#14234: Restructuring Diagram/Partition Algebras to match category structure
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Reporter: ghseeli | Owner:
Type: enhancement | AlexGhitza
Priority: minor | Status:
Component: algebra | needs_work
Keywords: Partition algebra, diagram | Milestone:
algebra, days38, days40 | sage-5.12
Authors: Stephen Doty, Aaron Lauve, | Resolution:
George H. Seelinger | Merged in:
Report Upstream: N/A | Reviewers: Travis
Branch: | Scrimshaw
Stopgaps: | Work issues:
| Dependencies: #10630
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Comment (by darij):
Another reason why floats are a bad thing:
{{{
sage: da.PartitionAlgebra(3+1/2, 1, QQ, 'part') ==
da.PartitionAlgebra(3+1/2, 1, QQ, 'part')
True
sage: da.PartitionAlgebra(3+1/2, 1, QQ, 'part') ==
da.PartitionAlgebra(3.5, 1, QQ, 'part')
False
}}}
I think the code should use rationals, and floats in the input should be
normalized to the nearest semi-integer.
Remove the word "with" from {{{with propogating number less than}}}, since
there is already a "with" on the preceding line.
There is a typo ("usualy") here:
{{{
Returns the product of two basis diagrams. Usually it is not
called
directly, but indirectly through usualy arithmetic operators.
}}}
but actually the word can be removed.
I think the docstrings should mention the fact that the partition-to-
diagram correspondence is not 1-to-1, and diagrams are usually seen just
as intuitive representations of set partitions, with several different
diagrams corresponding to the same set partition.
Put "k" in backticks in {{{The Brauer algebra of rank k}}}.
The docstring {{{ ambient returns the partition algebra the Brauer
algebra is a sub-algebra of.}}} should be adjusted as it is defined not
just for a Brauer algebra but for any subalgebra.
It seems to me that the {{{SubPartitionAlgebra}}} docstring should say
that the subalgebra is spanned by a subset of the basis of the partition
algebra. Otherwise the code of the {{{retract}}} method makes no sense.
--
Ticket URL: <http://trac.sagemath.org/ticket/14234#comment:20>
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