Presa una data del tipo:
g
g
/
m
m
/
s
s
a
a
{\displaystyle gg/mm/ssaa\,\!}
G
s
=
(
S
+
A
+
M
+
G
−
2
X
)
mod
7
{\displaystyle Gs=\left(S+A+M+G-2^{X}\,\!\right){\bmod {7}}}
S
=
[
2
×
(
4
−
s
s
mod
4
)
]
mod
7
{\displaystyle S=\left[2\times \left(4-ss\ {\bmod {4}}\right)\right]{\bmod {7}}}
A
=
[
(
a
a
mod
2
8
)
mod
4
+
5
×
(
b
a
a
mod
2
8
4
c
)
]
mod
7
{\displaystyle A=\left[\left(aa\ {\bmod {2}}8\right){\bmod {4}}+5\times \left({\mathcal {b}}{\frac {aa\ {\bmod {2}}8}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}}
M
=
[
3
×
b
(
m
m
2
+
b
m
m
9
c
×
1
2
)
c
+
2
×
(
b
m
m
5
c
+
b
m
m
7
c
+
b
m
m
12
c
)
]
mod
7
{\displaystyle M=\left[3\times {\mathcal {b}}\left({\frac {mm}{2}}+{\mathcal {b}}{\frac {mm}{9}}{\mathcal {c}}\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left({\mathcal {b}}{\frac {mm}{5}}{\mathcal {c}}+{\mathcal {b}}{\frac {mm}{7}}{\mathcal {c}}+{\mathcal {b}}{\frac {mm}{12}}{\mathcal {c}}\right)\right]{\bmod {7}}}
G
=
g
g
mod
7
{\displaystyle G=gg\ {\bmod {7}}}
Errore del parser (funzione sconosciuta '\begin{cases}'): {\displaystyle X = \begin{cases}0, & mm > 3\quad o \quad aa \bmod4 ≠ 0 \quad o \quad (S ≠ 1 e aa = 0) \\ 1, & altrimenti \end{cases}}
Gs indica il giorno della settimana (0 = sabato, 1 = domenica, 2 = lunedì..).
S = 2
S
=
[
2
×
(
4
−
19
mod
4
)
]
mod
7
{\displaystyle S=\left[2\times \left(4-19\ {\bmod {4}}\right)\right]{\bmod {7}}}
=
[
2
×
(
4
−
3
)
]
mod
7
=
2
mod
7
=
2
{\displaystyle =\left[2\times \left(4-3\right)\right]{\bmod {7}}=2{\bmod {7}}=2}
A = 6
A
=
[
(
89
mod
2
8
)
mod
4
+
5
×
(
b
89
mod
2
8
4
c
)
]
mod
7
{\displaystyle A=\left[\left(89\ {\bmod {2}}8\right){\bmod {4}}+5\times \left({\mathcal {b}}{\frac {89\ {\bmod {2}}8}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}}
=
[
5
mod
4
+
5
×
(
b
5
4
c
)
]
mod
7
=
[
1
+
5
×
1
]
mod
7
=
6
mod
7
=
6
{\displaystyle =\left[5{\bmod {4}}+5\times \left({\mathcal {b}}{\frac {5}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}=\left[1+5\times 1\right]{\bmod {7}}=6{\bmod {7}}=6}
M
=
[
3
×
b
(
11
2
+
b
11
9
c
×
1
2
)
c
+
2
×
(
b
11
5
c
+
b
11
7
c
+
b
11
12
c
)
]
mod
7
{\displaystyle M=\left[3\times {\mathcal {b}}\left({\frac {11}{2}}+{\mathcal {b}}{\frac {11}{9}}{\mathcal {c}}\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left({\mathcal {b}}{\frac {11}{5}}{\mathcal {c}}+{\mathcal {b}}{\frac {11}{7}}{\mathcal {c}}+{\mathcal {b}}{\frac {11}{12}}{\mathcal {c}}\right)\right]{\bmod {7}}}
=
[
3
×
b
(
11
2
+
1
×
1
2
)
c
+
2
×
(
2
+
1
+
0
)
]
mod
7
=
[
3
×
b
6
c
+
2
×
3
]
mod
7
=
(
18
+
6
)
mod
7
=
24
mod
7
=
3
{\displaystyle =\left[3\times {\mathcal {b}}\left({\frac {11}{2}}+1\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left(2+1+0\right)\right]{\bmod {7}}=\left[3\times {\mathcal {b}}6{\mathcal {c}}+2\times 3\right]{\bmod {7}}=\left(18+6\right){\bmod {7}}=24{\bmod {7}}=3}
