finding big signature, based on old code
This commit is contained in:
Maria Marchwicka
parent
0337fedda0
commit
a02abef0ff
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@ -1,6 +1,7 @@
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#!/usr/bin/python
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# TBD: read about Factory Method, variable in docstring, sage documentation
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# move settings to sep file
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"""
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This script calculates signature functions for knots (cable sums).
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@ -76,9 +77,10 @@ class MySettings(object):
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# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
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# self.knot_formula = "[[k[0], k[1], k[2]], [k[3]],\
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# [-k[0], -k[1], -k[3]], [-k[2]]]"
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self.default_limit = 3
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self.limit = 3
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self.verbose = True
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# self.verbose = True
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self.verbose = False
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class SignatureFunction(object):
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@ -187,10 +189,12 @@ def main(arg):
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# search_for_null_signature_value(limit=new_limit)
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# searching for signture > 5 + #(v_i != 0)
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def search_for_large_signature_value(knot_formula=None,
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limit=None, verbose=None):
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limit=None,
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verbose=None):
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if limit is None:
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limit = config.default_limit
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limit = config.limit
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if knot_formula is None:
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knot_formula = config.knot_formula
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if verbose is None:
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@ -198,71 +202,59 @@ def search_for_large_signature_value(knot_formula=None,
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k_vector_size = extract_max(knot_formula) + 1
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limit = max(limit, k_vector_size)
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print limit
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combinations = it.combinations(range(1, limit + 1), k_vector_size)
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for k in combinations:
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print
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print k
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# P = Primes()
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# sage: P.unrank(0)
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# 2
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# sage: P.unrank(5)
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# 13
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# sage: P.unrank(42)
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return None
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with open(config.f_results, 'w') as f_results:
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for k in combinations:
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if verbose:
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print
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print k
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# TBD: maybe the following condition or the function
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# get_shifted_combination should be redefined to a dynamic version
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if config.only_slice_candidates and k_vector_size == 5:
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k = get_shifted_combination(k)
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# print k
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knot_sum = eval(knot_formula)
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print "knot_sum"
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print knot_sum
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P = Primes()
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if is_trivial_combination(knot_sum):
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if verbose:
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print "\nTrivial combination" + str(knot_sum)
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continue
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with open(config.f_results, 'w') as f_results:
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for c in combinations:
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k = [(P.unrank(i) - 1)/2 for i in c]
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knot_sum = eval(knot_formula)
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result = eval_cable_for_large_signature(knot_sum,
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print_results=False)
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if result is not None:
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knot_description, null_comb, all_comb = result
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line = (str(k) + ", " + str(null_comb) + ", " +
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str(all_comb) + "\n")
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f_results.write(line)
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# if result is not None:
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# knot_description, large_comb, all_comb = result
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# line = (str(k) + ", " + str(all_comb) + ", " +
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# str(all_comb) + "\n")
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# f_results.write(line)
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def eval_cable_for_large_signature(knot_sum, print_results=True, verbose=None):
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# searching for signture > 5 + #(v_i != 0)
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def eval_cable_for_large_signature(knot_sum,
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print_results=True,
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verbose=None):
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if verbose is None:
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verbose = config.verbose
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if verbose:
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print "\neval_cable_for_large_signature"
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if len(knot_sum) != 4:
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print "Wrong number of cable direct summands!"
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return None
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q = 2 * abs(knot_sum[-1][-1]) + 1
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print "q is " + str(q)
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f = get_function_of_theta_for_sum(*knot_sum, verbose=False)
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knot_description = get_knot_descrption(*knot_sum)
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all_combinations = get_number_of_combinations(*knot_sum)
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null_combinations = 0
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zero_theta_combinations = []
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# large_value_combinations = 0
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# good_thetas_list = []
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ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
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if verbose:
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print "eval_cable_for_large_signature - knot_description: "
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print knot_description
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# if verbose:
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# print "eval_cable_for_large_signature - knot_description: "
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# print knot_description
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for v_theta in it.product(*ranges_list):
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if (v_theta[0]^2 - v_theta[1]^2 + v_theta[2]^2 - v_theta[3]^2) % q:
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continue
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y = f(*v_theta).value(1/2)
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print y
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if abs(y) > 5 + np.count_nonzero(v_theta):
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print "hura hura"
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print "\nLarge signature value"
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print knot_description
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print "v_theta: " + str(v_theta)
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condition = (str(v_theta[0]^2) + " - " + str(v_theta[1]^2) + " + " +
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str(v_theta[2]^2) + " - " + str(v_theta[3]^2))
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print condition
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print "non zero value in v_theta: " + str(np.count_nonzero(v_theta))
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print "signature at 1/2: " + str(y)
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# == 0:
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# zero_theta_combinations.append(v_theta)
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# m = len([theta for theta in v_theta if theta != 0])
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@ -270,23 +262,24 @@ def eval_cable_for_large_signature(knot_sum, print_results=True, verbose=None):
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# else:
