def gamma_B3():
# first glue b-piece to the switch-piece, using the sign formula for switches
step_1 = signs.switch_mod2(wsb_dim - 1, wsb_dim, wsb_dim)
#print(step_1)
#then glue this to the first end-piece at the Y_0-vertex.
step_2 = signs.Y0_mod2(0, 0, 0, 0, 0, 1, n, n, n, 1, wsb_dim - 1,
wsb_dim - 1, wsb_dim - 1, b + 1)
#print(step_2)
#then glue this to the secont end-piece at the Y_1-vertex.
step_3 = signs.Y1_mod2(1, 1, 0, 0, 1, 1, n, n, n, 1, k_dim, wsb_dim - 1,
wsb_dim, b + 2)
#print(step_3)
# and finally glue the positive a-piece to the thing
step_4 = signs.pos_1val_mod2(0, n, wua_dim, a, 2, 2, k_dim)
#print(step_4)
tot = (step_1 + step_2 + step_3 + step_4).subs([(b, a),
(wsb_dim, n + 1 + wua_dim),
(n**2, n)])
if tot.is_constant():
return tot % 2
else:
return trunc(tot, 2)
def tree_III():
step_1 = signs.Y1_mod2(0, 0, 0, 0, 0, 1, n, n, n, 1, n - wua_dim,
n - wua_dim - 1, n - wua_dim - 1, b)
step_2 = signs.pos_1val_mod2(0, n, wua_dim, a, 1, 1, n - wua_dim)
res = (step_1 + step_2).subs(n**2, n)
if res.is_constant():
return res % 2
else:
return trunc(res, 2)
def case_I2_pert1a():
#first two gluings are the same as in the unperturbed case
step_1 = signs.Y0_mod2(0, 0, 0, 0, 0, 0, n, wsb2, wsb2, b2,
wsb2 + wsb1 + n, wsb1, wsb1, b1)
#print('step 1 \n', step_1, '\n')
step_2 = signs.Y0_mod2(1, 1, 0, 0, 0, 0, n, wsb3, wsb3, b3, k_dim,
wsb1 + wsb2 + n, wsb1 + wsb2 + n + 1, b1 + b2)
step_3 = signs.Y1_mod2(0, 0, 2, 2, 1, 0, n, n + wua + 1, k_dim, a, k1_dim,
n, n, 1)
#print('step 2 \n', step_2, '\n')
finish = signs.pos_1val_mod2(0, n, wua, a, 1, 3, k1_dim)
#print('finish \n', finish, '\n')
return trunc(step_1 + step_2 + step_3 + finish, 2)
def case_I2_pert1b():
#first two gluings are the same as in the unperturbed case
step_1 = signs.Y0_mod2(0, 0, 0, 0, 0, 0, n, wsb2, wsb2, b2,
wsb2 + wsb1 + n, wsb1, wsb1, b1)
#print('step 1 \n', step_1, '\n')
step_2 = signs.Y0_mod2(1, 1, 0, 0, 0, 0, n, wsb3, wsb3, b3, k_dim,
wsb1 + wsb2 + n, wsb1 + wsb2 + n + 1, b1 + b2)
#this is the new gluing
step_3 = signs.Y1_mod2(2, 2, 0, 0, 0, 1, n, n, n, 1, k1_dim, k_dim,
n + wua + 1, a)
finish = signs.pos_1val_mod2(0, n, wua, a, 3, 3, k1_dim)
#print('finish \n', finish, '\n')
#res=(step_1 + step_2 + finish).subs([(a,b1+b2+b3), (wua,3*n+1+wsb1+wsb2+wsb3),(n**2,2)])
return trunc(step_1 + step_2 + step_3 + finish, 2)
def case_I1_pert1a():
#first and second step is similar to the unperturbed tree
step_1 = signs.Y0_mod2(0, 0, 0, 0, 0, 0, n, wsb3, wsb3, b3,
wsb3 + wsb2 + n, wsb2, wsb2, b2)
#print('step 1 \n', step_1, '\n')
step_2 = signs.Y0_mod2(0, 0, 1, 1, 0, 0, n, wsb3 + wsb2 + n + 1,
wsb3 + wsb2 + n, b2 + b3, k_dim, wsb1, wsb1, b1)
#print('step 2 \n', step_2, '\n')
#this is the new gluing
step_3 = signs.Y1_mod2(0, 0, 1, 2, 1, 0, n, n + wua + 1, k_dim, a, k1_dim,
n, n, 1)
finish = signs.pos_1val_mod2(0, n, wua, a, 1, 3, k1_dim)
#print('finish \n', finish, '\n')
#res=(step_1 + step_2 + finish).subs([(a,b1+b2+b3), (wua,3*n+1+wsb1+wsb2+wsb3),(n**2,2)])
return trunc(step_1 + step_2 + step_3 + finish, 2)