#19011: Add Jones representation of braid groups and Jones polynomials of braid
closures
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Reporter: fuglede | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers:
Authors: Søren Fuglede | Work issues:
Jørgensen | Commit:
Report Upstream: N/A | 679f5c46e12fd05edcf7e4ae9e006e220e47e43e
Branch: | Stopgaps:
u/fuglede/jones_rep |
Dependencies: |
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Comment (by tscrim):
In case nobody has said it yet, welcome to Sage.
I know this isn't yet set to needs review, but some quick comments from a
look-over (from my curiosity):
- Could you remove the changes to `diagram_algebras.py`, this will be
taken care of in #18720 (which does some large refactoring of the
classes)?
- For latex, use single backticks, e.g., {{{`A + B \neq 5`}}}, instead of
dollar signs.
- Make the first sentence for method definitions short and succinct. For
example:
{{{
def foo(x):
r"""
Return bar.
This is where you put a longer explanation. This is a python
convention and
makes it clear what the method does and then has this information for
the
interested user who wants more details.
"""
}}}
- Also note the `r"""` for the beginning of the docstring, this makes it
into "raw" format, where the string gets interpreted as written, whereas
when you don't have it, backslash `\` gets interpreted as a special
character (ex. `\n` is a newline). For what you have here, this does not
appear to be necessary, but I always include it anytime I have latex code
for extra safety/my paranoia.
- For `markov_trace`, I would write it like this:
{{{#!python
def markov_trace(self, variab='A', ring=IntegerRing()):
R = LaurentPolynomialRing(ring, variab)
A = R.gens()[0]
delta = -A**2 - A**(-2)
n = self.strands()
def weighted_trace(b, d):
return (A**(2*i) - A**(-2*i))/(A**2 - A**(-2)) * b.TL_matrix(d,
variab, ring).trace()
trace = sum(weighted_trace(self, d, variab, ring) for d in range(n+1)
if (n+d) % 2 == 0)
return trace / (-delta)**n
}}}
- You should try to avoid abbreviations in method names as it makes it
slightly harder to detect with tab completion and can expand those out
quickly using tab completion.
- For the caching of polynomials, I would have a private method which does
the computation in a specific ring with a specific variable, cache that,
and have the public method take that output and do a `subs` on the result
from the private method. This way you can't cache the "same" polynomial
over and over again (and your private methods can call each other knowing
what their output will be). For an optimization, the defaults for the
public method could be `None` and if they are both `None`, then return
immediately the result of the private method.
--
Ticket URL: <http://trac.sagemath.org/ticket/19011#comment:5>
Sage <http://www.sagemath.org>
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