Dear Tim,
perhaps the following is a better explanation.
In the above situation, "for X in F" yields a list of pairs (x-1,2), (x
+1,2) etc. In particular, X is not a polynomial. It is a pair, formed
by a polynomial and a number.
Hence, I am *not* applying a function called "Factorization" to some
polynomial. "Factorization" is the constructor for an object of type
<class 'sage.structure.factorization.Factorization'>. It takes as
input a list of pairs.
"Factorization" does *not* try to factorize the input any further! So,
if you feed it with a reducible polynomial, it simply swallows it:
sage: Factorization([(x^2+2*x+1,3)])
(x^2 + 2*x + 1)^3
And when I define Factorization([X]), the output is guaranteed to
coincide with (X[0]^X[1]).factor(), by construction of X.
Yours,
Simon
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