Hey SFA users...
I've been working on a patch to change how symmetric functions are used in
the future. I will be deprecating some common functions soon on the sage
combinat queue and we will try to get this into sage in an upcoming
version. Starting soon: SFAxxx where xxx in {Schur, Monomial, Homogeneous,
Elementary, Power} will not be the way to access these functions.
Old notation:
sage: s = SFASchur(QQ)
sage: h = SFAHomogeneous(QQ)
sage: e = SFAElementary(QQ)
...
The new notation will be:
sage: SF = SymmetricFunctions(QQ)
sage: s = SF.schur() # or .s()
sage: h = SF.homogeneous() # or .h()
sage: e = SF.elementary() # or .e()
sage: p = SF.power() # or .p()
sage: m = SF.monomial() # or .m()
Moreover, LLT polynomials, Hall-Littlewood, Jack and Macdonald symmetric
functions have all been moved into SymmetricFunctions(R).
sage: Mac = SF.macdonald()
gives an error because q and t are not in the ring! (this is different
behavior than before where the q and t were added to the base ring)
New notation:
sage: SF = SymmetricFunctions(QQ['q','t'].fraction_field())
sage: Mac = SF.macdonald()
sage: MP = Mac.P() # or .Q() or .J() or .H() or .Ht()
sage: HL = SF.hall_littlewood()
sage: HLP = HL.P() # or .Q() or .Qp()
sage: Jack = SF.jack()
sage: JP = Jack.P() # or .Q() or .Qp() or .J()
sage: LLT = SF.llt(2) # 2 is the level here which needs to be specified
sage: HS = LLT.hspin() # .hcospin()
The real improvements are behind the scenes. Your field can be more
general than before and your q and t parameters should be something in that
field.
sage: SF = SymmetricFunctions(QQ['x','y'].fraction_field()); (x,y) =
SF.base_ring().gens()
sage: MPxy = SF.macdonald(q=x,t=y).P()
sage: MPy5 = SF.macdonald(q=y,t=5).P()
sage: MPy5(MPxy[2,1])
Other changes include bringing .omega_qt(), .scalar_qt() and .nabla() to
all bases and adding q=value, t=value as optional parameters.
I could use some help testing. If you use symmetric functions and notice
any bad behavior please pass along odd doc tests.
If you want functionality does not seem to be part of these changes, please
feel free to add your two cents.
-Mike
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