Matrix Isomorphism Checks.sagews

#take two complexes, matrix or otherwise

# if poly, turn into matrix pls and ty
# append the row [B,C,D……P] on top of each matrix

m_a= matrix ([
#B sub
[1,1, 1,0,0,0,0,0,0,0,0,0,0],
[1,0,0,1, 1,0,0,0,0,0,0,0,0],
[1,0,0,0,0,1, 1,0,0,0,0,0,0],
[1,0,0,0,0,0,0, 1,1,0,0,0,0],
[1,0,0,0,0,0,0,0,0, 1,1,0,0],
[1,0,0,0,0,0,0,0,0,0,0, 1,1],
])

m_b= matrix ([
#C sub
[1,1, 1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0, 1,0, 1,0,0,0,0,0,0,0,0,0],
[0,1,0,0, 1,0, 1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0, 1,0, 1,0,0,0,0,0],
[0,1,0,0,0,0,0,0, 1,0, 1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0, 1,0,1,0],
[0,1,0,0,0,0,0,0,0,0,0,0,1,0,1],
])

#the following is the modified "not" C matrix!
#m_b= matrix ([
#C sub
#[1,1, 1,0,0,0,0,0,0,0,0,0,0,0,0],
#[0,1,0, 1,0, 1,0,0,0,0,0,0,0,0,0],
#[0,1,0,0, 1,0, 1,0,0,0,0,0,0,0,0],
#[0,1,0,0,0,0,0, 1,0, 1,0,0,0,0,0],
#[0,1,0,0,0,0,0,0, 1,0, 1,0,0,0,0],
#[0,1,0,0,0,0,0,0,0,0,0, 1,0,1,0],
#[0,1,0,0,0,0,0,0,0,0,0, 1,0,1,0]])

# check to see if the ranks are the same bc if htey’re not then they got redundancies that don’t match nicely!

if m_a.rank() != m_b.rank():
    print('These bitches don’t have the same rank (number of points)! Booooo.')


if m_a.nrows() != m_b.nrows():
    print('These bitches don’t even have the same number of lines!')
	# then kill the code

# this is how you find the incidence/frequency matrix

# pull the number of columns of a
# col_a = m_a.ncols()
# phi_a = matrix(QQ, 1, col_a, lambda i, j=1)
# inc_a= m_a*phi_a

# col_b = m_b.ncols()
# phi_b = matrix(QQ, 1, col_b, lambda i, j=1)
# inc_b = m_b*phi_b


# import incident code
# import incident sorting code , file name “INCIDENT SORTING”

# reduce the matrices by removing all columns completely filled with 0
# take the column summation, which i named inc, from the 2nd row and beyond (because the first row is just naming)
# organize in numerical order, greatest to least, using entries in second row. Make sure to move first row with it as that’s the name of hte points!

# else: L=length(inc_a)
	# for i in[1,L]
	# call on index of inc matrices, line by line
	# if inc_a[i]==inc_b[i], i=i+1
	# else: print (“These complexes are not isomorphic because the incident counts aren’t the same, so there cannot be an isomorphism between the two”)
		# print out both matrices, then kill the code

# now we’re going to make the original matrix without the 0 padding. This bad boy should have the same number of rows and columns, and their incident matrix is also the same

# what we’ll do now is we’ll take the ordered inc_a and move the columns around on m_a until the letters in the first row of m_a matches the letters on the first row of inc_a. This will give you incident from greatest to least. Repeat for m_b

# we’re going to do this by way of duplicating our matrices, not by assignment, but by like actual projection so we don’t fuck with our original matrix

# m_a2 = copy(m_a)

# m_b2 = copy(m_b)

# let’s organize m_a2 with accordance of inc_a

# now is the time we’ll build an isomorphism between m_b2 back to m_a2