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Regarding rational canonical form/frobenius form of matrices over finite fields

asked 2018-01-18 04:12:53 -0600

Ramachandran gravatar image

Hi,

The sagemath documentation on linear algebra describes a function frobenius which computes the frobenius normal form (rational canonical form) of a matrix over integers. The same command doesnt work on matrices over finite fields. Can someone help me to find the frobenius form of matrices over finite fields

Sample code :

A = matrix(GF(2),[[1,0,0],[0,0,1],[1,1,0]])

A.frobenius()

This code gives the error

'sage.matrix.matrix_mod2_dense.Matrix_mod2_dense' object has no attribute 'frobenius'

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Comments

There is work in progress about this kind of thing here : https://trac.sagemath.org/ticket/22397 But it is kind of stuck currently.

FrédéricC gravatar imageFrédéricC ( 2018-01-18 12:25:05 -0600 )edit

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answered 2018-01-18 12:26:18 -0600

FrédéricC gravatar image

Like that:

sage: A = matrix(GF(2),[[1,0,0],[0,0,1],[1,1,0]])
sage: A.rational_form()
[0 0 1]
[1 0 1]
[0 1 1]
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Asked: 2018-01-18 04:12:53 -0600

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Last updated: Jan 18