def get_f(self, grade):
# chain map, from cells --> critical cells
chain = self.chain
src = chain.get_cells(grade)
tgt = self.get_critical(grade)
f = Matrix(tgt, src, {}, self.ring)
A = self.get_up_match(grade) # grade --> grade+1 --> grade
C = Matrix.retraction(tgt, src, self.ring)
while C.nonzero():
f += C
C = C * A
return f
def get_bdymap(self, grade): # grade --> grade-1
chain = self.chain
src = self.get_critical(grade) # CM_grade
tgt = self.get_critical(grade - 1) # CM_{grade-1}
bdy = Matrix(tgt, src, {}, self.ring) # CM_grade --> CM_{grade-1}
A = self.get_down_match(grade) # C_grade --> C_grade-1 --> C_grade
B = chain.get_bdymap(grade) # C_grade --> C_grade-1
cells = chain.get_cells(grade)
cells_1 = chain.get_cells(grade - 1)
L = Matrix.retraction(tgt, cells_1,
self.ring) # C_grade-1 --> CM_grade-1
B = L * B
R = Matrix.inclusion(cells, src, self.ring) # CM_grade --> C_grade
while R.nonzero():
bdy += B * R
R = A * R
return bdy