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Allow coercion from Frac(QQ[x]) to LaurentSeriesRing(QQ) #39365

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@user202729 user202729 commented Jan 22, 2025

If A is a field then self = LaurentSeriesRing(A) is a field, by universal property of fraction field, a coercion P.base() → self can be uniquely extended to P → self. So this makes sense.

As a side effect, this coercion allows the user to write things such as

sage: R.<x> = QQ[]
sage: 1/(x-1)+O(x^100)
-1 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14 - x^15 - x^16 - x^17 - x^18 - x^19 + O(x^20)

Another side effect: If the base ring is something like Zmod(5) or QQ["x"].quotient(...) then a primality/irreducibility check will be carried out.

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