From d9986b63c1adadfa6626d6c5bdde0e7d75bda098 Mon Sep 17 00:00:00 2001
From: Maria Marchwicka <maria.marchwicka@gmx.net>
Date: Mon, 31 Aug 2020 18:12:47 +0200
Subject: [PATCH] classes as separate module - now working

---
 cable_signature.sage | 291 ++++++++++++++++++++++++++++++++++++++++++-
 my_signature.sage    | 291 ++++---------------------------------------
 2 files changed, 312 insertions(+), 270 deletions(-)

diff --git a/cable_signature.sage b/cable_signature.sage
index 44f4b64..4c547a0 100644
--- a/cable_signature.sage
+++ b/cable_signature.sage
@@ -1,6 +1,8 @@
 #!/usr/bin/python
 import collections
-
+import numpy as np
+import itertools as it
+import re
 
 class TorusCable(object):
     def __init__(self, knot_formula, k_vector=None, q_vector=None):
@@ -514,3 +516,290 @@ class SignatureFunction(object):
 
 def mod_one(n):
     return n - floor(n)
+
+def get_untwisted_signature_function(j):
+    # return the signature function of the T_{2,2k+1} torus knot
+    k = abs(j)
+    w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
+         [((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
+         for a in range(k + 1, 2 * k + 1)])
+    return SignatureFunction(values=w)
+
+
+def get_signature_summand_as_theta_function(*arg):
+    def get_signture_function(theta):
+        # TBD: another formula (for t^2) description
+
+        k_n = abs(arg[-1])
+        if theta > k_n:
+            msg = "k for the pattern in the cable is " + str(arg[-1]) + \
+                  ". Parameter theta should not be larger than abs(k)."
+            raise ValueError(msg)
+
+        # twisted part
+        cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
+
+        # untwisted part
+        for i, k in enumerate(arg[:-1][::-1]):
+            ksi = 1/(2 * k_n + 1)
+            power = 2^i
+            a = get_untwisted_signature_function(k)
+            shift = theta * ksi * power
+            b = a >> shift
+            c = a << shift
+            for _ in range(i):
+                b = b.double_cover()
+                c = c.double_cover()
+            cable_signature += b + c
+            test = b - c
+            test2 = -c + b
+            assert test == test
+        return cable_signature
+    get_signture_function.__doc__ = get_signture_function_docsting
+    return get_signture_function
+
+
+def get_blanchfield_for_pattern(k_n, theta):
+    if theta == 0:
+        a = get_untwisted_signature_function(k_n)
+        return a.square_root() + a.minus_square_root()
+
+    results = []
+    k = abs(k_n)
+    ksi = 1/(2 * k + 1)
+
+    # lambda_odd, i.e. (theta + e) % 2 != 0
+    for e in range(1, k + 1):
+        if (theta + e) % 2 != 0:
+            results.append((e * ksi, 1 * sgn(k_n)))
+            results.append((1 - e * ksi, -1 * sgn(k_n)))
+
+    # lambda_even
+    # print("normal")
+    for e in range(1, theta):
+        if (theta + e) % 2 == 0:
+            results.append((e * ksi, 1 * sgn(k_n)))
+            results.append((1 - e * ksi, -1 * sgn(k_n)))
+    # print("reversed")
+    for e in range(theta + 1, k + 1):
+        if (theta + e) % 2 != 0:
+            continue
+        results.append((e * ksi, -1 * sgn(k_n)))
+        results.append((1 - e * ksi, 1 * sgn(k_n)))
+    return SignatureFunction(values=results)
+
+
+def get_signature_summand_as_theta_function(*arg):
+    def get_signture_function(theta):
+        # TBD: another formula (for t^2) description
+
+        k_n = abs(arg[-1])
+        if theta > k_n:
+            msg = "k for the pattern in the cable is " + str(arg[-1]) + \
+                  ". Parameter theta should not be larger than abs(k)."
+            raise ValueError(msg)
+
+        # twisted part
+        cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
+
+        # untwisted part
+        for i, k in enumerate(arg[:-1][::-1]):
+            ksi = 1/(2 * k_n + 1)
+            power = 2^i
+            a = get_untwisted_signature_function(k)
+            shift = theta * ksi * power
+            b = a >> shift
+            c = a << shift
+            for _ in range(i):
+                b = b.double_cover()
+                c = c.double_cover()
+            cable_signature += b + c
+            test = b - c
+            test2 = -c + b
+            assert test == test
+        return cable_signature
+    get_signture_function.__doc__ = get_signture_function_docsting
+    return get_signture_function
+
+
+def get_untwisted_signature_function(j):
+    # return the signature function of the T_{2,2k+1} torus knot
+    k = abs(j)
+    w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
+         [((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
+         for a in range(k + 1, 2 * k + 1)])
+    return SignatureFunction(values=w)
+
+
+TorusCable.get_number_of_combinations_of_theta.__doc__ = \
+    """
+    Arguments:
+        arbitrary number of lists of numbers, each list encodes a single cable
+    Return:
+        number of possible theta values combinations that could be applied
+        for a given cable sum,
+        i.e. the product of q_j for j = {1,.. n},
+        where n is a number of direct components in the cable sum,
+        and q_j is the last q parameter for the component (a single cable)
+    """
+
