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Univariate Polynomial Ring in x over Ring of integers modulo 5
[ x^2 + x + 3 4*x^2 + x + 1 4*x^2 + 1]
[4*x^2 + x + 3 2*x^2 + 2*x 3*x^2 + x + 2]
[ x^2 + x + 3 x^2 + x + 3 3*x^2 + 3*x]
([ 1 0 0]
[ 0 1 0]
[ 0 0 2*x^5 + 2*x^3 + x + 2], [ 3*x + 3 3*x + 4 0]
[ 4*x^2 + 2*x + 2 x^2 + x + 3 2*x^2 + 2*x]
[ x^6 + x^5 + 2*x^4 + x^3 + 3*x + 1 4*x^6 + x^5 + 4*x^4 + 4*x^3 + 4*x^2 + 3 3*x^6 + 2*x^5 + 4*x^4 + x^3 + 3*x^2 + 2*x + 1], [ 1 x^5 + x^4 + x^3 + 4 2*x^6 + x^5 + x^4 + 3*x^2 + x + 2]
[ 0 3*x^2 + 4*x + 1 x^3 + 3*x + 2]
[ 0 3 x + 2])
6*x + 4
Univariate Quotient Polynomial Ring in a over Finite Field of size 7 with modulus x^2 + 3*x + 6
5*a + 4
[5*a + 6 2 6*a + 1]
[ 5*a 5*a 4*a + 4]
[ 3 3*a + 5 3*a + 3]
(
[1 0 0] [6*a + 1 0 0] [ 1 2*a + 5 3*a + 6]
[0 1 0] [5*a + 4 5 0] [ 0 1 6*a + 2]
[0 0 1], [5*a + 3 5*a + 5 a + 3], [ 0 0 1]
)