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。

lilianjie

F7 := FiniteField(3^2);
F7;
5 u2 q3 V; _8 q  NSet(F7);
Degree(F7) ;
& `- Z* c  x2 XF7 := FiniteField(3^2);
( R! o: ?, y8 x9 S2 xF7;
2 A4 y4 O& R% D! ySet(F7);
3 c4 s9 d! S/ v; `7 J- RDegree(F7) ;
D:=DefiningPolynomial(F7) ;
/ f( [: \) D4 S% l# s; Y+ tD;
P:=IrreduciblePolynomial(F7 ,2);
" I1 e% d: G4 B% l0 @P;
: Q2 o! O9 S/ ~$ c" o

+ r0 V1 g& o0 pFinite 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 }
/ J$ x9 @& x: g& U' U8 Q. r2
Finite field of size 3^2
1 @6 @, F3 [& u# J/ `8 O( K3 w{ 1, F7.1, F7.1^2, F7.1^3, 2, F7.1^5, F7.1^6, F7.1^7, 0 }
# E: g0 p# Z9 \; b; |' y; [2
2 A. b4 C8 f3 A% [$.1^2 + 2*$.1 + 2
$.1^2 + F7.1

柳林风生

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