def dim_fancy_relation(degree):
admissible_words = cl.generate_Words(degree)
size = 0
for i in range(2, degree - 1):
size += (2**(i - 2)) * (2**(degree - i - 2))
A = np.zeros([len(admissible_words), size])
current_column = 0
for i in range(2, degree - 1):
deg_i_words = cl.generate_Words(i)
for v in deg_i_words:
v_word = cl.Word([1], [v])
deg_n_minus_i_words = cl.generate_Words(degree - i)
for w in deg_n_minus_i_words:
result = v_word.fancy_shuffle(cl.Word([1], [w]))
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
S = np.linalg.svd(A.astype(int))[1]
rank = 0
for i in S:
if abs(i) > 0.01:
rank += 1
return rank #len(A.rref()[1])
def check_if_new_relatiion(relation):
relation.simplify()
degree = len(relation.word[0])
admissible_words = cl.generate_Words(degree)
#Fill the b vector
b = np.zeros([len(admissible_words), 1])
for i in range(len(relation.word)):
a = admissible_words.index(relation.word[i])
b[a] = relation.q[i]
A = np.zeros([len(admissible_words), (degree - 2) * (2**(degree - 3))])
current_column = 0
for n in range(1, degree - 1):
deg_n_words = cl.generate_Words(degree - n)
deg_n_forests = cl.generate_Fn(n)
for j in range(len(deg_n_forests)):
for i in range(len(deg_n_words)):
result = deg_n_forests[j](cl.Word([1], [deg_n_words[i]]))
result.simplify()
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
if len(sp.Matrix(A.astype(int)).rref()[1]) < len(
sp.Matrix(np.concatenate((A, b), axis=1).astype(int)).rref()[1]):
return True
else:
return False
def compare_tree_fancy(degree):
admissible_words = cl.generate_Words(degree)
size = 0
for i in range(2, degree - 1):
size += (2**(i - 2)) * (2**(degree - i - 2))
cutoff = size
size += (2**(degree - 3)) * ((degree - 1) // 2)
A = np.zeros([len(admissible_words), size])
current_column = 0
for i in range(2, degree - 1):
deg_i_words = cl.generate_Words(i)
for v in deg_i_words:
v_word = cl.Word([1], [v])
deg_n_minus_i_words = cl.generate_Words(degree - i)
for w in deg_n_minus_i_words:
result = v_word.fancy_shuffle(cl.Word([1], [w]))
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
for i in range(1, (degree + 1) // 2):
deg_i_words = cl.generate_Words_Hy(i)
deg_n_minus_i_words = cl.generate_Words_Hy(degree - i - 1)
for v in deg_i_words:
v_word = cl.Word([1], [v])
for w in deg_n_minus_i_words:
result = kawashima_1(v_word, cl.Word([1], [w]))
result.simplify()
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
fancy_matrix = A[:, :cutoff]
kaw_matrix = A[:, cutoff:]
S = np.linalg.svd(A.astype(int))[1]
K = np.linalg.svd(kaw_matrix.astype(int))[1]
F = np.linalg.svd(fancy_matrix.astype(int))[1]
rank = 0
rank_K = 0
rank_F = 0
for i in S:
if abs(i) > 0.01:
rank += 1
for i in K:
if abs(i) > 0.01:
rank_K += 1
for i in F:
if abs(i) > 0.01:
rank_F += 1
return ("Total dim:", rank, "Kawashima dim:", rank_K, "Fancy dim:", rank_F,
"intersect", rank_K + rank_F - rank) # len(A.rref()[1])
def dim_kaw(degree):
admissible_words = cl.generate_Words(degree)
if degree >= 4:
size = (2**(degree - 3)) * ((degree - 1) // 2) + (2**(degree - 4)) * (
(degree - 2) // 2)
else:
size = (2**(degree - 3)) * ((degree - 1) // 2)
A = np.zeros([len(admissible_words), size])
current_column = 0
for i in range(1, (degree + 1) // 2):
deg_i_words = cl.generate_Words_Hy(i)
deg_n_minus_i_words = cl.generate_Words_Hy(degree - i - 1)
for v in deg_i_words:
v_word = cl.Word([1], [v])
for w in deg_n_minus_i_words:
result = kawashima_1(v_word, cl.Word([1], [w]))
result.simplify()
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
if degree >= 4:
for i in range(1, (degree) // 2):
deg_i_words = cl.generate_Words_Hy(i)
deg_n_minus_i_words = cl.generate_Words_Hy(degree - i - 2)
for v in deg_i_words:
v_word = cl.Word([1], [v])
for w in deg_n_minus_i_words:
result = kawashima_2(v_word, cl.Word([1], [w]))
result.simplify()
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
S = np.linalg.svd(A.astype(int))[1]
#print(len(sp.Matrix(A.astype(int)).rref()[1]))
rank = 0
for i in S:
if abs(i) > 0.1:
rank += 1
return rank
def compare_kaw_fancy(degree):
admissible_words = cl.generate_Words(degree)
size = 0
for i in range(2, degree - 1):
size += (2**(i - 2)) * (2**(degree - i - 2))
if degree >= 4:
size += (2**(degree - 3)) * ((degree - 1) // 2) + (2**(degree - 4)) * (
(degree - 2) // 2)
else:
size += (2**(degree - 3)) * ((degree - 1) // 2)
A = np.zeros([len(admissible_words), size])
current_column = 0
for i in range(2, degree - 1):
deg_i_words = cl.generate_Words(i)
for v in deg_i_words:
v_word = cl.Word([1], [v])
deg_n_minus_i_words = cl.generate_Words(degree - i)
for w in deg_n_minus_i_words:
result = v_word.fancy_shuffle(cl.Word([1], [w]))
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
for i in range(1, (degree + 1) // 2):
deg_i_words = cl.generate_Words_Hy(i)
deg_n_minus_i_words = cl.generate_Words_Hy(degree - i - 1)
for v in deg_i_words:
v_word = cl.Word([1], [v])
for w in deg_n_minus_i_words:
result = kawashima_1(v_word, cl.Word([1], [w]))
result.simplify()
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
if degree >= 4:
for i in range(1, (degree) // 2):
deg_i_words = cl.generate_Words_Hy(i)
deg_n_minus_i_words = cl.generate_Words_Hy(degree - i - 2)
for v in deg_i_words:
v_word = cl.Word([1], [v])
for w in deg_n_minus_i_words:
result = kawashima_2(v_word, cl.Word([1], [w]))
result.simplify()
for k in range(len(result.word)):
a = admissible_words.index(result.word[k])
A[a, current_column] = result.q[k]
current_column += 1
S = np.linalg.svd(A.astype(int))[1]
rank = 0
for i in S:
if abs(i) > 0.1:
rank += 1
return rank # len(A.rref()[1])
def table_gen():
#input_list = ["xy","xxy","xyy","xyxy","xxyy","xxxy","xyyy","xxxxy","xyxyy","xyxxy","xyyyy"]
five_words = cl.generate_Words(5)
cl.generate_table(five_words)