From ebce3008aabf9a78621619c7ca65125802a66de3 Mon Sep 17 00:00:00 2001 From: maria Date: Thu, 22 Jul 2021 23:41:55 +0200 Subject: [PATCH] lit --- gaknot/main.sage | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/gaknot/main.sage b/gaknot/main.sage index 2e48332..d77fe2e 100644 --- a/gaknot/main.sage +++ b/gaknot/main.sage @@ -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.