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# assert sum(v_theta) != 0
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if print_results:
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print
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print knot_description
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print "Zero cases: " + str(null_combinations)
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print "All cases: " + str(all_combinations)
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if zero_theta_combinations:
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print "Zero theta combinations: "
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for el in zero_theta_combinations:
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print el
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if null_combinations^2 >= all_combinations:
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return knot_description, null_combinations, all_combinations
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# if print_results:
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# print
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# print knot_description
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# print "Zero cases: " + str(null_combinations)
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# print "All cases: " + str(all_combinations)
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# if zero_theta_combinations:
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# print "Zero theta combinations: "
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# for el in zero_theta_combinations:
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# print el
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# if null_combinations^2 >= all_combinations:
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# return knot_description, null_combinations, all_combinations
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return None
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# searching for signature == 0
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def search_for_null_signature_value(knot_formula=None, limit=None):
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if limit is None:
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limit = config.default_limit
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limit = config.limit
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if knot_formula is None:
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knot_formula = config.knot_formula
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@ -307,42 +300,34 @@ def search_for_null_signature_value(knot_formula=None, limit=None):
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if is_trivial_combination(knot_sum):
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continue
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result = search_for_thetas(knot_sum, print_results=False)
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result = search_for_large_thetas(knot_sum, print_results=False)
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if result is not None:
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knot_description, null_comb, all_comb = result
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line = (str(k) + ", " + str(null_comb) + ", " +
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str(all_comb) + "\n")
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f_results.write(line)
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def search_for_thetas(knot_sum, print_results=False, verbose=None):
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# searching for signature == 0
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def eval_cable_for_null_signature(knot_sum, print_results=True, verbose=None):
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# search for zero combinations
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if verbose is None:
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vebose = confi.verbose
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if verbose:
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print "search_for_thetas"
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f = get_function_of_theta_for_sum(*knot_sum)
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f = get_function_of_theta_for_sum(*knot_sum, verbose=False)
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knot_description = get_knot_descrption(*knot_sum)
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all_combinations = get_number_of_combinations(*knot_sum)
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large_value_combinations = 0
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good_theta_list = []
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null_combinations = 0
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zero_theta_combinations = []
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ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
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if verbose:
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print "knot_description:"
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print
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print knot_description
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for v_theta in it.product(*ranges_list):
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if (v_theta[0]^2 - v_theta[1]^2 + v_theta[2]^2 - v_theta[3]^2) % q:
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print "ojojoj"
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print (v_theta[0]^2 - v_theta[1]^2 + v_theta[2]^2 - v_theta[3]^2) % q
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continue
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print f(*v_theta).value(-1)
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if f(*v_theta).value(-1):
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print "Hip hip hura"
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good_theta_list.append(v_theta)
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if f(*v_theta, verbose=False).sum_of_absolute_values() == 0:
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zero_theta_combinations.append(v_theta)
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m = len([theta for theta in v_theta if theta != 0])
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large_value_combinations += 2^m
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else:
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print "smuteczek"
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null_combinations += 2^m
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# else:
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# assert sum(v_theta) != 0
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@ -492,43 +477,6 @@ def get_function_of_theta_for_sum(*arg, **key_args):
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return signature_function_for_sum
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def eval_cable_for_null_signature(knot_sum, print_results=True, verbose=None):
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# search for zero combinations
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if verbose is None:
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vebose = confi.verbose
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f = get_function_of_theta_for_sum(*knot_sum, verbose=False)
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knot_description = get_knot_descrption(*knot_sum)
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all_combinations = get_number_of_combinations(*knot_sum)
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null_combinations = 0
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zero_theta_combinations = []
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ranges_list = [range(abs(knot[-1]) + 1) for knot in knot_sum]
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if verbose:
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print
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print knot_description
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for v_theta in it.product(*ranges_list):
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if f(*v_theta, verbose=False).sum_of_absolute_values() == 0:
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zero_theta_combinations.append(v_theta)
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m = len([theta for theta in v_theta if theta != 0])
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null_combinations += 2^m
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# else:
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# assert sum(v_theta) != 0
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if print_results:
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print
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print knot_description
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print "Zero cases: " + str(null_combinations)
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print "All cases: " + str(all_combinations)
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if zero_theta_combinations:
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print "Zero theta combinations: "
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for el in zero_theta_combinations:
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print el
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if null_combinations^2 >= all_combinations:
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return knot_description, null_combinations, all_combinations
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return None
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def get_number_of_combinations(*arg):
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number_of_combinations = 1
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for knot in arg:
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@ -756,7 +704,6 @@ main.__doc__ = \
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Optionaly a parameter (a limit for k_0 value) can be given.
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Thought to be run for time consuming calculations.
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"""
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config = MySettings()
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if __name__ == '__main__' and '__file__' in globals():
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# not called in interactive mode as __file__ is not defined
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