+TorusCable.get_knot_descrption.__doc__ = \
+    """
+    Arguments:
+        arbitrary number of lists of numbers, each list encodes a single cable.
+    Examples:
+        sage: get_knot_descrption([1, 3], [2], [-1, -2], [-3])
+        'T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)'
+    """
+
+TorusCable.eval_cable_for_null_signature.__doc__ = \
+    """
+    This function calculates all possible twisted signature functions for
+    a knot that is given as an argument. The knot should be encoded as a list
+    of its direct component. Each component schould be presented as a list
+    of integers. This integers correspond to the k - values in each component/
+    cable. If a component is a mirror image of a cable the minus sign should
+    be written before each number for this component. For example:
+    eval_cable_for_null_signature([[1, 8], [2], [-2, -8], [-2]])
+    eval_cable_for_null_signature([[1, 2], [-1, -2]])
+
+    sage: eval_cable_for_null_signature([[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_null_signature
+    are k-values for each component/cable in a direct sum.
+    """
+
+TorusCable.get_signature_as_function_of_theta.__doc__ = \
+    """
+    Function intended to construct signature function for a connected
+    sum of multiple cables with varying theta parameter values.
+    Accept arbitrary number of arguments (depending on number of cables in
+    connected sum).
+    Each argument should be given as list of integer representing
+    k - parameters for a cable: parameters k_i (i=1,.., n-1) for satelit knots
+    T(2, 2k_i + 1) and - the last one - k_n for a pattern knot T(2, 2k_n + 1).
+    Returns a function that will take theta vector as an argument and return
+    an object SignatureFunction.
+
+    To calculate signature function for a cable sum and a theta values vector,
+    use as below.
+
+    sage: signature_function_generator = get_signature_as_function_of_theta(
+                                             [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
+
+    Or like below.
+    sage: print(get_signature_as_function_of_theta([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
+    """
+
+SignatureFunction.__doc__ = \
+    """
+    This simple class encodes twisted and untwisted signature functions
+    of knots. Since the signature function is entirely encoded by its signature
+    jump, the class stores only information about signature jumps
+    in a dictionary self.cnt_signature_jumps.
+    The dictionary stores data of the signature jump as a key/values pair,
+    where the key is the argument at which the functions jumps
+    and value encodes the value of the jump. Remember that we treat
+    signature functions as defined on the interval [0,1).
+    """
+
+get_signture_function_docsting = \
+    """
+    This function returns SignatureFunction for previously defined single
+    cable T_(2, q) and a theta given as an argument.
+    The cable was defined by calling function
+    get_signature_summand_as_theta_function(*arg)
+    with the cable description as an argument.
+    It is an implementaion of the formula:
+        Bl_theta(K'_(2, d)) =
+            Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t)
+            + Bl(K')(ksi_l^theta * t)
+    """
+
+signature_as_function_of_theta_docstring = \
+    """
+    Arguments:
+
+    Returns object of SignatureFunction class for a previously defined
+    connected sum of len(arg) cables.
+    Accept len(arg) arguments: for each cable one theta parameter.
+    If call with no arguments, all theta parameters are set to be 0.
+    """
+
+mod_one.__doc__ = \
+    """
+    Argument:
+        a number
+    Return:
+        the fractional part of the argument
+    Examples:
+        sage: mod_one(9 + 3/4)
+        3/4
+        sage: mod_one(-9 + 3/4)
+        3/4
+        sage: mod_one(-3/4)
+        1/4
+    """
+
+get_blanchfield_for_pattern.__doc__ = \
+    """
+    Arguments:
+        k_n:    a number s.t. q_n = 2 * k_n + 1, where
+                T(2, q_n) is a pattern knot for a single cable from a cable sum
+        theta:  twist/character for the cable (value form v vector)
+    Return:
+        SignatureFunction created for twisted signature function
+        for a given cable and theta/character
+    Based on:
+        Proposition 9.8. in Twisted Blanchfield Pairing
+        (https://arxiv.org/pdf/1809.08791.pdf)
+    """
+
+get_signature_summand_as_theta_function.__doc__ = \
+    """
+    Argument:
+        n integers that encode a single cable, i.e.
+        values of q_i for T(2,q_0; 2,q_1; ... 2, q_n)
+    Return:
+        a function that returns SignatureFunction for this single cable
+        and a theta given as an argument
+    """
diff --git a/my_signature.sage b/my_signature.sage
index 11a2344..138e514 100644
--- a/my_signature.sage
+++ b/my_signature.sage
@@ -11,6 +11,11 @@ import collections
 import itertools as it
 import numpy as np
 import re
+# try:
+#     from cable_signature import SignatureFunction, TorusCable
+# except ModuleNotFoundError:
+os.system('sage --preparse cable_signature.sage')
+os.system('mv cable_signature.sage.py cable_signature.py')
 from cable_signature import SignatureFunction, TorusCable
 
