# 单位群

## 单位

OK ${\displaystyle \simeq }$ Z⊕r⊕（有限循环群）。

## 例子

O7:=MaximalOrder(Q7);O7;
Discriminant(Q7) ;
ClassGroup(Q7);
a:=O7!5;a;
aa:=O7!500;aa;
Factorization(a);
Factorization(aa);
FundamentalUnit(Q17);
Discriminant(Q17) ;
ClassGroup(Q17);

Quadratic Field with defining polynomial \$.1^2 + 11 over the Rational Field
Maximal Order of Q7
-11
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to Set of ideals of O7
5
500
[ <\$.2 + 1, 1>, <-\$.2 + 2, 1> ]
<-1, 0>
[ <2, 2>, <\$.2 + 1, 3>, <-\$.2 + 2, 3> ]
<-1, 0>
Quadratic Field with defining polynomial \$.1^2 - 17 over the Rational Field
-Q17.1 + 4
17
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to Set of ideals of Maximal Order of Q17