The video suggests using isomorphisms because they allow complex structural problems to be mapped to simpler, more familiar structures. In this case, finding prime ideals in a quotient ring was transformed into a straightforward polynomial factorization problem over a finite field, which is algorithmically easier to solve.
Conditions: An isomorphism exists between the original structure and a simpler target structure.; The problem in the simpler structure is easier to solve.
The video suggests using isomorphisms because they allow complex structural problems to be mapped to simpler, more familiar structures. In this case, finding prime ideals in a quotient ring was transformed into a straightforward polynomial factorization problem over a finite field, which is algorithmically easier to solve.
Conditions: An isomorphism exists between the original structure and a simpler target structure.; The problem in the simpler structure is easier to solve.