 class Config(object):
@@ -189,7 +194,7 @@ def search_for_null_signature_value(knot_formula=None, limit=None):
         for k in combinations:
             if config.only_slice_candidates and k_vector_size == 5:
                 k = get_shifted_combination(k)
-                cable = TorusCable(knot_formula, k_vector=k)
+            cable = TorusCable(knot_formula, k_vector=k)
             if is_trivial_combination(cable.knot_sum):
                 print(cable.knot_sum)
                 continue
@@ -201,6 +206,11 @@ def search_for_null_signature_value(knot_formula=None, limit=None):
                         str(all_comb) + "\n")
                 f_results.write(line)
 
+def extract_max(string):
+    numbers = re.findall('\d+', string)
+    numbers = map(int, numbers)
+    return max(numbers)
+
 def is_trivial_combination(knot_sum):
     # for now is applicable only for schema that are sums of 4 cables
     if len(knot_sum) == 4:
@@ -209,144 +219,6 @@ def is_trivial_combination(knot_sum):
             return True
     return False
 
-def get_shifted_combination(combination):
-    # for now applicable only for schama
-    # "[[k[0], k[1], k[2]], [k[3], k[4]],
-    # [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]"
-    # shift the combination so that the knot can be a candidate for slice
-    combination = [combination[0], 4 * combination[0] + combination[1],
-         4 * (4 * combination[0] + combination[1]) + combination[2],
-         4 * combination[0] + combination[3],
-         4 * (4 * combination[0] + combination[3]) + combination[4]]
-    return combination
-
-def get_blanchfield_for_pattern(k_n, theta):
-    if theta == 0:
-        a = get_untwisted_signature_function(k_n)
-        return a.square_root() + a.minus_square_root()
-
-    results = []
-    k = abs(k_n)
-    ksi = 1/(2 * k + 1)
-
-    # lambda_odd, i.e. (theta + e) % 2 != 0
-    for e in range(1, k + 1):
-        if (theta + e) % 2 != 0:
-            results.append((e * ksi, 1 * sgn(k_n)))
-            results.append((1 - e * ksi, -1 * sgn(k_n)))
-
-    # lambda_even
-    # print("normal")
-    for e in range(1, theta):
-        if (theta + e) % 2 == 0:
-            results.append((e * ksi, 1 * sgn(k_n)))
-            results.append((1 - e * ksi, -1 * sgn(k_n)))
-    # print("reversed")
-    for e in range(theta + 1, k + 1):
-        if (theta + e) % 2 != 0:
-            continue
-        results.append((e * ksi, -1 * sgn(k_n)))
-        results.append((1 - e * ksi, 1 * sgn(k_n)))
-    return SignatureFunction(values=results)
-
-def get_signature_summand_as_theta_function(*arg):
-    def get_signture_function(theta):
-        # TBD: another formula (for t^2) description
-
-        k_n = abs(arg[-1])
-        if theta > k_n:
-            msg = "k for the pattern in the cable is " + str(arg[-1]) + \
-                  ". Parameter theta should not be larger than abs(k)."
-            raise ValueError(msg)
-
-        # twisted part
-        cable_signature = get_blanchfield_for_pattern(arg[-1], theta)
