#15150: Implement NCSym
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15143, #15164 | Stopgaps:
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Comment (by zabrocki):
I am not comfortable making `NCSym` and `NSym -> Sym` coercions because
when I say that they preserve the Hopf structure I mean that the Hopf
structure of `NCSym` is mapped onto the Hopf structure of `Sym` but
`NCSym` does not exist as a Hopf subalgebra of `Sym`. For `Sym -> QSym`
it is the case that `Sym` exists as a subalgebra of `QSym`.
That is, let phi : NCSym -> Sym
then sometimes we have,
F != G
but
phi(F) = phi(G) (e.g. F = A*B, G =B*A)
That is, "equalities go to equalities, but sometimes inequalities also go
to equalities." (to my eye, not something I want as a coercion). This
isn't a hard fast rule, but it seems counter-intuitive to be able to
coerce from NCSym to Sym rather than use the method
`to_symmetric_function` to project onto that space.
For psi: Sym -> NCSym^*^ we have psi(F)=psi(G) iff F=G, that is,
"equalities going to equalities and inequalities going to inequalities"
--
Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:76>
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