1 | initial version |

How are you defining `f`

? This works for me:

```
sage: R = GF(2)['y']
sage: R.inject_variables()
Defining y
sage: f = y^2 + y + 1
sage: f(f(y))
y^4 + y + 1
```

2 | No.2 Revision |

How are you defining `f`

? This works for me:

```
sage: R = GF(2)['y']
sage: R.inject_variables()
Defining y
sage: f = y^2 + y + 1
sage: f(f(y))
y^4 + y + 1
```

Edit: if you want to do something like `f(y) = y^2 + ny`

, then you need two variables, and you could make one a polynomial variable, one a symbolic variable. Make sure that the symbolic one comes after the polynomial one, alphabetically:

```
sage: var('m')
sage: R = QQ['a']
sage: R.inject_variables()
sage: f = a^2 + m*a
sage: f(f(a))
(a^2 + a*z)^2 + (a^2 + a*z)*z
sage: f(f(a)).expand()
a^4 + 2*a^3*z + a^2*z^2 + a^2*z + a*z^2
```

Then

```
sage: f(f(f(f(f(a))))).expand()
```

works, but gives a very long expression.

(You need the polynomial generator to come alphabetically before the symbolic variable because `f`

depends on two variables, and when you call `f(3)`

, for example, it chooses to substitute the 3 for the first of the variables. You want to substitute `f(a)`

for `a`

by default, so make sure `a`

comes before `m`

.)

3 | No.3 Revision |

How are you defining `f`

? This works for me:

```
sage: R = GF(2)['y']
sage: R.inject_variables()
Defining y
sage: f = y^2 + y + 1
sage: f(f(y))
y^4 + y + 1
```

Edit: if you want to do something like `f(y) = y^2 + ny`

, then you need two variables, and you could make one a polynomial variable, one a symbolic variable. Make sure that the symbolic one comes after the polynomial one, alphabetically:

```
sage: var('m')
sage: R = QQ['a']
sage: R.inject_variables()
sage: f = a^2 + m*a
sage: f(f(a))
(a^2 +
```~~a*z)^2 ~~a*m)^2 + (a^2 + ~~a*z)*z
~~a*m)*m
sage: f(f(a)).expand()
a^4 + ~~2*a^3*z + a^2*z^2 + a^2*z + a*z^2
~~2*a^3*m + a^2*m^2 + a^2*m + a*m^2

Then

```
sage: f(f(f(f(f(a))))).expand()
```

works, but gives a very long expression.

(You need the polynomial generator to come alphabetically before the symbolic variable because `f`

depends on two variables, and when you call `f(3)`

, for example, it chooses to substitute the 3 for the first of the variables. You want to substitute `f(a)`

for `a`

by default, so make sure `a`

comes before `m`

.)

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