-
-        # untwisted part
-        for i, k in enumerate(arg[:-1][::-1]):
-            ksi = 1/(2 * k_n + 1)
-            power = 2^i
-            a = get_untwisted_signature_function(k)
-            shift = theta * ksi * power
-            b = a >> shift
-            c = a << shift
-            for _ in range(i):
-                b = b.double_cover()
-                c = c.double_cover()
-            cable_signature += b + c
-            test = b - c
-            test2 = -c + b
-            assert test == test
-        return cable_signature
-    get_signture_function.__doc__ = get_signture_function_docsting
-    return get_signture_function
-
-def get_untwisted_signature_function(j):
-    # return the signature function of the T_{2,2k+1} torus knot
-    k = abs(j)
-    w = ([((2 * a + 1)/(4 * k + 2), -1 * sgn(j)) for a in range(k)] +
-         [((2 * a + 1)/(4 * k + 2), 1 * sgn(j))
-         for a in range(k + 1, 2 * k + 1)])
-    return SignatureFunction(values=w)
-
-def extract_max(string):
-    numbers = re.findall('\d+', string)
-    numbers = map(int, numbers)
-    return max(numbers)
-
-def mod_one(n):
-    return n - floor(n)
-
-
-get_blanchfield_for_pattern.__doc__ = \
-    """
-    Arguments:
-        k_n:    a number s.t. q_n = 2 * k_n + 1, where
-                T(2, q_n) is a pattern knot for a single cable from a cable sum
-        theta:  twist/character for the cable (value form v vector)
-    Return:
-        SignatureFunction created for twisted signature function
-        for a given cable and theta/character
-    Based on:
-        Proposition 9.8. in Twisted Blanchfield Pairing
-        (https://arxiv.org/pdf/1809.08791.pdf)
-    """
-
-TorusCable.get_number_of_combinations_of_theta.__doc__ = \
-    """
-    Arguments:
-        arbitrary number of lists of numbers, each list encodes a single cable
-    Return:
-        number of possible theta values combinations that could be applied
-        for a given cable sum,
-        i.e. the product of q_j for j = {1,.. n},
-        where n is a number of direct components in the cable sum,
-        and q_j is the last q parameter for the component (a single cable)
-    """
-
-TorusCable.get_knot_descrption.__doc__ = \
-    """
-    Arguments:
-        arbitrary number of lists of numbers, each list encodes a single cable.
-    Examples:
-        sage: get_knot_descrption([1, 3], [2], [-1, -2], [-3])
-        'T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)'
-    """
-
-mod_one.__doc__ = \
-    """
-    Argument:
-        a number
-    Return:
-        the fractional part of the argument
-    Examples:
-        sage: mod_one(9 + 3/4)
-        3/4
-        sage: mod_one(-9 + 3/4)
-        3/4
-        sage: mod_one(-3/4)
-        1/4
-    """
 
 search_for_null_signature_value.__doc__ = \
     """
@@ -367,6 +239,17 @@ search_for_null_signature_value.__doc__ = \
     Data for knots that are candidates for slice knots are saved to a file.
     """
 
