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Solving modular systems of equation

asked 2017-04-02 17:31:52 +0200

anonymous user


I am trying to solve a system of equations mod $p$, for $p$ prime. I have build matrices $A$ and $b$ and I am using the function solve_right() to solve $Ax = b$. But I need to solve $Ax = b$ mod $p$. Is there any functions that could do that ? thanks !

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answered 2017-04-02 21:24:13 +0200

B r u n o gravatar image

If you define your matrices containing elements of the field $\mathbb Z/p\mathbb Z$, solve_right does what you need.

sage: A = matrix(GF(17), [[6,3], [3,8]])
sage: b = matrix(GF(17), [1, 2]).transpose()
sage: A.solve_right(b)


If for some reason you need matrices over (say) $\mathbb Z$ but still need to solve modulo some prime $p$, you can use change_ring.

sage: A = matrix(ZZ, [[1,2], [3,4]])
sage: b = matrix(ZZ, [5, 6]).transpose()
sage: A.change_ring(GF(17)).solve_right(b.change_ring(GF(17)))

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great, thanks. I'll try the last option.

Sasha-dpt gravatar imageSasha-dpt ( 2017-04-02 22:27:03 +0200 )edit

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Asked: 2017-04-02 17:31:52 +0200

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Last updated: Apr 02 '17