using of M.permute_rows_and_columns

asked 2021-09-01 09:35:21 +0100

ortollj
1341 ●23 ●63 ●98

I am aware that with this question my Karma will drop a notch !

I don't understand the use of M.permute_rows_and_columns() how to use it to do this function below ?

M = matrix(ZZ,[[1,0,0,0,0],[0,2,0,0,0],[0,0,3,0,0],[0,0,0,4,0],[0,0,0,0,5]])

def permRandC(a,b) :
    "permute row and column a,b"
    Mc=copy(M)
    Mc[:,a]=M[:,b]
    Mc[:,b]=M[:,a]
    Mr=copy(Mc)    
    Mr[a,:]=Mc[b,:]
    Mr[b,:]=Mc[a,:]
    return Mr

show(permRandC(0,1))

answered 2021-09-01 13:05:34 +0100

philipp7
391 ●7 ●13 ●28

The following yields the same result as your function perRandC:

G = SymmetricGroup(5) # create the symmetric group on 5 
perm = G((1,2)) # create the permutation (1, 2) in G, i.e. perm just swaps 1 and 2
M.permute_rows_and_columns(perm, perm) 
show(M)

G contains all possible permutations of {1,2,3,4,5}. Note that permute_rows_and_columns works with 1-based indices, i.e. since we want to swap the 0th and 1st row we have to use (1,2). Alternatively, using the same method as in the documentation, we could also do:

G = PermutationGroup(['(1,2)'])
perm = G.gens()[0]
M.permute_rows_and_columns(perm, perm)
show(M)

All three yield the same result.

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thank you @philipp7

ortollj ( 2021-09-01 13:26:37 +0100 )edit

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