Let $A=\mathbf{Q}[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over the rational numbers. Let $B$ and $C$ be two finitely generated $\mathbf{Q}$-subalgebras of $A$.

Q1: Is there a finite time (efficient) algorithm that allows one to say when is $B\simeq C$ as $\mathbf{Q}$-algebra?

Q2: Is there a finite time (efficient) algorithm that allows one to say when is $Frac(B)\simeq Frac(C)$?

Here $Frac(B)$ denotes the fraction field.

Let $A=\mathbf{Q}[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over the rational numbers. Let $B=\mathbf{Q}[f_1,\ldots,f_r]$ and $C=\mathbf{Q}[g_1,\ldots,g_s]$ be two finitely generated $\mathbf{Q}$-subalgebras of $A$ with explicit generators.

Q1: Is there a finite time (efficient) algorithm that allows one to say when is $B\simeq C$ as $\mathbf{Q}$-algebra?

Q2: Is there a finite time (efficient) algorithm that allows one to say when is $Frac(B)\simeq Frac(C)$?

Here $Frac(B)$ denotes the fraction field. In both questions I really mean isomorphic and not equal.