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Echelon form of matrix with coefficients in Zp

asked 2014-12-05 17:10:06 +0100

hypercube gravatar image

updated 2017-07-31 21:47:00 +0100

FrédéricC gravatar image

I was wondering if there was a way to find the echelon form of a matrix with coefficients in Zp with sage? I tried

Matrix(Zp(5), 3, 3, [1..9]).echelon_form()

but this gives a NotImplementedError as echelon_form is not implemented over generic non-exact rings at present. I would also very much like the transformation matrix used to get to echelon form if possible.

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answered 2014-12-05 20:04:07 +0100

vdelecroix gravatar image

Hello,

NotImplementedError exactly tells you the current state of Sage library on that function... one workaround is to go over QQ (or possibly ZZ) make the echelon form and go back to Zp

sage: m = Matrix(Zp(5), 3, 3, [1..9])
sage: m.change_ring(QQ).echelon_form().change_ring(Zp(5))
[ 1 + O(5^20)  0             4 + 4*5 + 4*5^2 + ...  + O(5^20)]
[ 0            1 + O(5^20)   2 + O(5^20)                     ]
[ 0            0             0                               ]

(note that I slightly edited the output)

Vincent

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Asked: 2014-12-05 17:10:06 +0100

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Last updated: Dec 06 '14