1 | initial version |

Yes, you can do it like this:

```
sage: R.<x> = PolynomialRing(ZZ)
sage: p = 1+x+2*x^2+x^3+x^4
sage: K.<z> = CyclotomicField(5)
sage: p(z)
z^2
```

Here it's important that `x`

is the generator of a polynomial ring.

It doesn't work when `x`

is symbolic, as you noticed.

If you *have* to start with a symbolic polynomial, then you can convert it first using the `polynomial()`

method:

```
sage: var('y')
sage: q = 1+y+2*y^2+y^3+y^4
sage: q.polynomial(ZZ)(z)
z^2
```

2 | No.2 Revision |

Yes, you can do it like this:

```
sage: R.<x> = PolynomialRing(ZZ)
sage: p = 1+x+2*x^2+x^3+x^4
sage:
```~~K.<z> ~~K.<w> = CyclotomicField(5)
sage: ~~p(z)
z^2
~~p(w)
w^2

Here it's important that `x`

is the generator of a polynomial ring.

It doesn't work when `x`

is symbolic, as you noticed.

If you *have* to start with a symbolic polynomial, then you can convert it first using the `polynomial()`

method:

```
sage: var('y')
sage: q = 1+y+2*y^2+y^3+y^4
sage:
```~~q.polynomial(ZZ)(z)
~~q.polynomial(ZZ)(w)
z^2

3 | No.3 Revision |

Yes, you can do it like this:

```
sage: R.<x> = PolynomialRing(ZZ)
sage: p = 1+x+2*x^2+x^3+x^4
sage: K.<w> = CyclotomicField(5)
sage: p(w)
w^2
```

Here it's important that `x`

is the generator of a polynomial ~~ring.~~

ring. It doesn't work when `x`

is symbolic, as you noticed.

If you *have* to start with a symbolic polynomial, then you can convert it first using the `polynomial()`

method:

```
sage: var('y')
sage: q = 1+y+2*y^2+y^3+y^4
sage: q.polynomial(ZZ)(w)
z^2
```

4 | No.4 Revision |

Yes, you can do it like this:

```
sage: R.<x> = PolynomialRing(ZZ)
sage: p = 1+x+2*x^2+x^3+x^4
sage: K.<w> = CyclotomicField(5)
sage: p(w)
w^2
```

Here it's important that `x`

is the generator of a polynomial ring. It doesn't work when `x`

is symbolic, as you ~~noticed.~~

noticed. If you *have* to start with a symbolic polynomial, then you can convert it first using the `polynomial()`

method:

```
sage: var('y')
sage: q = 1+y+2*y^2+y^3+y^4
sage: q.polynomial(ZZ)(w)
z^2
```

5 | No.5 Revision |

Yes, you can do it like this:

```
sage: R.<x> = PolynomialRing(ZZ)
sage: p = 1+x+2*x^2+x^3+x^4
sage: K.<w> = CyclotomicField(5)
sage: p(w)
w^2
```

Here it's important that `x`

is the generator of a polynomial ring. It doesn't work when `x`

is symbolic, as you noticed. If you *have* to start with a symbolic polynomial, then you can convert it first using the `polynomial()`

method:

```
sage: var('y')
sage: q = 1+y+2*y^2+y^3+y^4
sage: q.polynomial(ZZ)(w)
```~~z^2
~~w^2

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