求助！！！！ 构造一个9元域

hyxh

构造一个9元域，写出其加法和乘法表，其中非零元的逆元和阶。

柳林风生

$Z_3[x]/(x^2+1)$

lilianjie

F7 := FiniteField(3^2);
5 L, p! F( U7 V( HF7;
' e3 H1 {* @3 K0 g4 E' E! N/ D2 ~1 \Set(F7);
6 L0 u4 r" O$ h; _7 ~Degree(F7) ;
F7 := FiniteField(3^2);
4 \$ x/ p/ |! ?) \0 T- x7 ^5 AF7;
% X1 e* @+ L5 GSet(F7);
Degree(F7) ;
/ {  o( T6 J- u5 |) ^D:=DefiningPolynomial(F7) ;
  }# J5 @/ ?0 C% R# C2 @( BD;
P:=IrreduciblePolynomial(F7 ,2);
P;
4 k' Y! B4 o/ h! Z+ X2 ^
3 q6 M9 S5 `5 q: J7 F( G
9 q7 r$ b0 @2 }/ `) CFinite field of size 3^2
{ 1, F7.1, F7.1^2, F7.1^3, 2, F7.1^5, F7.1^6, F7.1^7, 0 }
2
5 T% k- u+ i: T+ j- {6 ^) TFinite field of size 3^2
{ 1, F7.1, F7.1^2, F7.1^3, 2, F7.1^5, F7.1^6, F7.1^7, 0 }
, x: G$ K2 s7 y7 z; N2
2 I+ |& p: h! I* D' t4 `$.1^2 + 2*$.1 + 2
+ `, x. L  s% ]! P. I, U' k0 V$.1^2 + F7.1