return True
557 for Tested_xPos in Relevant_Columns :
558 #Already_Tested = dict({})
--> 559 yield ( Tested_xPos , [ Tested_yPos for Tested_yPos in range(len(New_Orbit)) if Test_For( Tested_xPos , Tested_yPos ) ] )
File /tmp/ipykernel_518/80901849.py:559
, in <listcomp>(.0)
555 return True
557 for Tested_xPos in Relevant_Columns :
558 #Already_Tested = dict({})
--> 559 yield ( Tested_xPos , [ Tested_yPos for Tested_yPos in range(len(New_Orbit)) if Test_For( Tested_xPos , Tested_yPos ) ] )
File /tmp/ipykernel_518/80901849.py:554
, in Lefschetz_Collection.Test_For_Numerically_Exceptional_Proper_Extension.<locals>.Test_For(xPos1, yPos1)
550 if not next( Object1.Is_SemiOrthogonal_To( Object2 , Test_Numerically=Test_Numerically ) ) : return False
551 else :
552 #if not yPos2-yPos1 in Already_Tested[xPos2][1] :
553 # Already_Tested[xPos2][1].add( yPos2-yPos1 )
--> 554 if not next( Object2.Is_SemiOrthogonal_To( Object1 , Test_Numerically=Test_Numerically ) ) : return False
555 return True
File /tmp/ipykernel_518/1108572515.py:267
, in Equivariant_Vector_Bundle.Is_SemiOrthogonal_To(self, others, Test_Numerically)
264 else : yield False
266 elif Test_Numerically == True :
--> 267 if self.Euler_Sum( other ) == WCR(Integer(0)) : yield True
268 else : yield False
270 else :
File /tmp/ipykernel_518/1108572515.py:160
, in Equivariant_Vector_Bundle.Euler_Sum(self, other)
158 """Returns sum_{ p } (-1)^p EXT^p(``self``,``other``)."""
159 WCR = self.Base_Space().Parent_Group().Weyl_Character_Ring()
--> 160 Result = sum([ (-Integer(1))**Degree * Weyl_Character for Degree , Weyl_Character in self.EXT(other).items() ])
161 if Result == Integer(0) : return WCR(Integer(0))
162 else : return Result
File /tmp/ipykernel_518/1108572515.py:178
, in Equivariant_Vector_Bundle.EXT(self, other, *p)
175 elif isinstance( other , Extension_Of_Equivariant_Vector_Bundles ) : E2 = other.SemiSimplification()
176 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.')
--> 178 return ( E1.Dual() * E2 ).Cohomology( *p )
File /tmp/ipykernel_518/1189217894.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_518/1108572515.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_518/1189217894.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_518/1189217894.py:399
, in Direct_Sum_Of_Equivariant_Vector_Bundles.Tidy_Up(self)
397 Summands = []
398 for Summand_Counter_1 , ( Vector_Bundle_1 , Multiplicity_1 ) in enumerate( self.Summands() ) :
--> 399 if Multiplicity_1 == Integer(0) :
400 pass
401 else :
File /ext/sage/9.8/src/sage/structure/element.pyx:1111
, in sage.structure.element.Element.__richcmp__()
1109 return (<Element>self)._richcmp_(other, op)
1110 else:
-> 1111 return coercion_model.richcmp(self, other, op)
1112
1113 cpdef _richcmp_(left, right, int op):
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973
, in sage.structure.coerce.CoercionModel.richcmp()
1971 # Coerce to a common parent
1972 try:
-> 1973 x, y = self.canonical_coercion(x, y)
1974 except (TypeError, NotImplementedError):
1975 pass
File /ext/sage/9.8/src/sage/structure/coerce.pyx:1315
, in sage.structure.coerce.CoercionModel.canonical_coercion()
1313 x_elt = x
1314 if y_map is not None:
-> 1315 y_elt = (<Map>y_map)._call_(y)
1316 else:
1317 y_elt = y
File /ext/sage/9.8/src/sage/categories/morphism.pyx:601
, in sage.categories.morphism.SetMorphism._call_()
599 3
600 """
--> 601 return self._function(x)
602
603 cpdef Element _call_with_args(self, x, args=(), kwds={}):
File /ext/sage/9.8/src/sage/categories/unital_algebras.py:377
, in UnitalAlgebras.WithBasis.ParentMethods.from_base_ring_from_one_basis(self, r)
359 def from_base_ring_from_one_basis(self, r):
360 """
361 Implement the canonical embedding from the ground ring.
362
(...)
375 3*B[word: ]
376 """
--> 377 return self.term(self.one_basis(), r)
File /ext/sage/9.8/src/sage/combinat/root_system/weyl_characters.py:623
, in WeylCharacterRing.one_basis(self)
613 """
614 Return some elements of ``self``.
615
(...)
619 [A3(1,0,0,0), A3(1,1,0,0), A3(1,1,1,0)]
620 """
621 return [self.monomial(x) for x in self.fundamental_weights()]
--> 623 def one_basis(self):
624 """
625 Return the index of 1 in ``self``.
626
(...)
632 A3(0,0,0,0)
633 """
634 return self._space.zero()
File src/cysignals/signals.pyx:310
, in cysignals.signals.python_check_interrupt()
KeyboardInterrupt:
In [0]:
In [0]:
In [0]: