From 9922ef9ee152dd3984efd55cd02e3bd05e0599f7 Mon Sep 17 00:00:00 2001 From: Maria Marchwicka Date: Tue, 26 May 2020 18:48:29 +0000 Subject: [PATCH] Update 'README.md' --- README.md | 61 ------------------------------------------------------- 1 file changed, 61 deletions(-) diff --git a/README.md b/README.md index c0c2639..ecbbf3b 100644 --- a/README.md +++ b/README.md @@ -1,64 +1,3 @@ This script calculates signature functions for knots (cable sums). - The script can be run as a sage script from the terminal or used in interactive mode. - A knot (cable sum) is encoded as a list where each element (also a list) corresponds to a cable knot. - -To calculate the number of characters for which signature function vanish use the function eval_cable_for_thetas as shown below. - -sage: eval_cable_for_thetas([[1, 3], [2], [-1, -2], [-3]]) - -T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7) -Zero cases: 1 -All cases: 1225 -Zero theta combinations: -(0, 0, 0, 0) - -sage: - - -The numbers given to the function eval_cable_for_thetas are k-values for each -component/cable in a direct sum. - - -To calculate signature function for a knot and a theta value, use function -get_function_of_theta_for_sum as follow: - -sage: signature_function_generator = get_function_of_theta_for_sum([1, 3], [2], [-1, -2], [-3]) -sage: sf = signature_function_generator(2, 1, 2, 2) -sage: print sf -0: 0 -5/42: 1 -1/7: 0 -1/5: -1 -7/30: -1 -2/5: 1 -3/7: 0 -13/30: -1 -19/42: -1 -23/42: 1 - 17/30: 1 -4/7: 0 -3/5: -1 -23/30: 1 -4/5: 1 -6/7: 0 -37/42: -1 -sage: - -or like below: - -sage: print get_function_of_theta_for_sum([1, 3], [2], [-1, -2], [-3])(2, 1, 2, 2) -0: 0 -1/7: 0 -1/6: 0 -1/5: -1 -2/5: 1 -3/7: 0 -1/2: 0 -4/7: 0 -3/5: -1 -4/5: 1 -5/6: 0 -6/7: 0 -sage: \ No newline at end of file