#15408: corrections and improvements to `inner_plethysm` method in symmetric
functions
-------------------------+-------------------------------------------------
Reporter: zabrocki | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: | Keywords: symmertic functions, inner
combinatorics | plethysm
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
-------------------------+-------------------------------------------------
The current documentation for `inner_plethysm` reads
{{{
f.inner_plethysm(g + h) == f.inner_plethysm(g) + f.inner_plethysm(h).
}}}
This is false (see an example below), and in fact
{{{
(f+g).inner_plethysm(h) == f.inner_plethysm(h) + g.inner_plethysm(h)
}}}
and it is only true that
{{{
p[k].inner_plethysm(f+g) == p[k].inner_plethysm(f) +
p[k].inner_plethysm(g).
}}}
It is also true that
{{{
(f*g).inner_plethsym(h) ==
(f.inner_plethsym(h)).itensor(g.inner_plethsym(h)).
}}}
In fact these three statements and the definition for
`p[k].inner_plethysm(p(mu))` is how inner plethysm is defined.
For example
{{{
sage:
s[3].inner_plethysm(s[2,1]+s[3])-s[3].inner_plethysm(s[2,1])-s[3].inner_plethysm(s[3])
2*s[2, 1] + s[3]
sage:
(s[3]+s[2,1]).inner_plethysm(s[2,1])-s[3].inner_plethysm(s[2,1])-s[2,1].inner_plethysm(s[2,1])
0
sage:
p[5].inner_plethysm(s[2,1]+s[3])-p[5].inner_plethysm(s[2,1])-p[5].inner_plethysm(s[3])
0
sage:
p[3,2].inner_plethysm(s[2,1])-p[3].inner_plethysm(s[2,1]).itensor(p[2].inner_plethysm(s[2,1]))
0
}}}
Moreover the doc tests don't catch errors that were (probably?) introduced
in edits since #3342.
{{{
sage: p[4,3].inner_plethysm(p[2,2,1])
---------------------------------------------------------------------------
AttributeError Traceback (most recent call
last)
...
AttributeError: 'int' object has no attribute 'itensor'
sage: p[3].inner_plethysm(p[3])
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
...
ValueError: Codomain could not be determined
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15408>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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