#18664: Implement (left and right) Zassenhaus basis of NSym
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Reporter: amypang | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: days65 | Merged in:
Authors: amypang, saliola | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/amypang/implementation_of_zassenhaus_basis_of_nsym|
80230bb4f12b46e4e3d63a93b9f0aba7edfe5cf5
Dependencies: | Stopgaps:
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Comment (by tscrim):
Hey Amy and Franco,
You will need to rebase this off the latest `develop` and make sure all
functions have doctests (some don't have docstrings). I would also just
move the `_register_coercion_` method into the `__init__` (so really
you're removing that method). Also the `_to_complete_on_generator` has a
misaligned docstring. I'd also change the `if n == 0 or n == 1:` to `if n
<= 1`.
I would also use:
{{{#!python
def _from_complete_on_basis(self, I):
n = I.size()
m = self._complete_to_zassenhaus_transition_matrix(n).invers()
C = Compositions(n)
i = C.rank(I) # this is typically faster than list(C).index(I)
return self._from_dict({comp: m[i,j] for j,comp in enumerate(C)})
}}}
Actually, since you only use the inverses, I would cache the inverse
matrices instead.
On a more optimization point (which is not necessary to handle now):
{{{#!python
for partition in Partitions(n):
if len(partition) > 1:
...
}}}
I would instead do this:
{{{#!python
P = Partitions(6)
it = iter(P)
it.next()
for p in it:
...
}}}
If you really wanted to go crazy with optimization, I'd use
{{{#!python
from sage.combinat.partitions import ZS1_iterator
it = ZS1_iterator(n)
it.next()
for p in it:
d = {}
for part in self:
d[part] = d.get(part, 0) + 1
coeff = prod(factorial(d[e]) for e in d)
...
}}}
Yet as I said, that's going crazy.
--
Ticket URL: <http://trac.sagemath.org/ticket/18664#comment:5>
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