1 | initial version |

In your example, having defined

```
sage: R1.<a,b,c,t> = PolynomialRing(QQ)
sage: L = (a*t^2+b*t+c).subs(a=2,b=3,c=4)
```

we get

```
sage: L
2*t^2 + 3*t + 4
```

(did you mean `L = a*t^2+b*t+c`

without substituting values for `a`

, `b`

, `c`

?)

Having then defined

```
sage: R2.<A,B,C,D,t> = PolynomialRing(QQ)
sage: p = (A*t+B)^2+(C*t+D)^2
```

you can convert polynomials from one ring to the other

```
sage: R2(L)
2*D^2 + 3*D + 4
```

Here, the order of the variables matters, more than their names:
`t`

, the fourth variable in `R1`

, is mapped to `D`

, the fourth variable in `R2`

.

If you want `a`

, `b`

,`c`

, `t`

to be mapped to `A`

, `B`

, `C`

, `t`

, you might
want to include an extra variable `d`

in `R1`

and not use it.

Or you could compare string representations of your polynomials, applying
string replacements as necessary. Or you could use `p.monomials()`

and `p.coefficients()`

.

You could also define a ring homomorphism from `R1`

to `R2`

mapping the variables to the variables of your choice, see the reference manual.

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