Introduction à l`algorithmique algébrique 1 Généralités sur les

n∈N∗
k∈Zl
(k, n)l∈ {0, . . . , n −1}k≡l[n]
nj −k j ∈Z
nj0−k n(j0−1) ≤k < nj0l=k−n(j0−1)
n
(k, n)∈Z×N
l∈ {0, . . . , n −1}k≡l[n]
x≥n
x:= x−n
x < 0
x:= x+n

:=
x k
x
x
n= 19 k=−25
19 −25
−25 x x
x
−25 → −6→13
−25 ≡13 [ 19]

1 1
2 2
k k
k+1
i0i∈ {1, . . . , k}
i i0
i k+1
1 2
1 2

−25
13
N
x n/2
x x n
n
x k l k
n l x
0≤l < n n
(a, b)∈Z×N∗
(q, r)∈Z×Za=bq +r0≤r≤b
(x, y) := (0, a)
y≥b
(x, y) := (x+ 1, y −b)
y < 0
(x, y) := (x−1, y +b)
b/2
y
y=b

bx +y
a
∀(a, b)∈Z×N∗∃(q, r)∈Z×Za=bq +r0≤r < b
a(A, +,∗)
e n ∈N
an
an
an=a∗ · · · ∗ a n ≥1
e n = 0
(a, n)∈A×N
an
x:= e
n > 0
i n
x:= a∗x
x
n= 5
x
e→a→a2→a3→a4→a5
ann
n