1 | initial version |

From your data, you can get the list of indeterminates and make a new polynomial ring from them:

```
sage: R = PolynomialRing(QQ, P.gens()+S.gens())
sage: R(poly)
c0*t0
sage: R(poly).parent()
Multivariate Polynomial Ring in c0, c1, c2, c3, c4, c5, t0, t1, t2, t3, t4, t5 over Rational Field
```

If you want to only use `S`

, you can replace `P.gens()`

with `S.base_ring().gens()`

2 | No.2 Revision |

From your data, you can get the list of indeterminates and make a new polynomial ring from them:

```
sage: R = PolynomialRing(QQ, P.gens()+S.gens())
sage: R(poly)
c0*t0
sage: R(poly).parent()
Multivariate Polynomial Ring in c0, c1, c2, c3, c4, c5, t0, t1, t2, t3, t4, t5 over Rational Field
```

If you want to only use `S`

, you can ~~replace ~~recover ~~P.gens()~~P~~with ~~from

, and get the desired flattening:~~S.base_ring().gens()~~S.base_ring()

```
sage: PolynomialRing(QQ, S.base_ring().gens()+S.gens())
Multivariate Polynomial Ring in c0, c1, c2, c3, c4, c5, t0, t1, t2, t3, t4, t5 over Rational Field
```

3 | No.3 Revision |

From your data, you can get the list of indeterminates and make a new polynomial ring from them:

```
sage: R = PolynomialRing(QQ, P.gens()+S.gens())
sage: R(poly)
c0*t0
sage: R(poly).parent()
Multivariate Polynomial Ring in c0, c1, c2, c3, c4, c5, t0, t1, t2, t3, t4, t5 over Rational Field
```

If you want to only use `S`

, you can recover `P`

from `S.base_ring()`

, and get the desired flattening:

```
sage: PolynomialRing(QQ, S.base_ring().gens()+S.gens())
Multivariate Polynomial Ring in c0, c1, c2, c3, c4, c5, t0, t1, t2, t3, t4, t5 over Rational Field
```

If you want to directly build a polynomial ring from a list of strings with two prefixes, you can also do:

```
sage: PolynomialRing(QQ,["c{}".format(i) for i in range(6)]+["t{}".format(i) for i in range(6)])
Multivariate Polynomial Ring in c0, c1, c2, c3, c4, c5, t0, t1, t2, t3, t4, t5 over Rational Field
```

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