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"""
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Symmetric functions, with their multiple realizations
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"""
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- #** ***************************************************************************
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+ # ***************************************************************************
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# Copyright (C) 2007 Mike Hansen <[email protected] >
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# 2009-2012 Jason Bandlow <[email protected] >
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# 2012 Anne Schilling <anne at math.ucdavis.edu>
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#
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# The full text of the GPL is available at:
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#
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- # http ://www.gnu.org/licenses/
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- #** ***************************************************************************
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+ # https ://www.gnu.org/licenses/
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+ # ***************************************************************************
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from sage .categories .fields import Fields
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from sage .categories .graded_hopf_algebras import GradedHopfAlgebras
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from sage .categories .principal_ideal_domains import PrincipalIdealDomains
@@ -885,7 +885,7 @@ def a_realization(self):
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"""
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return self .schur ()
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- def _repr_ (self ): # could be taken care of by the category
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+ def _repr_ (self ): # could be taken care of by the category
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r"""
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Representation of ``self``
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@@ -907,7 +907,7 @@ def schur(self):
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"""
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return schur .SymmetricFunctionAlgebra_schur (self )
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s = schur
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- Schur = schur # Currently needed by SymmetricFunctions.__init_extra__
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+ Schur = schur # Currently needed by SymmetricFunctions.__init_extra__
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def powersum (self ):
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r"""
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"""
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return powersum .SymmetricFunctionAlgebra_power (self )
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p = powersum
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- power = powersum # Todo: get rid of this one when it won't be needed anymore
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+ power = powersum
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+ # Todo: get rid of the line above when it won't be needed anymore
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def complete (self ):
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r"""
@@ -1321,7 +1322,7 @@ def jack(self, t='t'):
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sage: JQp = Sym.jack().Qp(); JQp
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Symmetric Functions over Fraction Field of Univariate Polynomial Ring in t over Rational Field in the Jack Qp basis
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"""
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- return jack .Jack ( self , t = t )
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+ return jack .Jack (self , t = t )
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def abreu_nigro (self , q = 'q' ):
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"""
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sage: SymmetricFunctions(QQ).zonal()
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Symmetric Functions over Rational Field in the zonal basis
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"""
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- return jack .SymmetricFunctionAlgebra_zonal ( self )
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+ return jack .SymmetricFunctionAlgebra_zonal (self )
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def llt (self , k , t = 't' ):
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"""
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sage: llt3.hcospin()
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Symmetric Functions over Fraction Field of Univariate Polynomial Ring in t over Rational Field in the level 3 LLT cospin basis
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"""
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- return llt .LLT_class ( self , k , t = t )
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+ return llt .LLT_class (self , k , t = t )
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def from_polynomial (self , f ):
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"""
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else :
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morphism .codomain ().register_coercion (morphism )
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+ # keep them sorted in alphabetic order
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_shorthands = ('e' , 'f' , 'h' , 'm' , 'p' , 's' )
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- _shorthands_all = tuple ( sorted ( _shorthands + ( ' ht' , 'o' , 'sp' , 'st' , 'w' )) )
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+ _shorthands_all = ( 'e' , 'f' , 'h' , ' ht' , 'm' , ' o' , 'p' , 's' , ' sp' , 'st' , 'w' )
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def __init_extra__ (self ):
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"""
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sage: f(p.an_element()) == p.an_element()
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True
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"""
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- #powersum = self.powersum ()
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- #complete = self.complete ()
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- #elementary = self.elementary()
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- #schur = self.schur ()
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- #monomial = self.monomial ()
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+ # powersum = self.powersum ()
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+ # complete = self.complete ()
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+ # elementary = self.elementary()
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+ # schur = self.schur ()
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+ # monomial = self.monomial ()
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iso = self .register_isomorphism
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@@ -1465,7 +1467,7 @@ def __init_extra__(self):
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for (basis1_name , basis2_name ) in conversion_functions :
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basis1 = getattr (self , basis1_name )()
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basis2 = getattr (self , basis2_name )()
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- on_basis = SymmetricaConversionOnBasis (t = conversion_functions [basis1_name ,basis2_name ], domain = basis1 , codomain = basis2 )
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+ on_basis = SymmetricaConversionOnBasis (t = conversion_functions [basis1_name , basis2_name ], domain = basis1 , codomain = basis2 )
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from sage .rings .rational_field import RationalField
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if basis2_name != "powersum" or self ._base .has_coerce_map_from (RationalField ()):
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iso (basis1 ._module_morphism (on_basis , codomain = basis2 ))
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