dingchangxin's profile - activity

Thank you for editing my question so that it looks neat. This is a wonderful place.

Thank you so much for your answer! You have even corrected the code, which saves me a lot of time.

I have been using Sage in my research recently.

I am not sure which part is wrong but the following code gives the wrong results. The code is long, but I think you may only need to read the last four rows to understand my question.

All the rows before that generate a matrix D where the columns are the cycles of the complete graph K_5 (each cycle is a vector in Z^10, 10 is the number of edges.)

Then I produce a linear matroid from D and calculate T(2, 0) using tutte_polynomial(). The weird thing is that the result is an odd number, which is impossible because the Tutte polynomial has no constant term. The more weird thing is that if I repeat the order again, I get a different result.

If I run the code for the graph K_4, nothing is wrong, which is why I need to give the complete code. The code is run by CoCalc.

import numpy as np 
from sage.matroids.advanced import *

graph = graphs.CompleteGraph(5)

g = graph.to_directed()
allcycles = g.all_simple_cycles()
nv = g.order()  # nv is number of vertices
ne = nv*(nv-1)/2  # ne is the number of edges
ncycle = (len(allcycles)-g.size()/2)/2  # ncycle is number of simple cycles


def cycle(array):  # array is a cycle in vertices notation eg. [0,1,2,3,0]
    l = len(array) - 1  # l is the length of the cycle
    if l <= 2:
        return False
    C = np.zeros(nv*(nv-1)/2)  # C is to be a cycle in Z^E
    for X in range(l):
        i = array[X] + 1
        j = array[X+1] + 1
        if i < j:
            C[(2*nv-i)*(i-1)/2+j-i-1] = 1
        else:
            C[(2*nv-j)*(j-1)/2+i-j-1] = -1
    return(C)

D = np.zeros((ne,ncycle*2))  # D is all directed cycles
X = 0
for list in allcycles:
    array = np.array(list)
    if len(array) > 3:
        D[:, X] = cycle(array).transpose()
        X = X + 1

for X in range(ncycle):  # reduce D so that D is all cycles with one orientation
    positivecolumn = D[:, X]
    Y = X + 1
    while any(D[:, Y] + positivecolumn):
        Y = Y + 1
    D = np.delete(D, Y, 1)

print(D)
M = Matroid(Matrix(D))
print("M.tutte_polynomial(2, 0) =", M.tutte_polynomial(2, 0))
print("M.tutte_polynomial(2, 0) =", M.tutte_polynomial(2, 0))

The results are

[[ 1.  1.  1.  0.  0.  0.  0.  0.  0.  0.  1.  1.  1.  1.  1.  1.  0.  0.
   0.  0.  0.  0.  0.  0.  0.  1.  1.  1.  1.  1.  1.  0.  0.  0.  0.  0.  0.]
 [-1.  0.  0.  1.  1.  0.  0.  0.  0.  0.  0.  0. -1.  0. -1.  0.  1.  1.
   1.  1.  0.  0.  0.  0.  0.  0.  0.  0. -1.  0. -1.  1.  1.  1.  1.  0.  0.]
 [ 0. -1.  0. -1.  0.  1.  0.  0.  0.  0. -1.  0.  0.  0.  0. -1. -1.  0.
   0. -1.  1.  1.  0.  0.  0.  0. -1.  0.  0. -1.  0.  0. -1.  0. -1.  1.  1.]
 [ 0.  0. -1.  0. -1. -1.  0.  0.  0.  0.  0. -1.  0. -1.  0.  0.  0. -1.
  -1.  0. -1. -1.  0.  0.  0. -1.  0. -1.  0.  0.  0. -1.  0. -1.  0. -1. -1.]
 [ 1.  0.  0.  0.  0.  0.  1.  1.  0.  0.  1.  1.  0.  0.  0.  0. -1. -1.
   0.  0.  0.  0.  1.  1.  0.  1.  1.  0.  0.  0.  0. -1. -1.  0.  0.  1. -1.]
 [ 0.  1.  0.  0.  0.  0. -1.  0.  1.  0.  0.  0.  1.  1.  0.  0.  1.  0.
   0.  0. -1.  0.  0. -1.  1.  0.  0.  1.  1.  0.  0.  1.  0. -1.  1. -1.  0.]
 [ 0.  0.  1.  0.  0.  0.  0. -1. -1.  0.  0.  0.  0.  0.  1.  1.  0.  1.
   0.  0.  1.  0. -1.  0. -1.  0.  0.  0.  0.  1.  1.  0.  1.  1. -1.  0.  1.]
 [ 0.  0.  0.  1.  0.  0.  1.  0.  0.  1.  1.  0. -1.  0.  0.  0.  0.  0.
   1.  0.  0. -1.  1.  0. -1.  1.  0. -1.  0.  1. -1.  0.  0.  1.  0.  0. -1.]
 [ 0.  0.  0.  0.  1.  0.  0.  1.  0. -1.  0.  1.  0.  0. -1.  0.  0.  0.
   0.  1.  0.  1.  0.  1.  1.  0.  1.  1. -1. -1.  0.  0.  0.  0.  1.  1.  0.]
 [ 0.  0.  0.  0.  0.  1.  0.  0.  1.  1.  0.  0.  0.  1.  0. -1.  0.  0.
   1. -1.  0.  0.  1. -1.  0.  1. -1.  0.  1.  0. -1.  1. -1.  0.  0.  0.  0.]]
M.tutte_polynomial(2, 0) = 46229
M.tutte_polynomial(2, 0) = 52640

tutte_polynomial (sage, matroid theory) gives the wrong result I have been using sage in my research recently. I am not