1 | initial version |

Here is way to do it.

```
sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):
return F.hom([z^p])
....:
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^2
sage: Frob(3)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3
sage: Frob(5)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^5
sage: Frob(97)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1
```

2 | No.2 Revision |

Here is way to do it.

~~ ~~sage: F.<z> = CyclotomicField(7)
sage: def Frob(p): ~~ ~~ return F.hom([z^p])
....:
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
~~ ~~Defn: z |--> z^2
~~sage: Frob(3)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
~~ sage:Frob(3)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3
~~sage: Frob(5)
~~

sage:Frob(5)

Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^5
~~sage: ~~ sage: Frob(97) ~~ ~~

Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - ~~1
~~

1

3 | No.3 Revision |

Here is way to do it.

```
sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):
return F.hom([z^p])
....:
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^2
```~~ ~~sage:Frob(3)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3

sage:Frob(5) Ring endomorphism of Cyclotomic Field of order 7 and degree 6

~~ ~~

Defn: z |--> z^5
sage: Frob(97)

Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1

4 | No.4 Revision |

Here is way to do it.

```
sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):
return F.hom([z^p])
....:
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^2
sage:Frob(3)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3
sage:Frob(5)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
```

Defn: z |--> z^5
~~ ~~sage: Frob(97) Ring endomorphism of Cyclotomic Field of order 7 and degree 6

~~ ~~Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - ~~1~~

5 | No.5 Revision |

Here is way to do it.

```
sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):
```~~ ~~ return F.hom([z^p])
....:
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^2
~~sage:Frob(3) ~~sage: Frob(3)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3
~~sage:Frob(5) ~~sage: Frob(5)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^5
sage: ~~ ~~Frob(97) ~~ ~~
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1

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