+main.__doc__ = \
+    """
+    This function is run if the script was called from the terminal.
+    It calls another function, search_for_null_signature_value,
+    to calculate signature functions for a schema
+    of a cable sum defined in the class Config.
+    Optionaly a parameter (a limit for k_0 value) can be given.
+    Thought to be run for time consuming calculations.
+    """
+
+
 extract_max.__doc__ = \
     """
     Return:
@@ -378,136 +261,6 @@ extract_max.__doc__ = \
         3300
     """
 
-TorusCable.eval_cable_for_null_signature.__doc__ = \
-    """
-    This function calculates all possible twisted signature functions for
-    a knot that is given as an argument. The knot should be encoded as a list
-    of its direct component. Each component schould be presented as a list
-    of integers. This integers correspond to the k - values in each component/
-    cable. If a component is a mirror image of a cable the minus sign should
-    be written before each number for this component. For example:
-    eval_cable_for_null_signature([[1, 8], [2], [-2, -8], [-2]])
-    eval_cable_for_null_signature([[1, 2], [-1, -2]])
-
-    sage: eval_cable_for_null_signature([[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_null_signature
-    are k-values for each component/cable in a direct sum.
-    """
-
-TorusCable.get_signature_as_function_of_theta.__doc__ = \
-    """
-    Function intended to construct signature function for a connected
-    sum of multiple cables with varying theta parameter values.
-    Accept arbitrary number of arguments (depending on number of cables in
-    connected sum).
-    Each argument should be given as list of integer representing
-    k - parameters for a cable: parameters k_i (i=1,.., n-1) for satelit knots
-    T(2, 2k_i + 1) and - the last one - k_n for a pattern knot T(2, 2k_n + 1).
-    Returns a function that will take theta vector as an argument and return
-    an object SignatureFunction.
-
-    To calculate signature function for a cable sum and a theta values vector,
-    use as below.
-
-    sage: signature_function_generator = get_signature_as_function_of_theta(
-                                             [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
-
-    Or like below.
-    sage: print(get_signature_as_function_of_theta([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
-    """
-
-get_signature_summand_as_theta_function.__doc__ = \
-    """
-    Argument:
-        n integers that encode a single cable, i.e.
-        values of q_i for T(2,q_0; 2,q_1; ... 2, q_n)
-    Return:
-        a function that returns SignatureFunction for this single cable
-        and a theta given as an argument
-    """
-SignatureFunction.__doc__ = \
-    """
-    This simple class encodes twisted and untwisted signature functions
-    of knots. Since the signature function is entirely encoded by its signature
-    jump, the class stores only information about signature jumps
-    in a dictionary self.cnt_signature_jumps.
-    The dictionary stores data of the signature jump as a key/values pair,
-    where the key is the argument at which the functions jumps
-    and value encodes the value of the jump. Remember that we treat
-    signature functions as defined on the interval [0,1).
-    """
-get_signture_function_docsting = \
-    """
-    This function returns SignatureFunction for previously defined single
-    cable T_(2, q) and a theta given as an argument.
-    The cable was defined by calling function
-    get_signature_summand_as_theta_function(*arg)
-    with the cable description as an argument.
-    It is an implementaion of the formula:
-        Bl_theta(K'_(2, d)) =
-            Bl_theta(T_2, d) + Bl(K')(ksi_l^(-theta) * t)
-            + Bl(K')(ksi_l^theta * t)
-    """
-
-signature_as_function_of_theta_docstring = \
-    """
-    Arguments:
-
-    Returns object of SignatureFunction class for a previously defined
-    connected sum of len(arg) cables.
-    Accept len(arg) arguments: for each cable one theta parameter.
-    If call with no arguments, all theta parameters are set to be 0.
-    """
-
-main.__doc__ = \
-    """
-    This function is run if the script was called from the terminal.
-    It calls another function, search_for_null_signature_value,
-    to calculate signature functions for a schema
-    of a cable sum defined in the class Config.
-    Optionaly a parameter (a limit for k_0 value) can be given.
-    Thought to be run for time consuming calculations.
-    """
 
 if __name__ == '__main__':
     global config