G = 6
G
=
27
mod
7
=
6
{\displaystyle G=27\ {\bmod {7}}=6\,\!}
X = 0
Giorno della settimana : Lunedì (2)
G
s
=
(
S
+
A
+
M
+
G
−
2
X
)
mod
7
{\displaystyle Gs=\left(S+A+M+G-2^{X}\,\!\right){\bmod {7}}}
=
(
2
+
6
+
3
+
6
−
2
0
)
mod
7
=
(
17
−
1
)
mod
7
=
16
mod
7
=
2
{\displaystyle =\left(2+6+3+6-2^{0}\,\!\right){\bmod {7}}=\left(17-1\,\!\right){\bmod {7}}=16{\bmod {7}}=2}
Data 15/2/14
![{\displaystyle S=\left[2\times \left(4-ss\ {\bmod {4}}\right)\right]{\bmod {7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69ce7900b87a3a0d5cf565d4207474403dfec545)
![{\displaystyle A=\left[\left(aa\ {\bmod {2}}8\right){\bmod {4}}+5\times \left({\mathcal {b}}{\frac {aa\ {\bmod {2}}8}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c2683e1c703e98e60615a7b9c0433695d6dc9e7)
![{\displaystyle M=\left[3\times {\mathcal {b}}\left({\frac {mm}{2}}+{\mathcal {b}}{\frac {mm}{9}}{\mathcal {c}}\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left({\mathcal {b}}{\frac {mm}{5}}{\mathcal {c}}+{\mathcal {b}}{\frac {mm}{7}}{\mathcal {c}}+{\mathcal {b}}{\frac {mm}{12}}{\mathcal {c}}\right)\right]{\bmod {7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7194314d143570d1391c2419f665f1b70dde5c4e)
![{\displaystyle S=\left[2\times \left(4-19\ {\bmod {4}}\right)\right]{\bmod {7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a2866f8ff56a168069968c4e223e779046cabb9)
![{\displaystyle =\left[2\times \left(4-3\right)\right]{\bmod {7}}=2{\bmod {7}}=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/190fe8ee7a595d3743889c71e250662a4536b3a9)
![{\displaystyle A=\left[\left(89\ {\bmod {2}}8\right){\bmod {4}}+5\times \left({\mathcal {b}}{\frac {89\ {\bmod {2}}8}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69874bb3728ed9f6cd79ed0c3b07551c3914ad01)
![{\displaystyle =\left[5{\bmod {4}}+5\times \left({\mathcal {b}}{\frac {5}{4}}{\mathcal {c}}\right)\right]{\bmod {7}}=\left[1+5\times 1\right]{\bmod {7}}=6{\bmod {7}}=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f4b2ffc9dd5212406d900a6c265d7c6eea02908)
![{\displaystyle M=\left[3\times {\mathcal {b}}\left({\frac {11}{2}}+{\mathcal {b}}{\frac {11}{9}}{\mathcal {c}}\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left({\mathcal {b}}{\frac {11}{5}}{\mathcal {c}}+{\mathcal {b}}{\frac {11}{7}}{\mathcal {c}}+{\mathcal {b}}{\frac {11}{12}}{\mathcal {c}}\right)\right]{\bmod {7}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3abb38353d22019133c02c965b5d9c3d9e8384d3)
![{\displaystyle =\left[3\times {\mathcal {b}}\left({\frac {11}{2}}+1\times {\frac {1}{2}}\right){\mathcal {c}}+2\times \left(2+1+0\right)\right]{\bmod {7}}=\left[3\times {\mathcal {b}}6{\mathcal {c}}+2\times 3\right]{\bmod {7}}=\left(18+6\right){\bmod {7}}=24{\bmod {7}}=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/407f170c51805ef2ca2ee9788d49d9c79182eab6)
