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Hi,

I want to create the multiplicative group (Z/7Z)*={1,2,3,4,5,6} so I did these steps:

sage: n=7
sage: Zn=Zmod(n)
sage: G=Zn.unit_group()
sage: list(G)
[1, f, f^2, f^3, f^4, f^5]

sage: Zn(f)
3

Then I want to create the subgroups generate by 2=f^2 which is {1,2,4} So I did the following steps:

sage: H=G.subgroup([f^2])
sage: list(H)
[1, f, f^2]

my problem is when I did sage: Zn(f)
It returns 3

But here f need to be 2 ? How can I solve this ? replaces f by value?

Hi,

I want to create the multiplicative group (Z/7Z)*={1,2,3,4,5,6} $(\mathbb{Z}/7\mathbb{Z})^*={1,2,3,4,5,6}$ so I did these steps:

sage: n=7 
n = 7                                                                                            
sage: Zn=Zmod(n) 
Zn = Zmod(n)                                                                                     
sage: G=Zn.unit_group() 
G = Zn.unit_group()                                                                              
sage: list(G) 
 
[1, f, f^2, f^3, f^4, f^5]
 
f^5]

sage: Zn(f) 

3                                                                                         
3

sage: H=G.subgroup([f^2]) 
H = G.subgroup([f^2])                                                                            
sage: list(H) 
 
[1, f, f^2]
f^2]

sage: Zn(f) 

It returns
3
                                                                                         
3

Hi,

I want to create the multiplicative group $(\mathbb{Z}/7\mathbb{Z})^*={1,2,3,4,5,6}$ $(\mathbb{Z}/7\mathbb{Z})^*=\{1,2,3,4,5,6\}$ so I did these steps:

sage: n = 7                                                                                            
sage: Zn = Zmod(n)                                                                                     
sage: G = Zn.unit_group()                                                                              
sage: list(G)                                                                                        
[1, f, f^2, f^3, f^4, f^5]

sage: Zn(f)                                                                                          
3

Then I want to create the subgroups generated by $2=f^2$ which is ${1,2,4}$ So I did the following steps:

sage: H = G.subgroup([f^2])                                                                            
sage: list(H)                                                                                        
[1, f, f^2]

my problem is when I did

sage: Zn(f)                                                                                          
3

But here f needs to be 2. How can I solve this? Replace f by value?

Hi,

I want to create the multiplicative group $(\mathbb{Z}/7\mathbb{Z})^*=\{1,2,3,4,5,6\}$ so I did these steps:

sage: n = 7                                                                                            
7
sage: Zn = Zmod(n)                                                                                     
Zmod(n)
sage: G = Zn.unit_group()                                                                              
sage: list(G)                                                                                        
Zn.unit_group()
sage: list(G)
[1, f, f^2, f^3, f^4, f^5]

sage: Zn(f)                                                                                          
3

Then I want to create the subgroups generated by $2=f^2$ which is ${1,2,4}$ So I did the following steps:

sage: H = G.subgroup([f^2])                                                                            
sage: list(H)                                                                                        
[1, f, f^2]

my My problem is when I did

sage: Zn(f)                                                                                          
3

But here f f needs to be 2. How can I solve this? Replace f by value?

Hi,

I want to create the multiplicative group $(\mathbb{Z}/7\mathbb{Z})^*=\{1,2,3,4,5,6\}$ so I did these steps:

sage: n = 7
sage: Zn = Zmod(n)
sage: G = Zn.unit_group()
sage: list(G)
[1, f, f^2, f^3, f^4, f^5]

Then I want to create the subgroups generated by $2=f^2$ which is ${1,2,4}$ $\{1,2,4\}$ So I did the following steps:

sage: H = G.subgroup([f^2])                                                                            
sage: list(H)                                                                                        
[1, f, f^2]

My problem is when I did

sage: Zn(f)                                                                                          
3

But here f needs to be 2. How can I solve this? Replace f by value?

Hi,

I want to create the multiplicative group $(\mathbb{Z}/7\mathbb{Z})^*=\{1,2,3,4,5,6\}$ so $(\mathbb{Z}/7\mathbb{Z})^*=\{1,2,3,4,5,6\}$.

I did these steps:

sage: n = 7
sage: Zn = Zmod(n)
sage: G = Zn.unit_group()
sage: list(G)
[1, f, f^2, f^3, f^4, f^5]

Then I want to create the subgroups generated by $2=f^2$ which is $\{1,2,4\}$ So $\{1,2,4\}$.

I did the following steps:

sage: f = G.gen()
sage: H = G.subgroup([f^2])                                                                            
G.subgroup([f^2])
sage: list(H)                                                                                        
list(H)
[1, f, f^2]

My problem is when I did

sage: Zn(f)                                                                                          
Zn(f)
3

But here f needs to be 2. How can I solve this? Replace f by value?