More Sym and NSym functionality

[darijgr]

• Gessel-Reutenauer symmetric functions
• "Carlitz-Shareshian-Wachs symmetric functions"
• dendriform operations on QSym
• free-algebra expansion of functions in NSym
• expansion of functions in Sym now also works in the 0-variables border case

CC: @nthiery @tscrim @sagetrac-sage-combinat @zabrocki

Component: combinatorics

Keywords: symmetric functions, noncommutative symmetric functions

Author: Darij Grinberg

Branch/Commit: 6c6e606

Reviewer: Travis Scrimshaw, Mike Zabrocki

Issue created by migration from https://trac.sagemath.org/ticket/17125

[zabrocki]

comment:2

I've briefly looked over the branch changes but haven't tried out your code yet. I'm always intimidated by your patches because they are never minor. :) This looks good though.

Before even testing anything, the GR symmetric functions and the CSW quasi-symmetric functions need INPUT: OUTPUT: sections in the documentation.

I kind of found it strange that you put in the functionality to compute h.gessel_reutenauer(n) with n an integer when it is more generally defined for h.gessel_reutenauer(lam) and the integer ones aren't the generators of the elements. Maybe there is a reason to consider this sequence though.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ba59047

documentation fixes

[sagetrac-git]

Changed commit from 6f9e5f8 to ba59047

[darijgr]

comment:4

Thanks, I spent so long without programming that I forgot about these conventions.

Why an extra syntax for the one-row partitions? Just because they're defined first in Gessel-Reutenauer (they are also characters of the free Lie algebra as S_n-representations, I believe).

[tscrim]

comment:5

Replying to @darijgr:

Why an extra syntax for the one-row partitions? Just because they're defined first in Gessel-Reutenauer (they are also characters of the free Lie algebra as S_n-representations, I believe).

I somewhat feel that this can muddy things because you really want partitions. Although if you do want the extra semantic (I don't have a strong opinion), then I think you should just check if lam in ZZ:.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

dbc1f22

ZZ instead of IntegerRing()

[sagetrac-git]

Changed commit from ba59047 to dbc1f22

[darijgr]

comment:7

Thanks, I forgot about the right way to get these standard rings too.

I thought people would want a simpler syntax for the simple cases. I am fine with or without it just as much.

---

New commits:

dbc1f22

ZZ instead of IntegerRing()

[tscrim]

Reviewer: Travis Scrimshaw, Mike Zabrocki

[tscrim]

Changed branch from u/darij/moresym to public/combinat/moresym-17125

[tscrim]

Changed commit from dbc1f22 to 47d8ff7

[tscrim]

comment:8

Some review changes. I also marked some tests as long (and made some of them correctly marked). If you're happy with my changes, then it's a positive review.

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New commits:

1d5094e	Merge branch 'u/darij/moresym' of trac.sagemath.org:sage into u/darij/moresym
a045989	Made some lines shorter and some very minor code cleanup.
ec43e87	Marked some tests as long (and some correctly marked).
e7f1ecd	Some more doctests for dendriform_less.
47d8ff7	Marked some more tests as long.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6c6e606

revert of one simple edit; thanks for the rest, Travis

[sagetrac-git]

Changed commit from 47d8ff7 to 6c6e606

[darijgr]

comment:10

Travis: thank you for the review!

(The last change was discussed on Skype.)

[vbraun]

Changed branch from public/combinat/moresym-17125 to 6c6e606