How can i prove the following ring isomorphism in Sage?
$R_{X-a}\ = R/(X-a)\ = Z[X]/⟨X^n +1⟩/(X-a) \cong Z/(a^n+1)$
Would I use an evaluation homomorphism?
$R_{X-a}$ = $Z[X]/(X − a,X^n + 1)$ = $Z[X]/(X − a,a^n + 1)$ $\cong$ $Z/(a^n+1)Z$
Start with much simpler concrete example
$Z2/Z[X]/(X^4 + 1)$ $\cong$ $Z/2Z$
Z_2 = IntegerModRing(2)
P.<x> = PolynomialRing(Z_2)
I = P.ideal(x^4+1)
R = P.quotient(I)
a = R.an_element()
(a+1)^4 == a^4+1 # True
Hom(R,Z_2)
