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Great idea. Please open a ticket for that if there is not already one.

One thing to decide is, for partial factorisations such as:

sage: f = Factorization([(10, 1), (20, 1)])
sage: f
10 * 20

whether f.factor() and factor(f) should factor them further.

Somewhat related:

• Sage Trac ticket 18917: Speed up NumberField.zeta()
• Sage Trac ticket 31686: Speed up factoring finite field multiplicative order