lit
This commit is contained in:
parent
10c79cb47c
commit
ebce3008aa
@ -40,7 +40,7 @@ cs = import_sage('cable_signature', package=package, path=path)
|
||||
# self.f_results = os.path.join(os.getcwd(), "results.out")
|
||||
|
||||
class Schema:
|
||||
r"""This class stores inreresting schema of cable sums.
|
||||
r"""This class stores interesting schema of cable sums.
|
||||
|
||||
Cable knots sum can be given as a scheme, e.g. a scheme from the paper:
|
||||
K(p_1 , p_2 , q_1 , q_2 , q_3 ) =
|
||||
@ -60,24 +60,24 @@ class Schema:
|
||||
See k_vector setter in class CableTemplate in cable_signature.sage module.
|
||||
|
||||
Remark 1
|
||||
In the paper we used p_i and q_i to describe torus knots and cables.
|
||||
It was convinient for writing, but in all the code and documentation
|
||||
In the paper, we used p_i and q_i to describe torus knots and cables.
|
||||
It was convenient for writing, but in all the code and documentation
|
||||
only 'q' letter is used to encode torus knots or cables.
|
||||
|
||||
Remark 2
|
||||
There are two ways to set k[i] values for a scheme:
|
||||
via q_vector or via k_vector.
|
||||
via q_vector or k_vector.
|
||||
Both should be lists and the relation is q[i] = 2 * k[i] + 1,
|
||||
i.e. q should be an odd prime and k should be an even number such that
|
||||
2 * k + 1 is prime.
|
||||
To fill the scheme listed above we shoud use a list of lenght 8,
|
||||
and k[0] will be ommited as it is not used in the scheme.
|
||||
To fill the scheme listed above we should use a list of length 8,
|
||||
and k[0] will be omitted as it is not used in the scheme.
|
||||
|
||||
Remark 3
|
||||
Except for development purposes, q_vector was computed with
|
||||
a methode CableTemplate.get_q_vector and flag slice=True.
|
||||
a method CableTemplate.get_q_vector and flag slice=True.
|
||||
The reason for that is that we were interested only in cases
|
||||
where a specific relation for each cabling-level is preserved.
|
||||
where a specific relation for each cabling level is preserved.
|
||||
Consider a cable T(2, q_0; 2, q_1; ...; 2, q_n).
|
||||
Then for every q_i, q_(i + 1): q_(i + 1) > q_i * 4.
|
||||
|
||||
|
Loading…
Reference in New Issue
Block a user